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Production of a well collimated neutron beam using the associated particle technique Tripard, Gerald Edward 1967

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The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of GERALD EDWARD TRIPARD B.Sc., The University of B r i t i s h Columbia, 1962 M.Sc., The University of B r i t i s h Columbia, 1964 IN ROOM 301, HENNINGS BUILDING THURSDAY, AUGUST 31 , 1967, AT 3:30 P. COMMITTEE IN CHARGE Chairman:. I. McT. Cowan M.K. Craddock D.IL. Livesey J.S. MacDonald J.M. McMillan E.W. Vogt B.L. White External Examiner: J.T. Sample University of Alberta Edmonton Research Supervisor: B.L. White THE PRODUCTION OF A WELL COLLIMATED NEUTRON BEAM USING THE ASSOCIATED PARTICLE TECHNIQUE ABSTRACT An accurately colliraated monenergetic fast neutron beam of small angular width was produced by bombarding a deuterium target with 2 MeV deuterons. Background reduction was achieved by using the associated p a r t i c l e technique and extensive shielding. Dual parameter pulse height analysis was used to reduce the coin-cidence time resolution between the detected 3 neutrons and the associated He r e c o i l p a r t i c l e to 4.6 nanoseconds by taking into account the 3 variations i n f l i g h t times of the He p a r t i c l e s . A r o t a t i n g thin f i l m deuterated polyethylene target was developed which enabled a substantial increase i n the neutron flux to be made. The beam of 7 0 neutrons/second/millisteradian produced, was of s u f f i c i e n t i n t e n s i t y to perform a small angle scattering experiment. The technique was tested by a measurement of the angular d i s t r i b u t i o n from 40 degrees to 10 degrees of neutrons e l a s t i c a l l y scattered from lead. PUBLICATIONS L.F.C. Monier, G.E. Tripard and B.L. White. Accurately Collimated P a r t i a l l y Polarized 5 MeV Neutron Beam. Paper 9.7, CAP Meeting, University of B r i t i s h Columbia, (1965). L.F.C. Monier, G.E. Tripard and B.L. White Accurately Defined Neutron Beams from D(d:,n)He3 at Ed = 50 keV, using the Associated P a r t i c l e Method. Nuclear Instr. and Meth., 45, 282 (1966). L.F. Monier and G.E. Tripard. Detection of Pulse Pile-ups with Pulse Overlap to Pulse Height Converter. 1 Rev. of S c i e n t i -f i c Instr. 32/ No.3, 315 (1966). G.E. Tripard and B.L. White. Preparation of Thin Film Deuterated Polyethylene Targets. Rev. of S c i e n t i f i c Instr. _38, No.3,435 (1967) GRADUATE STUDIES F i e l d of Study: Nuclear Physics Elementary Quantum Mechanics Electromagnetic Theory Nuclear Physicsl Theory of Solids Low Temperature Physics Nuclear Reactions Theory of R e l a t i v i t y Cosmic Rays and High Energy Physics Advanced Quantum Mechanics E l e c t r o n i c Instrumentation Theory of Nuclear Physics W. Opechowski G.M. Volkoff J.V. Warren R. Barrie J.B. Brown B.L. White H. Schmidt J.B. Warren F.A. Kaempffer J.S. McDonald M. McMillan AWARDS 1958 Chris Spencer Foundation Scholarship 1958 University Scholarship for Univer-s i t y Entrance 1958-62 General Motors Canadian Scholarship Programme 1960 University Scholarship i n Arts and Science 1962 Woodrow Wilson Foundation Honorary Fellowship 1962-66 National Research Council Bursary and Scholarships 1967 National Research Council Postdoc^. torate Fellowship THE PRODUCTION OF A WELL COLLIMATED NEUTRON BEAM USING THE ASSOCIATED PARTICLE TECHNIQUE BY GERALD EDWARD TRIPARD B.Sc, University of British Columbia, M.Sc, University of British Columbia, 196*f A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, I967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h.iis r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tmen t o f The U n i v e r s i t y o f B r i t i s h Co lumb ia Vancouver 8, Canada ABSTRACT An accurately collimated monoenergetlc fast neutron beam of small angular width was produced by bombarding a deuterium target with 2 MeV deuterons. Background reduction was achieved by using the associated particle technique and extensive shielding. Dual parameter pulse height analysis was used to reduce the coincidence time resolution between the detected neutrons and the associated He^.recoil particle to k,$ nanoseconds by taking into account the variations in flight times of the He3 particles. A rotating thin film deuterated polyethylene target was developed which enabled a substantial increase in the neutron flux to be made. The beam of 70 neutrons/second/ milllsteradlan produced, was of sufficient intensity to perform a small angle scattering experiment. The technique was tested by a measurement of the angular distribution from 0^ degrees to 10 degrees of neutrons elastlcally scattered from leade TABLE OF CONTENTS page Chapter I - INTRODUCTION 1 A. Neutron Sources 2 B. Comparison of the Associated Particle Method with the Pulsed Source Method *f i . Pulsed Source Method (P. S. M.) 5 i i . Associated Particle Method (A. P. Mo) 6 C. Thesis Outline 7 Chapter II - PRELIMINARY STUDIES WITH A 5 MeV POLARIZED NEUTRON BEAM 12 A. Introduction 12 B. Choice of Angle and Energy 12 C. Target and Beam Geometry 13 D. Deuterium Target 13 E. The Mass Spectrometer and Recoil Particle Ik Detector Ik F. The Neutron Detector l^f G. Electronics 15 H. Beam Profile 17 I. Neutron Energy Spectra 17 J. Conclusions 18 Chapter III - PRODUCTION OF A k.% MeV POLARIZED NEUTRON BEAM 20 Ao Introduction 20 B. Choice of Angle and Energy 20 C. Target and Beam Arrangement 21 Do The Target Chamber 23 page E. Rotating Deuterated Polyethylene Target 2h i . Preparation 26 i i . Testing the Stationary Targets 27 i i i . Large Targets 28 iv. Rotating Mount 28 v. Performance of ttie Rotating Targets 30 F* . Electronics 30 i . D(d,p)T Reaction Protons 30 i i . He3 Recoil Particles 31 a) Elimination of pulse pile-ups 31 b) Time pick-off unit 3*+ i i i . Transmitted Neutrons 38 iv. Scattered Neutrons *+0 v. Two Parameter Analysis of Time and Energy 1^ a) Tlme-To-Pulse-Helght Converter kl b) Two Parameter Pulse Height Analyser G. Charged Particle Spectrometry *+7 1. Thin Foils In Front of Detector *+7 i i . Electrostatic Analyser k7 i i i . Magnetic Analyser -^9 iv. Thin Deuterium Targets 51 H. • Shielding ' 5.2 I. Beam Characteristics 5^  .1. Beam Size and Divergence 5^  i i . Beam Profile 57 page i l l . Possible Improvement In Angular Resolution 58 iv. Beam Intensity 59 Chapter IV - SCATTERING OF k.55 MeV NEUTRONS FROM LEAD 60 A. Introduction 60 B. Scatterer and Detector Arrangement 60 C. Flux Monitors and Detector Efficiency 63 D. Effective Solid Angle of the Neutron Detector 66 E. Multiple Scattering and Absorption Corrections 68 i . Introduction 68 i i . Input and Assumptions 70 i i i . Results of Monte Carlo Calculation 72 F. Inelastic Scattering ?k G. Elastic Scattering Results From Lead 76 H. Projected Experiment Using a Thin Slab Detector 79 Chapter V - A RESUME OF THEORY AND EXPERIMENTS LEADING TO AND INVOLVING SMALL ANGLE SCATTERING OF NEUTRONS 81 A. Introduction 8 l B. The Optical Model 82 C. Schwinger Scattering 85 D. Electric Polarizability Scattering 90 E. Theoretical Calculations of the Neutron Polarizability 9^ F. Conclusions 97 APPENDIX A DETECTION OF PULSE PILE-UPS WITH PULSE OVERLAP TO PULSE HEIGHT CONVERTER - to follow page 97 APPENDIX B MONTE CARLO COMPUTER PROGRAM FOR MULTIPLE SCATTERING CORRECTIONS 98 APPENDIX C ACCURATELY DEFINED NEUTRON BEAMS FROM D(d,n)He3 AT Ed = 50 keV, USING THE ASSOCIATED PARTICLE METHOD - to follow page 102 APPENDIX D PREPARATION OF THIN FILM DEUTERATED POLYETHYLENE TARGETS - to follow page 102 LIST OF FIGURES T 0 follow page 1. Target and Beam Arrangement 13 2. Block diagram of Electronics 15 3. Operational Configuration of Pile-up and Scattered D Rejection 16 Semiconductor Detector Spectra with and without Pile-up Rejection 16 5. He3 Spectrum with Pile-up and Scattered D Rejection and a He^  Spectrum Gated with Neutrons 17 i 6. Horizontal and Vertical Neutron Profiles 17 7. Neutron Spectra- from NE - 213 Cylindrical Liquid Scintillator 17 8. The Product of the % He 3 + + times 6<rM& [D(c/;n)We3J as a Function of He3 Energy. 21 9. The General Arrangement of the Deuteron Beam Transport System, Shielding, Reaction Chamber, and Neutron Detectors. 21 10. Reaction Chamber 23 11. Reaction Protons from Deuterated Polyethylene Targets. 28 12. Rotating Target Mount 29 13. Relative Yield of Rotating Target with 1.5yua bombarding Beam 30 1^-. Block Diagram of Electronics Used for Monitoring D(d,p)T Protons 30 15. Experimental Arrangement of a Time Pick-off Unit Used for Leading Edge Timing. 35 To follow page 1 6 . Triggering Threshold of the Time Pick-off Unit as a function of Detector Capacity. 3 5 1 7 • Block Diagram of Electronics Used to Measure the Threshold Response of the T. P» 0 . Unit. 3 6 1 8 . Noise.in the Time Pick-off Unit as a Function of BNC Couplings 3 6 1 9 . Triggering efficiency of the Time Pick-off Unit as a Function of Proton Energy 3 6 2 0 . Equivalent Circuit of a Semiconductor Detector 3 7 2 1 . The Experimental Arrangement of the Electronics Used to Monitor the Transmitted Neutrons. 38 2 2 . Gated Spectrum for Neutron Flux Monitor 3 9 2 3 . Block Diagram of Experimental Arrangement Used to Detect Scattered Neutrons, kO 2k„ Gated Spectrum for Scattered Neutron Detector *+l 2 5 . Single Parameter Time-to-Pulse-Height Converter Spectra, 2 6 . Establishment of a "Zero Time" Corresponding to the He3 Energy. ^ 5 2 7 . Two Parameter Pulse Height Spectrum. ^ 6 2 8 . Time-to-Pulse Height Converter Spectra for Individual Energy Channels Compared to Integrated Spectrum. *+6 2 9 . Experimental Arrangement of the Magnetic Mass Spectrometer. 5 0 3 0 . Semiconductor Spectra for Various Mass Spectrometer To follow page Currents 50 31. Ungated Recoil P a r t i c l e Detector Spectrum for Thin Deuterium Targets,, 51 32. Semiconductor Spectrum Gated by Neutron -He^ Coincidences. 52 33. Divergence of the Neutron Beam Caused by the Kinematics of the D(d,n) He^ Reaction. 55 3k, V e r t i c a l Neutron Beam P r o f i l e 57 35. Horizontal Neutron Beam P r o f i l e 57 36. The Experimental Arrangement of the Target ,^ Chamber, Mechanical Collimator, Scatterer, Neutron Table, and Detector. 60 37. Single Scattering as a Function of Angle 7k 38. Double Scattering as a Function of Angle 7k 39* T r i p l e Scattering as a Function of Angle 7k ko. Thin Target Compared to Thick Target Scattering 7k kl* Scattering of Neutrons on Lead. 77 k2. Schwinger Scattering Calculations f or k056 MeV Neutrons on Lead 88 *+3. Cross Sections f o r the Scattering of Neutrons 91 kk. Idealized Geometry f o r a D i f f e r e n t i a l Cross-Section Measurement 98 H-5. Flow Chart f o r the Monte Carlo M u l t i p l e Scattering Calculation. 98 LIST OF TABLES To follow page 1. Effect of Side Channels on Random Background 2. Monte Carlo Calculations 7*+ 3« Elastic Scattering Results from Lead 77 ka Definitions of Quantities Used in Figure (**5) 98 PUBLICATIONS 1. Accurately Collimated Partially Polarized 5 MeV Neutron Beam, L. F. C. Monier, G. E. Tripard, and Bo L. White, Paper 9.7, CAP Meeting, University of British Columbia (1965) 2. Accurately Defined Neutron Beams From D(d,n)He3 at E<j = 50 keV, Using the Associated Particle Method L. Fo Co Monier, Go Eo Tripard, and B. L. White, Nuclear Instr, andMetho, ^ 5, 282, (1966)0 3. Detection of Pulse Pile-ups with Pulse Overlap to Pulse Height Converter, Lo F. Monier and Go E. Tripard, Rev. of Scientific Instr. Volo 37, No. 3, 316 (1966) h. Preparation of Thin Film Deuterated Polyethylene Targets G. E. Tripard and B. L. White, Rev. of Scientific Instr. Vol. 38, No. 3, V35 (1967) ACKNOWLEDGEMENTS I wish to express my gratitude to .Dr. B. L. White for his supervision and for much appreciated assistance during the initial stages of the experiment and to Dr. P. W. Martin for supervision and encouragement during the final year of this work. I would like to give special thanks to Mr. L. F. Monier with whom I worked during the preliminary studies. I also appreciate the help of my fellow graduate students and the Van de Graaff technicians, especially Mr. Robert McFadden for the painstaking job of making many of the large deuterium targets and Mr. Cyril Sedger for the construction of many pieces of equipment from thumbnail sketches. I gratefully acknowledge the receipt of three studentships and one bursary from the National Research Council and financial assistance from the Van de Graaff group during the last year. My deepest appreciation goes to my mother, father, and my wife, Angeline, for their love and support during my time of study and to Angeline for her typing. -1-CHAPTER I INTRODUCTION Our understanding of the properties of the nucleus has come largely from interpreting the results of experiments in which unbound particles collide with nuclei to produce a nuclear reaction. To study nuclear reactions in detail, i t is necessary to have a quantitative measure of the probability of a given nuclear reaction. In order to determine the probability for a particular reaction some or all of several properties of the.incident particles must be measured. These properties may include: the average momentum of the beam, <K0>, where Ko is the momentum of one of the beam particles; the spread in the momentum of the beam particles4 the average flux of the beam; the flux distribution of the beam,, or beam profile; and the polarization of the beam. The quantitative value of these properties and the accuracy with which they can be measured determine the usefulness of the information available from the nuclear reactions involved. Charged particle beams compared with uncharged particle beams are more easily obtained with a well defined average momentum, <K*0>, and a fraction of a percent spread in the momentum of the beam particles„ Such beams are readily obtained with a variety of particle accelerators„ The average flux of the beam can be measured accurately by integrating the charge accumulated on a target over a specified time interval. The flux distribution or beam profile in most cases can be assumed to be uniform over a confined area determined by -2-material collimation. The products of nuclear reactions have been found in several cases to be polarized. Measurements of the polarization can provide information about the nuclear energy, levels involved, and, in the case of nuclei containing few nucleons, aid-in ..distinguishing between the postulated types of nucleon-nueleon interaction 0+). In principle, the interactions that give rise to polarization can be used to determine the polarization parameters for both charged and uncharged particles. A. Neutron Sources Since its discovery in 1932 the neutron has provided a highly.useful tool in attempts to understand the nucleus. Neutron scattering experiments 'have been of particular importance because interpretation of the experiments does not require corrections for Rutherford scattering. Moreover, since there is no Coulomb barrier for the neutron i t can interact with the nucleons themselves even at low incident energies. The types of nuclear phenomena which can be studied and the nature of the results obtained are very dependent on the neutron beams available. The earliest experiments used sources that depended on the release of neutrons from various nuclei when oc-partieles or Jf-rays from naturally occurring radioactive disintegrations interacted with them. These (c<,n) and (^ ,n) sources have, by present day standards, low yields, broad energy spreads, and complex structure. For example, the spectrum of neutrons from a Pu-Be source shows particles of all energies up to about -3= 1 0 .MeV, with peaks in.the vicinity of l.k and 7 MeV. Photo neutron sources ( 1 ) are used frequently because the neutrons produced have a smaller energy spread. The most powerful sources of neutrons are those associated with nuclear reactors. If an experimental hole is opened through the reactor .shield and into the lattice itself, a beam of neutrons representative of the energy distribution present in the -lattice is obtained. The most important characteristic relating to a reactor, as far as neutron research is concerned, is the magnitude of the neutron flux. An example of the high flux available is the 2 x 1 0 L L F thermal neutrons/cm2 -second from the Chalk River heavy water reactor ( 2 ) . Neutrons can also be produced with particle accelerators ( 3 ) . For example, the reaction D(d,n)He3 is exoergic, with a Q-value of 3.268 MeV, and good neutron yields can be obtained with deuteron energies as low as 50-100 keV. However, until recent techniques had been developed, only approximately monoenergetic neutrons could be obtained with even this last source. Because of the nature of the sources described experimenters in the past did not have available to them neutron beams with both a high flux and a small momentum spread. The correct explanation and evaluation of previous measurements in the field of small angle scattering of neutrons by heavy nuclei is uncertain. A study of the small angle scattering of monoenergetic neutrons of a few MeV either polarized or unpolarized would provide data of value in resolving the existing confusion. For this reason an attempt was made to produce a well colliraated monoenergetic neutron beam of small angular resolution and sufficient flux to perform a small angle scattering experiment in this energy range. B. Comparison of the Associated Particle Method with the Pulsed Source Method Difficulty in adequately collimating neutrons is one of the more severe problems in the production of neutron beams. Attempts to collimate neutrons by mechanical means usually resulted in a high background of neutrons beyond the geometric cut-off of the collimator resulting in ah undesirable flux distribution unsuitable for performing some experiments such as small angle scattering of neutrons (*f). Coupled to the problems of producing a well colllmated monoenergetic source is the problem of detection and spectrometry of the neutron. In recent years many of these problems have been overcome by using time-of-flight techniques to measure the neutron energy and to descriminate against non-time correlated background neutrons and tf-rays. In this method the moment of production of a neutron at the target is fixed by a start signal. Neutrons and tf-rays from the scatterer which have resulted from the scattering of monoenergetic neutrons from the target will arrive in the detector at definite times after the production of the neutrons in the target. These times will be determined by the velocities and flight paths. Background neutrons and Y-rays will in general be randomly distributed in -5-time. The moments of arrival in the detector are measured relative to the moment of neutron production. To measure the neutron time-of-flight there are two general techniques for establishing a starting time for the neutrons: i . Pulsed Source Method (P.S.M.) The pulsed source method uses short neutron bursts spaced at regular time intervals produced at the target by bombarding the target with a pulsed beam of particles. The pulsing of the incident charged particle beam can be achieved with a mechanical chopper, by a deflection system which sweeps a continuous beam over a slit before the target, or by the natural bunching of the accelerator (cyclotron). The PSM has the advantage that the time resolution may be improved indefinitely by increasing the flight path provided that a corresponding increase in the flux of the pulsed beam is made to maintain counting rate and signal to background ratio. This technique is also suitable for use with ring geometry iii a scattering experiment although complicated corrections are necessary if an angular distribution measurement is desired. The major drawbacks of this technique are that part of the back-ground neutrons will be time correlated requiring separate runs to measure this background and the small total neutron source strength which is usually only a few percent of the source strength for a continuous beam. Improvements to the source strength have been made by the application of ion bunching with a Mobley magnet (8). This, however, produces a divergence -6-of the incident beam Impinging on the target thus reducing the angular resolution of the neutron beam. Also mechanical collimation is required to attenuate neutrons arriving in the detector directly from the source. 11. Associated Particle Method (A.P.M.) The second method for establishing the starting time for the production of neutrons requires the detection of a particle or tf-ray associated with the emission of the neutron. This second method called the associated particle method (5,7) has been used by many experimenters to produce accurately collimated neutron beams of small angular width and known absolute int e2s ity and energy. The beam is produced by detecting the [associated recoil nuclei which define not only the starting time but also the cone of the coincident neutrons determined by the kinematics of the reaction. For most experiments requiring a neutron beam the principal disadvantage of the associated particle technique is the limit Imposed on the source strength by the counting rate that can be tolerated in the recoil particle detector. There are several advantages which justify the selection of the A.P.M. in preferrence to the PaS.M. for performing a small angle scattering experiment,, The starting signal for the production of the neutrons is defined in a simple and economical manner. Small scattering samples can be used, reducing the effects of absorption and multiple scattering. If the recoil particle detection method is 10C# efficient an absolute measurement of the neutron flux can be easily made. Probably most important for small angle scattering is that the geometrical size of the neutron beam need not be defined by mechanical collimation or absorbers which would introduce a large background of degraded and scattered neutrons at small angles and the bombarding particles are accelerated and fpcussed in a relatively simple manner without introducing deterioration of the angular resolution of the Incident beam. C. Thesis Outline Chapter V provides a resume of the theory of small angle scattering and a review of the previous experimental work done in this field. It includes a brief discussion of the optical model, Schwinger scattering, and electric polariza-bility scattering. The first application of the associated particle technique in this laboratory for the production of an accurately colllmated neutron beam used the D(d,n)He3 reaction with a bombarding energy of 50 keV. This work was carried out by Mr. LoF.C. Monier and the author under the supervision of Dr. B.L. White. The 2.55 MeV neutron beam was used to measure the absolute neutron detection efficiency and pulse spectrum of a piece of plastic scintillator<> Good agreement was found between the theoretically predicted and experimental beam profiles. The results of this work are described by L.F»C. Monier, G.E. Tripard, and B.L. White (7) . Unfortunately, because of the limitations of the particular accelerator used, a maximum flux of 180 microamps/cm2 of deuterons could be put on the target. Therefore the neutron beam was of insufficient intensity to perform a scattering experiment with reasonable statistics. For two reasons the technique was extended to produce a neutron beam using the Van de Graaff accelerator and deuteron beams of about 2 MeV energy. First, i t was possible to improve the cross-section for D(d,n)He3 reaction which is higher at E d = 2 MeV than at « 50 keV. Second, at E<j = 2 MeV the beam.of neutrons is expected to be partially polarized ( 3 8 ) . Using 2 MeV deuterons, however, produced a new problem. With 50 keV bombarding deuterons there was no problem with Coulomb scattered deuterons since they were of much lower energy than the He^  recoil particles. But with 2 MeV bombarding deuterons in conjunction with the available deuterium targets there was a very large number of Coulomb scattered deuterons at al l angles, which rendered impossible placing a semiconductor detector inside the target chamber to detect He3 recoil particles directly. Such a counter would have been completely swamped with scattered deuterons. This problem was overcome by placing an analysing magnet at an appropriate angle with respect to the incoming deuteron beam and thereby selecting by momentum the particular He^  recoil particles going into the required solid angle while at the same time rejecting most of the undesired scattered deuterons. Chapter II describes the apparatus and the results obtained with the 5 MeV neutron beam. Since at the time of this work, the electronic units necessary for this experiment were too expensive or commercially unavailable, almost the entire - 9 -electronic system of logic units and amplifiers was constructed and tested by L.F.C. Monier and the author. The intensity of the neutron beam obtained with this apparatus was low, of the order of .3 neutrons/second/millisteradian, again of insuffi-cient intensity to perform a small angle scattering experiment. However with the experience gained from this work, It was decided that by making two major modifications a large enough -increase.In the beam intensity could be achieved to perform a small angle scattering experiment. These involved a change in the physical geometry of the apparatus and a moving target to accomodate a substantial increase in the incident deuteron beam. Chapter III describes the technological developments required to increase the neutron beam to a reasonable intensity of 70 neutrons/second/millisteradian. A new deuterium target, developed by the author, enabled not only a large increase in the incident deuteron beam but also reduced the scattered deuteron flux to a tolerable level. A whole new generation of electronics was used together with dual parameter pulse height analysis to reduce the resolving time of the system by a factor of 15 to h.6 nanoseconds FWHM. Extensive shielding was added resulting in a net decrease in background to signal ratio from the original apparatus by a factor of 30. The work described in this chapter was done solely by the author including the design, assembly, and testing of the rotating deuterated polyethylene targets, the experimental arrangement of the electronics, the remotely controlled beam transport system, the target chamber, -10-the scattering,table, and the shielding. The technique was tested by measuring the differential elastic scattering cross-section of neutrons on lead at five degree intervals from 10 degrees' to kO degrees. The results of this measurement together with an analysis of the sources of error are included in Chapter IV. A Monte Carlo computer program was written by the author to make the necessary corrections to the cross-sections for attenuation and multiple scattering. These measurements and their interpretation were the responsibility of the author. Values of the cross-section at these larger angles will be used to extrapolate to smaller angles that part of the cross-section due to purely "nuclear forces". It is at smaller angles that additional contributions to the cross-section can be expected from Schwinger scattering and electric polarizability scattering. A description is given at the end of Chapter IV of the necessary changes in the geometry of the neutron detector and mounting arrangement to extend the measurements to smaller angles. At the time of writing this thesis only one measurement of small angle scattering in this energy range using monoenergetic neutrons had been made (9) which unfortunately includes no details as to what technique was used to perform the experiment. To our knowledge no one as yet has succeeded in using the associated particle technique with the D(d,n)He3 reaction and bombarding energies exceeding a few hundred keV, probably because of the problems involving elimination of -11-scattered deuterons and the difficulty of reducing the background sufficiently. The results of this experiment indicate that a small angle scattering experiment can be performed using the *K56 MeV neutron beam produced by the associated particle technique, and that the previous problems of fine collimation, background, and sufficient neutron flux have been overcome. -12-CHAPTER II PRELIMINARY STUDIES WITH A 5 MeV POLARIZED NEUTRON BEAM A. Introduction The first attempt to produce an accurately colllmated neutron beam in the UoBoC. laboratory with the associated particle technique was with a 50 keV accelerator and the D(d,n )He3 reaction. A. 2.55 MeV neutron beam was obtained with a. low count rate of the order of two neutrons per second per milllsteradian. The results of this work are described in Tripard1sthesis (10) and in a paper by L.F.Go Monier et al (7). At the completion of this work i t was decided that to increase the neutron flux and at the same time obtain a neutron beam which was partially polarized a higher deuteron bombarding energy should be used. This chapter describes preliminary work done to produce an accurately colllmated fast neutron beam using the D(d,n)He3 reaction with sufficient intensity to perform small angle neutron scattering experiments. B. Choice of Angle and Energy According to Marion and Fowler (38) for the D(d,n)He3 reaction, toward higher bombarding energies the magnitude of the polarization of the D-D neutrons increases and seems to approach a maximum of about 17% near 2 MeV. Since 2 MeV was approximately the best energy for producing maximum polarization of. the neutron beam i t was decided that an attempt would be made to perform a nuclear scattering -13-experiment with neutrons produced at this bombarding etiergy. The^ He3 recoil angle was chosen for the maximum differential reaction cross section consistent with the need for performing accurate spectrometry and fast coincidences with the He^  recoil particles. This turned out to be at a lab angle of 89 degrees with respect to the incoming deuteron beam where the energy of the He3 recoil particle was 307 keV. From the kinematics of the reaction, the associated neutrons are emitted at 25 degrees with respect to the deuteron beam. C. Target and Beam Geometry Figure ( 1 ) shows the geometry of the apparatus used. To define the target spot the deuteron beam collimator was ,159 cm in diameter. The angle between the target and the beam was 55 degrees giving rise to an elliptical target spot* The recoil charged particle defining collimator was .318 cm in diameter and was placed 9*37 cm from the target. This collimator subtended an angle of .981 mlllisteradians git the target. D. Deuterium Target The target was D2O frozen onto a .00061* cm aluminium fo i l mounted on a thick copper rim maintained at liquid nitrogen temperature. The thickness of the aluminium foil was a compromise between thinner foils which would contribute fewer Coulomb scattered deuterons to the background in the recoil particle detector and thicker foils with better heat conduction which would maintain liquid nitrogen temperatures at NEUTRONS DEUTERON BEAM v KOVAR SEALS TO DETECTOR FIGURE 1 TARGET AND BEAM ARRANGEMENT / larger deuteron beam currents. Even with the thickness of fo i l used i t was difficult to maintain a stable D2O target with a deuteron beam of 1/3 of a microampere. This was achieved only by continuous evaporation of D2O vapour on the target backing. E. The Mass Spectrometer and Recoil Particle Detector In order to prevent Coulomb scattered deuterons originating at the target and target backing from directly striking the He3 recoil counter and swamping the electronics with counts, i t was necessary to use a mass spectrometer which would transmit the desired energy He3 particles and reject the majority of the scattered deuteron particles. The particular design used for this experiment was a **5 degree focusing magnet with a 10 cm radius of curvature. In order to optimise the He3 to background ratio in the recoil detector, the spectrometer was set to accept only He3++ ions, which at 3.00 keV comprise only 20% of the recoil ions„ The recoil particle detector was an Ortec Silicon Surface Barrier Detector SBEJ 050-60 with a diameter of .798 cm. It was located at a distance of 11.13 cm after the .318 cm diameter collimator on the trajectory of the recoil particle. F. The Neutron Detector The neutron detector was a cm diameter 2.51*- cm deep block of NE 102 scintillation plastic. It was supported on a light structure at a distance of 71«2 cm from the target subtending at the target a solid angle of 3»^  millisteradians. - 1 5 -In order to minimize the number of neutrons scattered back into the neutron counter and to allow small angle scattering experiments to be performed, there was no heavy material in the vicinity of th,e colllmated beam. The floor was 112 cm below the counter and there was a 1.27 cm thick layer of lead above the counter and on two sides at about 30 cm away to protect against X-rays coming from the Van de Graaff and from Y-rays produced by deuteron and neutron induced reactions in the beam lines and the room walls. G. Electronics The identification of a coincidence event between a neutron and a He3 recoil particle was made by a fast coincidence plus energy selection on both the charged particle detected by the semiconductor counter and on the neutrons detected by a liquid scintillator. Figure (2) is a block diagram of the electronics used. The discriminator at the output of the time sorter was adjusted so that the coincidence resolving time was 70 nanoseconds. This resolution was sufficient for the counting rates obtained. Further reduction of the time resolution would have reduced the fraction of He3++ ions accepted by the time sorter since there was an appreciable time jitter. This time jitter had several sources: i . The time of flight of ions of different energies which have been produced at different depths in the ice target varied by as much as 9.A nanoseconds. SEMICONDUCTOR COUNTER PHOTO MULTIPLIER SCINTILLATOR. PULSE SHAPE DISCRIMINATION PROBE L I N E A R G A T E JPlLE-UP a SCATTERED D REJECTION SYSTEM LINEAR GATE TRIGGER Z E R O D E L A Y C R O S S O V E R "Li* X T : W £ < z •J 3 SCPH.A PULSE SHAPE DISCRIMINATOR D E L A Y C-- ' i - -EL A N A L ' Z E 0 V U L T I -CHA.-i.\£'_ A N A L Y Z E R FIGURE 2 BLOCK DIAGRAM OF ELECTRONICS -16-The flight time for a 225 keV He^  particle over 20.5 cm is 53»9 nanoseconds whereas for a 350 keV He^  particle i t is **3«3 nanoseconds, ii. A large time uncertainty was caused by noise generated in the semiconductor detector producing h, distortions in the shape of the double delay-line pulses. This:could not be Improved much because of the poor signal to noise ratio caused by the low energy of the recoil particles. i i i . Considerable time walk in the zero cross-over pickoff resulted from the variation in pulse amplitudes. The energy selection of He3 was accomplished with a system of electronics which included a slow amplifier (0.8yusec double delay-line) with relatively low noise properties, a fast amplifier (O.lyusec double delay-line) with low electronic pile-up, and a tunnel diode discriminator to prevent noise pulses and 120 keV scattered deuterons accepted hy the magnetic spectrometer from triggering the zero cross-over pickoff which would have added considerably to the random coincidente rate of the time sorter. The operational configuration of this system is shown in Figure (3). Figure (*+) shows the energy spectra obtained with the semiconductor counter. The upper curve shows the spectrum without pile-up rejection and the lower curve shows the same energy spectrum with pile-up rejection. F I G U R E 3 O P E R A T I O N A L C O N F I G U R A T I O N O F P I L E - U P A N D S C A T T E R E D D R E J E C T I O N SLOW AMPU ELIMINATES NOISE LINEAR GATE A FAST AM PL. LOWER DISCRIMINATOR ELIMINATES PILE-UP ELIMINATES LOW LEVEL D PULSE CHANNEL NUMBER 32 48 64 80 96 CHANNEL NUMBER • FIGURE 4--17-The same He3 recoil particle spectrum gated with the. associated neutron is shown at the bottom of Figure (5) with the corresponding ungated spectrum at the top using the pile-up and scattered deuteron rejection system. The energy selection of the scintillator pulses was made by a single channel pulse height analyser with an upper and lower level discrimination corresponding to a neutron energy of 1 and 7 MeV respectively. A neutron-gamma discriminator was used to reduce the number of unwanted; pulses coming from some neutron and deuteron induced reactions in the vicinity of the detector. H. Beam Profile To measure the beam profile an NE 213 liquid scintillator slab detector 1.27 cm wide by 5.08 cm high and 7.62 cm long was used at a distance of 90.2 cm from the target. This slab subtended at the target an angle of 0.8 degrees in the horizontal direction and 3«2 degrees in the vertical direction when measuring the horizontal profile. Figure (6) shows the horizontal and vertical beam profiles obtained. They have respective widths of l.k and 0.9 degrees FWHM. I. Neutron Energy Spectra Figure (7) shows the neutron energy spectra for the cylindrical detector. Curve "A" shows the ungated neutron spectrum. Curve "B" shows the neutron spectrum gated with energy selection and neutron-gamma discrimination. Curve "C" 50 4 CO h-z n o o u_ o d z 25 4-3 0 0 keV \ 3 He SPECTRUM WITH PILE-UP AND SCATTERED D REJECTED 0 L t -0 4-—4— 16 32 . 4 8 6 4 CHANNEL NUMBER 8 0 9 6 300+ I 200+ o o o z 100+ 2 0 0 keV I He SPECTRUM GATED WITH NEUTRONS 10 20 30 CHANNEL NUMBER 5 0 FIGURE 5 ENERGY OR CHANNEL -18-shows the neutron spectrum gated by He3++ pulses. J. Conclusions The intensity of the neutron beam obtained in this experiment was low, of the order 0.3 neutrons/second. With a neutron detector, having an efficiency of about 1/3 this would mean a detectable beam of O o l neutrons/secondo The efficiency is further reduced by a factor of at least two if the pulse shape Y-ray discriminator is included. In order to maximise the neutron intensity three major modifications would have to be made; i c The apparatus would have to be scaled up to permit a larger beam spot on the target without losing beam resolution. 11o A moving target would have to be utilized to permit an Increase in target current from 0.3yua to 10 yua without deteriorating the target, i l l . A better He3 recoil angle would have to be chosen to reduce the loss of detectable recoil particles through charge exchange (see section B chapter III). With the experience gained from this experiment and the modifications listed i t was hoped that i t would be possible to increase the beam intensity by a factor of about one hundred. This would mean that the running time required to perform a small angle neutron scattering experiment on uranium or lead with an accuracy of 5% would take of the order of 12 to 15 hours per point. -19-This projection of neutron beam intensity assumed that further improvements could be made in the mechanical shielding, pile-up rejection system, and resolving time of the coincidence units to counteract increases in random count rates produced by the large increase in deuteron bombarding current. It was on this basis that the work described in the next chapter was initiated. =20-CHAFTER III PRODUCTION OF A ha% MeV POLARIZED NEUTRON BEAM A. Introduction This chapter describes the technological improvements in the apparatus necessary to increase the neutron beam intensity from the 0.3 neutrons/second achieved with the apparatus described in Chapter II to a usable intensity of 70 neutrons/second. Improvements were made in the geometry, reaction target, electronics, and shielding. The net result of these improvements has been an increase by a factor of 200 in the neutron beam intensity, a factor of 15 improvement in the coincidence time resolution in going from FWHM of 70 nano-seconds to h.6 nanoseconds, and a decrease in random background by a factor of 30 compared to the performance of the technique as described in Chapter II. B, Choice of Angle and Energy The reason for choosing a bombarding energy of Ed = 2MeV remains the same as that described in section B of Chapter II. However i t was expected that a different choice of He3 recoil angle would reduce the loss of detectable recoil particles through charge exchange and hence enhance the neutron flux. When charged particles pass through matter they capture and lose orbital electrons until an equilibrium charge distribution is attained for the moving ions within a few atomic -21-layers of the material used. He^  can exist in three stable charge states ? He^0, He3+, and He^++. Therefore i f a mass spectrometer is used to prevent Coulomb scattered deuterons from directly striking the recoil particle detector only He3 of one charge state would be accepted by the spectrometer. Since the D(d,n)He3 differential cross-section decreases with increasing energy of the He^  recoil particle whereas the fraction of the total He3 beam in the charge two state decreases, a compromise was made. Figure (8) is a graph which shows the product of the differential cross-section (10) times the fraction of the total helium beam in the charge two state (11) as a function of the He3 recoil particle energy. 700 keV was chosen for the recoil particle energy because increasing this energy by several hundred keV would not increase the product by more than 10$ and at the same time i t would make separation of the 2 MeV deuterons with a spectrometer more difficult. A choice of 700 keV for the recoil He-3 corresponds to a lab angle of 7^ .5 degrees for the He3 and a lab angle of 1^ degrees for the associated neutron of energy h.56 MeV. Co Target and Beam Arrangement. Figure (9) is a simplified diagram showing the arrangement of the deuteron beam transport system, shielding, reaction chamber, and neutron detectors. Not shown are the interconnecting glass tubes, valves, and bellows. Besides the vacuum systems attached to the reaction chamber and Van de Graaff an intermediate pumping station was located - 2 2 between the steering magnets and the switching magnet to reduce residual.gas scattering in the beam line. The sole purpose of the switching magnet was to orient the reaction chamber in such a way that the direction of the colllmated neutron beam would be approximately through the center of the room with the nearest object in the neutron beam line over 50 feet away. The electrostatic quadrupole lenses, steering magnets, and switching magnet were aligned optically with the analysing magnet of the Van de Graaff by sighting through them with a theodolite. A similar alignment was performed on the center of the target chamber, its collimator and the switching magnet. This alignment was checked with the beam of a continuous helium-neon gas laser. The laser was placed at the entrance to the port of the switching magnet's vacuum box pointing towards the reaction chamber. The beam passed through the collimators and illuminated the center line on a removable brass post placed in the center of the chamber. Initial voltage and current settings for the electrostatic lenses, steering magnets and switching mtignet were made by accellerating H 2 * with the Van de Graaff and locally adjusting the settings until sufficient current was focussed onto the target. It was found necessary to equip the lenses and magnets with a remote control system so that final adjustments to the focussing and steering could be made with the deuteron beam from a safe distance. Once these settings were made they were not touched throughout a profile measurement or a scattering experiment. Only small adjustments to the -23-accellerator lenses were made from time to time to maintain the beam on the target. D. The Target Chamber Figure (10) is a diagram of the reaction chamber. It was constructed of brass with a diameter of 20.3 cm and a depth of 23.5 cm. The large size was necessary to accomodate the rotating target. The deuteron beam is defined by two steel collimators 17.8 cm apart. They were mounted on a bellows assembly, to enable fine alignment with the chamber center, and insulated from the chamber with a lucite spacer. The first beam stop was .318 cm in diameter and the second .^ 76 cm. The perpendicular to the target plane was at an angle of 53 degrees with respect to the deuteron beam producing an elliptical target spot. The deuteron beam passed through the chamber into a steel Faraday Cup. Voltages were applied to both the collimator, target, and Faraday Cup for electron suppression. The position of the He3 detector which was used for much of the experimental work is shown in the diagram. It was placed at an angle of 7*+»5 degrees with respect to the deuteron beam and at a distance of 19 cm from the target. In this position, with a .635 cm diameter collimator in front, i t subtended a solid angle of .875 millisteradians at the target. Not shown in the diagram are the quartz and fluorine target holders, which enabled external positioning of the targets in front of the deuterium target, behind i t , or completely out of the bombarding deuteron beam. These targets were used for beam D E U T E R O N BEAM VACUUM PORT ROTATING VACUUM DRIVE MECHANISM FO(? WINDOW COLUMBTED NEUTRONS PROTON DETECTOR TEBL. F f l R A D A V C U P FIGURE 10 REACTION CHfltfSER focussing, Van de Graaff energy calibration measurements, and target thickness measurements. A lucite viewing port was mounted on the l i d of the chamber for target positioning and inspection. E. Rotating Deuterated Polyethylene Target _ In the preliminary studies of neutron beam production with the D(d,n)He3 reaction and a 2 MeV deuteron bombarding energy, the major limitation to a sufficient flux of neutrons was an inadequate deuterium target. The main problem was the need for a tar.get backing, either to maintain a liquid nitrogen cooled D2O target or to support some heavy metal that contained interstitial deuterium. The latter possibility was ruled out because the -available thickness of the deuterium target would be severely limited by the large dE/dx loss of He3 recoil energy in heavy elements. A gas target was not considered because i t would necessarily have either a thin foil window which would degrade the He^  particles or a large volume of deuterium gas between the reaction point and the detector for the particles to traverse. Liquid nitrogen cooled aluminium foil was satisfactory as a target backing for at low beam currents but the design and construction of an adequate and reliable rotating liquid nitrogen cooled target seemed too ambitious. The other alternative was attempted, that of producing a thin film deuterated polyethylene target. The advantages of this type of target for the production of a neutron beam would be many. There would be only the two -25-constituents, carbon ..and deuterium, with twice as many deuterium atoms as carbon atoms. The fact that the target would be very thin and self supporting would mean that the background of neutrons and tf-rays produced at the target spot which were not a part of the neutron beam would be greatly reduced. Most of the incident deuteron beam would pass right through the target and stop in a well shielded beam catcher. The thinness of the target would also reduce the number of deuterons coulomb scattered into the recoil detector. There would be very l i t t l e scattering material in the path of the neutron beam produced in the target. Finally, this type of target would not require cooling therefore making the construc-tion of a rotating target much easier. White (12) has described the preparation of thin polyethylene films between 900 and 2500 % thick by vacuum evaporation. The only disadvantage of this technique is that a large fraction of the evaporated polyethylene is lost in the vacuum chamber. Another technique (13) similar to the one described in this section was used to prepare targets 1-20 mg/cm2; The main difficulty with 100 ytXg/em2 targets is their poor stability in a charged particle beam due to their very low thermal and electrical conductivity,, The usual method of avoiding this problem is to add a conducting film of metal such as aluminium or gold. Tests with this technique failed because expansion and contraction of the polyethylene electrically isolated parts of the foil causing the film to tear under the electrical stresses. It was found that the evaporation of a - 2 6 -thin.film of carbon onto the polyethylene improved the target stability considerably i) Preparation Polyethylene films were prepared by dissolving OoOl gm of deuterated polyethylene ( 1 5 ) » ( Q 2 D L ) n In five gm of boiling xylene. The solution was kept near the boiling point for five minutes to completely dissolve the polyethylene. While s t i l l hot the solution was poured quickly onto six process clean micro slides ( 1 6 ) , The slides were set aside in a dust free environment to dry for 2h hours„ Using a carbon arc apparatus described by Dearnaley ( 1 7 ) , a thin carbon film 10^ig/cm2 was evaporated onto the polyethylene. The arc was produced by passing a current approximately 1 0 0 amps through two .635 cm carbon rods sharpened to a point where they touched. The evaporation was carried out under a vacuum of 1 0 " ° torr. The polyethylene film with its thin carbon coating was floated off the glass by lowering the glass into water at an angle of 3 0 degrees to the surface0 . The films had to be floated off very slowly to avoid tearingo The procedure used was to start the floating off procedure by hand at one end of the slide until about 2 mm of polyethylene had lifted. Then the slide was floated by surface tension in a pan of water about 3 slide thicknesses deep. Surface tension floated the remainder of the film from the slide with no damage to the film as the region of the slide uncovered by the film no longer supported by surface tension 27-sank beneath, t h e s u r f a c e 0 O n l y " p r o c e s s c l e a n " (16) s l i d e s were s u c c e s s f u l , i n . a v o i d i n g s t i c k i n g . When t h e s l i d e s had been used o n c e , t h e y c o u l d n o t be reusedo The f i l m s were p i c k e d up on f l a t m e t a l f rames w i t h a 0o3l8 cm d i a m e t e r h o l e by d i p p i n g t h e f rames i n t o t h e w a t e r and r a i s i n g them s l o w l y a t a s t e e p a n g l e , i i ) T e s t i n g t h e S t a t i o n a r y T a r g e t s ? Carbon t a r g e t s (17) were p r e p a r e d s e p a r a t e l y u s i n g t h e same e v a p o r a t i o n t i m e as used i n t h e c a r b o n e v a p o r a t i o n on p o l y e t h y l e n e . The t h i c k n e s s o f t h e c a r b o n t a r g e t s was measured by e l a s t i c a l l y s c a t t e r i n g p r o t o n s f r o m t h e c a r b o n . T h i s measurement was used t o e s t i m a t e t h e t h i c k n e s s o f t h e c a r b o n f i l m on t h e p o l y e t h y l e n e . The c a r b o n f i l m s were f o u n d t o be lC^g/em 2 +3pig /cm 2 o r abou t 2 , 5 keV t h i c k t o 870 keV p r o t o n s . The t h i c k n e s s o f t h e combined c a r b o n and p o l y e t h y l e n e f i l m s was d e t e r m i n e d by m e a s u r i n g t h e s h i f t o f t h e 873 ke¥ resonance o f ^FCpgOig %)^0 r e a c t i o n a f t e r t h e f i l m was p l a c e d i n f r o n t o f a t h i n c a l c i u m f l u o r i d e t a r g e t . The measured s h i f t i n t h e r e s o n a n c e f o r t h e combined f i l m s was 28 k e ¥ . To measure t h e t a r g e t d e t e r i o r a t i o n , r e a c t i o n p r o t o n s f r o m bombard ing t h e t a r g e t s w i t h 2 Me? d e u t e r o n s w e r e c o u n t e d w i t h a s e m i c o n d u c t o r c o u n t e r p l a c e d a t a l a b a n g l e o f 60 degrees w i t h r e s p e c t t o t h e i n c i d e n t d e u t e r o n s , A 0 , 0 5 nun a l u m i n i u m f o i l was p l a c e d i n f r o n t o f t h e d e t e c t o r t o c o m p l e t e l y degrade t h e T s and s c a t t e r e d d e u t e r o n s . 28 Figure ( 1 1 ) is an energy spectrum of the reaction protons from the reaction from the reactions and D(d,p)T. By monitoring the ratio of the number of counts in the two peaks i t was possible to detect any deterioration in the deuterated polyethylene resulting from possible melting or sublimation. With an incident deuteron beam of 1 0 0 nA through a 0 „ 3 l 8 cm diameter collimator, there was no detectable deterioration of the target after one hour of bombaraiment<, With 2 0 0 nA, there was about a 10% decrease in the d oh d proton yield with respect to the 12C proton yield after one hour of bombardment0 i i i ) Large Targets: To enable the use of a rotating mount a much larger target, was necessary than that described in the previous sections. Special "process clean" micro slides 7 » 6 2 cm x 7 o 6 2 cm with ground edges, . 9 6 to 1 . 0 6 mm thick were provided by J« Melvin Freed, Inc (18)0 Targets ^ . 1 3 cm' in diameter were prepared in the same manner as the small ones but with additional difficulty in removing the targets from the glass and lifting'the targets off the water onto the target mounto Often several hours were required to float the targets off the glass surface. The films were picked up on 5 . 0 8 cm x 5 ° 0 8 cm metal frames with a ^ o l 3 cm diameter hole. iv) Rotating Mount: Little attention is given in the literature to the problem of rotating a target because the targets used have had 90i Tfi ' 2.Q UTS 1 iT£ 3 . 4 EKiERSy I N M E V FIGURE II REACTION P R O T O N S FROM D E U T E R A T E D POLYETHYLENE TARGETS - 2 9 -reasonably heavy target backings which could be fixed at their center to a rotating rod. As early as 1952 work is described in .which a target,of this type is used (19)• Lithium targets were evaporated onto the tantalum end cap of a rotating target for the production of Li7(p,n)Be? neutronso Rotating a thin film target presents the difficulty of transferring motion to the target with no supporting material or drive mechanism in the path of the bombarding beam0 Figure (12) is a diagram of the rotating target mount, Strictly speaking the target does not actually rotate but each point of the target revolves about some center. Motion is transferred to the target mount by two axles each mounted on rotating discs "G" which are coupled together by a chain and gear drive "D". The radius of revolution "R" = 1,^-3 cm is defined by the distance from the axle in the center of the disc to the off center axle. The chain and gear assembly is driven by axle "F" which passes through a rotating vacuum seal to an external drive mechanism. The rotating seal is supported by a bellows assembly shown in figure (10) which can be adjusted for target alignment, One additional constraint is required to prevent the assembly from "rocking," This is provided by a lucite bar fixed to the center post of the chamber. The whole assembly is easily removed from the chamber by unscrewing the knurled knob "C" and slipping axle "F" out of its coupling to the rotating seal. The targets were -30-rotated at h cycles per second. v) Performance of the Rotating Targets: As with the stationary targets a proton monitor was used to test the deterioration of the moving target. Figure (13) shows the relative yield of one of the targets used in the scattering experiment described in Chapter IV. The main, difficulty with the targets was finding one that would not break in the first few minutes of use. The targets would either break within the first fifteen minutes or not at a l l with reasonable care. F. Electronics The electronics used in the experiment included systems for: 1) detecting and identifying the D(d,p)T reaction protons. 2) identifying and establishing the arrival time of the He3 recoil particles. 3) identifying and establishing the arrival time of neutrons transmitted through the scatterer. k-) identifying and establishing the arrival time of neutrons scattered by the scattering material . 5) dual analysis of time and energy. i / D(d,p)T Reaction Protons Figure (ih) is a block diagram of the electronics used for monitoring the D(d,p)T reaction protons. Pulses SEMI CONDUCTOR DETECTOR PWLSE SHAPER C H A R G E - S E N S I T I V E P R E - A M P 6 T E S T INPUT PULSE HEIGHT ANALYSER LINEAR AMPLIF/ER MUL.T-CHANNEL-PWLSE HElGiTT 4NALYSER F/SURE BLOCK DIAGRAM FOR MONITORING 14 OF ELECTRONICS USED T>(dyp)~r PROTONS. -31= produced in an Ortec partially depleted surface barrier detector were amplified by a charge sensitive preamplifier, the description and circuit diagram of which are given by Whalen (26) and Blackmore (27 ). The signal was then HC shaped for low noise and then amplified by a double delay-line amplifier. The energy selection and counting were then provided.by a single channel pulse height analyser together with a scaler or by a 512 channel pulse height analyser i f simultaneous monitoring of the C12(d,p)C13 protons was desired. 11/ He3 Reooll Particles a) Elimination of pulse plle-ups One of the principal disadvantages of the associated particle technique is the limit imposed on the source intensity by the counting rate that oan be tolerated in the reooil particle detector thus limiting the rate of data collection. The obvious limitation on this counting rate is caused by the accidental coincident rate "R" between the recoil particle detector and the neutron detector. Where is the counting rate of the recoil particle detector, }>n is the counting rate of the neutron detector and t> is the time resolution, FWHM, of the coincident circuit. However there is one additional random coincidence rate which must be considered especially i f an absolute neutron detector effi-ciency measurement is desired. If the assumption is made that the recoil particles are detected with 100% efficiency -32-suchas described in a paper by Monier et al. (7) then the efficiency of the neutron detector is the ratio of the number of neutrons detected divided by the number of associated recoil particles. If two recoil particles arrive within the resolving time of the amplifier causing their combined voltage signal to exceed the energy selection window of the single channel pulse height analyser then the assumption of 100$ detection efficiency is invalid. To give an example of the discrepancy that can be involved, consider a recoil particle count rate of 5 x id* He^  particles per second. Then the coincidence rate for electronic pile-up Rp lss Hp = .? x 106 sec x (5 x left sec" 1) 2 This pile-up rate is 3$ of the true count rate for an amplifier with a 700 nanosecond resolving time. If there is no energy window, pile-up would cause the experimental count rate to be 3# smaller than the true count rate whereas with energy selec-tion not only would pile-up cause two particles to appear as one but both particles would not be counted since their combined signal would exceed the upper window on the energy analyser. In the latter case there would be a 6$ decrease in the count rate. Further difficulties are encountered i f particles from competing reactions are present, contributing to the pile-up. Since i t was expected from the preliminary work described in Chapter II that the He3 recoil particles would -33-have to be detected in the presence of a large background of Coulomb scattered deuterons, considerable effort went intothe development of a pile-up rejector with a very fast resolving time. To reduce the pile-up resolving time various pile-up rejectors have been built (20-23), This can be done by RC shaping, delay-line clipping, or through the use of a charge pick-off device before the preamplifier of a semiconductor detector. The pile-up rejector developed examines the width of the positive going part of the output pulse from a ?k0 nanosecond double delay-line (DDL) clipped linear amplifier (23) by means of a "pulse overlap to pulse height converter" thereby distinguishing between single pulses and pile-up pulses with a pile-up resolving time as low as 20 nanoseconds. Similar systems have been used by Alexander and Goulding (2*0 as a particle discriminator selecting neutrons in a background of tf-rays and by Sayres and Coppola (25) as a risetime discriminator for reaction particles in an ionization chamber. A complete description of this pile-up rejector" is given in Appendix A together with graphs showing its characteristics and performance. The most important advantages offered by this pile-up rejector are its high pile-up rejection efficiency even for small signal-to-noise ratios, the simplicity and uncritical nature of the setting-up adjustments, and the fact that i t is used at the output of a DDL amplifier making i t suitable for semiconductor detectors without affecting energy resolution. The resolving time of this pile-up rejector represents an improvement by a factor of more than 5 over that achieved with the method described in Chapter II, The system as yet has not been incorporated into the experimental arrangement for a neutron scattering experiment, b) Time pick-off unit A critical part of the problem of time-of-flight measurements is the precise determination of the starting time of the particles. Three basic methods have been commonly used for obtaining this "zero time" ( 3 8 ) , 1 ) Oscillator Pickoff, The reference signal is obtained by tapping the ooil of the beam deflection oscillator or by using a pickoff loop* 2) Target pickoff. The beam pulse itself is used to provide the gere time signal. This can be done by detecting the beam charge on the target or by detecting the light pulse produced in a scintillator by the beam, 3 ) Associated Particle Method, The detection of the associated particle from the neutron-producing nuclear reaction provides the zero time signal. This is the only method which does not require a pulsed beam making time-of-flight measurements possible with dc beams. The development of a time pick-off system by Williams and Biggerstaff (29) has made possible simultaneous fast leading edge timing and high resolution energy analysis =35-with charged particleso Figure (15) shows the essential features of a time pick-off unit used in series between a semiconductor detector and a charge-sensitive preamplifier. A torroidal transformer having a high frequency band pass allows only the high frequency components of the detector signal to be transferred to a fast amplifier and tunnel diode discriminator. The slower components of the charge pulse used for high resolution energy analysis pass through the primary of the transformer with no significant deteriora-? tion. A Model 260 Time Piekoff Unit from Qrtec was used together with the Model 2 6 l Dual Time Piekoff Control Unit. The main problem encountered in using the unit for detecting the He3 recoils from the D(d,n)He3 reaction was its poor sensitivity to low energy charged particles. Figure (16) shows the triggering threshold as a function of detector capacitance as measured by Ortec with a pulse generator. From the kinematics of the reaction and energy degradation of the He3 particles emerging from the deuterium target the He3 were expected to range in energy from 750 keV to as low as 500 kev*. Therefore even with low capacity detectors i t was found necessary to set the triggering level of the tunnel diode discriminator at or very near threshold. The problem could be avoided by placing the time pick-off unit between the preamplifier and the main amplifier} however, the slow rise time of the charge sensitive preamplifier output pulse would have resulted in increased variation in PRECIS/ON DETECTOR PARTICLES CHARGE. TERMINATOR CHARGE SENSITIVE PREAMPLIFIER LINEAR AMPLIFIER T O ANRLY^ER E T C ^ POWER & CONTROL BJAS TORROIDFIL. TRANSFORMER FftNOUT BUFFER OUTPUTS O FAST RMPUFlER AND TUNNEL Pi ODE DISCRIMINATOR FI6URE I5-EXPERIMENTAL ARRANGEMENT OF A TIME. PICK-OFF UNIT USED FOR LEADING EDGE TIMING. 600 400 «J CD or UJ UJ o to or r-\ ..: A — i CAP O >F*CI F Dt US TANCE ETECTOR EO - \ ) -IOO z o o SIMULATED D E T E C T O R CAPACITY FIGURE. 16 TRIGGERING THRESHOLD OF THE TJ^JE PICK-OFF UNIT RS fi FUNCTION OF D E T E C T O R CftPfiC I T V -36-the threshold crossing times at the fast discriminator. Preliminary tests were performed on the time piek-off unit to establish its efficiency and energy detection threshold. Very l i t t l e was known at the time as to what parameters might be varied to improve the detection threshold and decrease the noise of the system. For ©/ample i t was discovered that changing the number of B N C connectors between the detector and T.P.O. unit and between the I.P.O. unit and charge.sensitive amplifier drastically affected the sensitiv-ity of the T.P.O. unit to external noise. The system acted as a tuned circuit whose frequency response was altered by the slight change in capacitance and inductance with the addition or removal of a small BNC coupling. Figure (18) shows the noise count rate at the output of the T.P.O. control unit as a function of the number of BNC couplings. The-sensitivity of the circuit to external noise is indicate^ by the two curves, one made with the Van de Graaff on and the other with i t off. Connecting the units with only three couplings required extremely cramped conditions and the inconvenient deletion of the test input shown in Figure (15) used for the setting of time delays although this gave the best results. The energy detection threshold was determined by measuring the response of the T.P.O. unit to protons of varying energies accelerated by the Van de Graaff and elastically scattered by an Aluminium f o i l . Figure (17) shows the experimental arrangement used to measure the DETECTOR T. P. G\ C O N T R O L P U L S E GENERATOR SINGLE CHANNEL ANALYSER COINC S C A L E R * 1 S C A L E R # 2 . F/SURE. 17 B L O C K D I A G R A M OF ELECTRONICS U S E D TO M E A S U R E T H E T H R E S H O L D RESPONSE. OP THE T P . O UNIT. u Ul X § VdeG ON 4 - 5 6 7 8 9 »0 TOT»L WO. OF BNC', CONNECTORS SETME£N o e r e c r o R RNO PRCAMR FIGURE 18 No/SE 'IN TH£ T / M £ PICK-OFF UNIT fiS Ft FUNCTION OF BNC COUPLING, 500 600 700 8 00 ENERGY OF PROTONS IN keV > IOOO FIGURE 19 TRIGGERING EFFICIENCY OF 7>V£ T'^E PICK-OFF UNIT /)S A FUNT/ON OF PROTON. ENERGY. -37-threshold response pf.the T.P.O. unit. The coincidence unit h.ad a resolving time of 0.^  microseconds which was required to eliminate the large.noise count rate .produced by the T.P.O. unit as shown in Figure (18)« Figure (19) shows the response curves for a partially depleted, *+500 ohm-cm, 100 pf detector operated with a bias 55 Volts higher than the recommended 25 Volts and a .partially depleted, 3500 ohm-cm, 6*f pf detector operated with a bias 95 Volts' higher than the recommended 65 Volts. Operating the detectors at their recommended biases resulted in response curves well below those shown in Figure (19)• The large variation in the response curves of the two detectors suggested that even better charaoteristios could be realized by careful selection of detector. Figure (20) is the suggested equivalent circuit of ; s - f - ^e - depletion l&yer ca.pa.ci*a-*cefK5 a semiconductor detector (32). C0/^ and Cs are the bulk resistance and capacitance due to the undepleted material, and Hc takes, into account every series resistance. The rise time T of the pulse delivered by the detector will then be equal to: T =X+ RSC0+ RCC0 where % is the collection time of the charge carriers. This rise time will be further Increased by any input capacitance of the preamplifier and connecting cable. It has been experimen-tally verified that T, according to the theory, is a linear function of V"^" where V is the detector bias (33). For a given .resistivity material, the breakdown voltage of the diode H V W v -1 C s — O F I G U R E 2 0 EQUIVALENT CIRCUIT OF A SEMICONDUCTOR D E T E C T O R - 3 8 -establishes an upper limit on the electric field strength, however the -large increase in noise and the decrease in energy resolution .at higher voltages reduces this limit further as was the case for the two detectors already described. As a result of this investigation a totally depleted detector was acquired which would have the advantage of no bulk resistance, Rs. Because of the differ-, ence in mounting i t has not yet been incorporated into the experiment, but a test with 600 keV protons indicates that it will be an improvement0 The 5200 ohm cm detector with 100 pf capacitance triggered the T.P.Q. for 80 percent of the 600 keV protons. A further discussion of spectrometry i s contained i n section G. which includes the use of electrostatic and magnetic analysers* 1*4/ Transmitted Neutrons Figure (21) is the experimental arrangement of the electronics used to monitor the neutrons transmitted through the scattering sample. The neutrons were detected with a liquid scintillator in a glass container 11 cm in diameter and 3.8 cm deep. A plastic light pipe coupled the glass container to a 56 A7P photomultiplier. With an H.T. of 2100 Volts the signal was large enough to be taken directly from the photomultiplier to a tunnel diode discrim-inator (30,3D* The pulses produced by this llmiter trig-gered a pulse generator with a continuously variable internal Sink 8 ~ ^  5 i r 3 ui < r Q. I 2 A A 1? Ui s UJ co ST Ul IS 3 H ar j -to 111 o 2 I-H ui co or K ct J a __ h . £ CC it] 13 °-—' ft <D uJ U- ui s <4 Q Q UJ ul 3 t: 3 i UJ -J til ul 5 f Ul I I s i £.3 to a u I 25 t 3 -co UJ —> ? X * ? 8 s -39-delay. The output of this pulse generator was used to gate two coincidence units one of which counted true coincidences (scaler #1) and the other monitored the random coincidence rate (scaler #2) between the neutrons and He3 particles. The timing requirements were not nearly as stringent for counting coincidences between He3 recoil particles and transmitted neutrons as was the case for scattered neutrons since one is not trying to detect a small number of true events in a large random background. A resolving time of 50 nanoseconds was used for the coincidence units which was provided by setting the pulses generated by the pulsers to the appropriate widths. The timing provided by the zero cross-over pickoff of the pulse height analyser in the He3 channel was adequate for the resolving time of the coincidence units. The timing was set during deuteron bombardment of the reaction target by observing the pulses on an oscillo-scope triggered by the tunnel diode limiter. The delays in the pulse generators were adjusted until the pulses coincided in time. An appropriate delay was set in one of the pulse generators in the He3 channel to produce a random coincidence rate. A linear signal was also obtained from the neutron monitor which could be used to check for drifts in the discrimination level of the tunnel diode limiter. Figure (22) shows a typical spectrum obtained by gating a multichannel pulse height analyser with the tunnel diode limiter. FIGURE 22 G A T E D S P E C T R U M FOR NEUTRON FLUX MONITOR. A 9-8-7-(A 3 ct 24 I/O2"-3 » IL * S 6 •4 it 2 + »o' , , , » • • • • • • • • a **" t * \LOiV ENERGY DISCRIMINATION. ZO 30 40 SO 60 70 80 go /OO |IO 120 CHANNEL N O . — - > -kO-lv/ Scattered Neutrons Figure (23) is the block diagram of the experimental arrangement used to detect the scattered neutrons. A 5.08 cm diameter by 7.62 cm deep NE 213 encapsulated liquid scintillator was mountedon an RCA 6810A photomultiplier. The tube was mounted on a "pulse shape discrimination probe", model N E 5 5 5 3 manufactured by Nuclear Enterprises. This provided a fast positive pulse for the time-to-pulse-height converter from dynode Ik and an amplified linear output from dynode 1 1 . The fast pulses were amplified by a model **62A Hewlett Packard wide bandpass linear amplifier (trise<3 nanoseconds), delayed and sent directly to the stop input of a time-to-pulse-helght converter. The linear signal was amplified by a Canberra Industries' Model 1^35 Timing Single Channel Analyser which combined the dual functions of single channel pulse height analysis and zero cross-over timing. A test of the time resolution of this unit with an actual coincidence experiment using the time pick-off unit for the He^  start pulse resulted in a time-to-pule-height converter peak with a FWHM of 15 nanoseconds. This is not surprising considering the poor rise time ( > 2 0 0 nanoseconds) of the linear pulse being used and the large dynamic range of the pulses ( 2 0 : 1 ) . The baseline bias of the single channel analyser was set emperically to eliminate noise and to reduce the count rate from the large flux of H(n,tf)D 2.2 MeV tf-rays arising from the wax and concrete shielding in the vicinity of the neutron source. The output of the timing pulse height analyser was P£UTBROH T E S T P l I L S E R SEMICONDUCTOR DETECTOR ._ / TARGET S C A L E R C H A R G E - SENS. P R E / * M R T P . a MOQgL. 2 6 Q SC /^TT-ERER T F A S T S I6WAL T.ft»6. CONTROL ft 6 NEUTRON D E T E C T O R T E S T PULSER U N E . O R BIAS ANO POWER S C A L E R PULSE GEM. WEKTER F A S T flMR T I M E - T O - P U L S E HEIGHT CONVERTER S T A R T D E L R y 1 T I M / N 6 PULSE WEIGHT ANALYSER E jlNI/ERTER E FIGURE. 23 B L O C K DIAGRAM OF E X P E R I M E N T A L A R R A N G E M E N T U S E D T O D E T E C T SCATTERED NEUTRONS. R I L S E STRETCHEF S C A L E R S T O P L I N E A R A M R OELAVED PROMPT T | f ) / N 6 S C P W R •*4-AOC 2 P A R A M E T E R M U L T I CHANNEL PULSE HEIGHT A N A L Y S E R MULTI CHANNEL. P U L S E H E ' S W T R N A L y S E R . ^ G A T E . PULSE GENERATOR -ki-ln coincidence with the slow channel of the He3 detection system to gate the 2 parameter multichannel pulse height analysero Pigure (2k) is a neutron spectrum for the scattered-neutron detector gated by the SCA showing the low energy cut-off point. v/ Two Parameter Analysis of Time and Energy Sections 1 and lv have described the methods used to obtain accurate time signals for the neutron and its associated He^  recoil particle together with a good resolution measurement of the energy of the He^  particle. This section describes a technique which extracts the maximum information available about the simultaneity of the two particles making use of the additional information provided by the energy measurement of the He^  particle. a) Tlme-To-Fulse-Helght Converter A Model 1 0 8 H LeCroy time-to-pulse-height-converter was used. It produced an output pulse whose amplitude was proportional to the time interval between the leading edges of a start and stop pulse provided by the recoil He3 particles and the neutrons respectively. Tunnel diode discriminators with a threshold of -250 millivolts employed at the start and stop inputs provided precise start-stop timing over a wide amplitude range of pulses. The relatively short time intervals (1-100 nanoseconds) which having been converted to •pulse amplitudes were then analyzed relatively slowly (approx-imately 30 microseconds) by a pulse height analyser. 3T A z 3 i S 2 B T 44-34 24 AD FIGURE 2 4 GATED SPECTRUM FOR SCATTERED NEUTRON DETECTOR. • t LOW EWERgy DISCRIMINATION i i /o 2o 3 0 40 £o 60 TO so go too no /ao C H A N N E L N U M B E R > • The various predominant factors which affect the time uncertainty in the associated particle technique have been discussed comprehensively by Martin ( 2 8). These comprise five separate sources: 1) At e; Electronic processes in the scintillator-multiplier system. Improvements certainly could have been made in the ultimate resolution had a better choice of photomultiplier been made such as an AMPEREX 56AVP. However this did not prove to be the most severe limitation. 2 ) At s; Physical dimensions of the scattering sample. This uncertainty for high energy neutrons is a function of the scattering angle and energy of the inelastically scattered neutron where applicable. For example, the flight path of a L . 5 6 MeV neutron scattered at a lab angle of 9 0 degrees would have an uncertainty equal to the thickness of the scattering sample. For a 2 cm sample this would represent an uncertainty of . 6 8 nanoseconds in flight time. 3 ) At nj Variation in the flight time of the neutron where where the flight path of the neutron in meters where E, 'n the energy of the neutron in MeV For a flight path of 83 cm and a neutron energy range of 1 +. l +9 MeV to L « 5 9 MeV, & t „ = loO nanoseconds k) At^j Physical dimensions of the detecting medium where At d = 72.3 d nanoseconds /*n~ where d = the effective thickness of the detector in meters and EQ = the energy of the neutron in MeV. For a M e V neutron and a detector thickness of 7.6 cm At d would be 2.6 nanoseconds. 5) At H e3$ Definition of time zero, resulting from the divergence of flight times of the He3 particles where AtHe3 " I-2? " -1 1 nsec. lej \/*He| where Lg 3 = the flight path of the recoil He^  (in cm.) Ejje3 = the energy of the He^  in MeV It is this uncertainty, A t H e 3 , which causes the most severe limitation on the time resolution for the D(d,n)He^  reaction at a bombarding energy of E<i = 2 MeV. For a flight path of 18 cm and a He3 energy range of 550 keV to 750 keV, Atjjg*!- = 0.1 nanosecondsv&s achieved by Martin (28) using the T(d,n)HeIf where the Re* recoil particles have an energy of several MeV. To measure the time resolution of the system and the effect of including energy discriminating side channels to gate a single parameter pulse height analyser, the experimental arrangement of Figure (23) was used (excluding the dual parameter multichannel pulse height analyser). Using a flight path of 18 cm for the He3 recoil particles and a neutron detector with an effective thickness of 7.6 cm placed directly in the neutron beam at a distance of 83 cm from the source, singleparameter pulse height analysis was performed on the output of the time-to-pulse-height converter. Figure (25) and table (1) show the results of these measure-ments. The time scale for the spectra in figure (25) was calibrated by inserting a delay of 30 nanoseconds in the He^  channel. Curves 3 and h of figure (25) are the resulting two peaks. This established a time scale of 0.8 nanoseconds per channel and a full width at half maximum of 7 nanoseconds for the system. This calibration was checked by changing the length of the .neutron ..flight path by a measured distance and hence changing the.flight time of the neutron by a known amount. The two calibrations agreed within the accuracy of the measurement. The-measured time resolution of 7 nanoseconds can be compared to an.uncertainty of 5.5 nanoseconds estimated from combining the three largest sources of time jitter ^He^' ^*di a*1*1 ^ t n . ^ a b l e (D shows the large decrease in the random count rate produced by the inclusion of side channel energy discrimination. b) Two Parameter Pulse Height Analyser Two parameter pulse height analysis was aimed at reducing the large time uncertainty AtHe3 and Atn caused by the difference in flight times of the He-3 particles and /CQ NEUTR0N ENERGY DISCRIMINATION BUT NO He 3 ENERGY DISCRIMINATION 5$ » » /O 20 30 40 50 60 /OOl- (D NEUTRON ENERGY DISCRIMINATION . • ' * AND We3 ENERGY DISCRIMINATION 0 » 501- . . . » 7 n s e c -»-/O 20 30 4-0 50 60 ® /CO. VV ^ ENE/?<Sy DISCRIMINATION i . «>»»»t • « «».»« .. (.. i«» . • . » . . . . , » , : — p i /O 20 30 4 0 5(9 60 l^OGj- VTV CALIBRATION PEAK UL 5D - • • ' U - ?or>sec . . DELAV (N /-/e 3 ^CHANNEL. o 1 1 » I » 10 20 30 40 so eo CHANNEL NUMBER FIGURE 2 5 * SINGLE: PARAMETER TIME-TO - PULSE -HEIGHT CONVERTER SPECTRA. TABLE I EFFECT OF SIDE CHANNELS ON RANDOM BACKGROUND SIDE CHANNEL RATIO OF ENERGY DISCRIMINATION COUNTS IN PEAK: RANDOM He 3 NEUTRON OUT OUT 9:1 IN OUT 1 7 i l OUT IN 69*1 IN IN 3 3 2 t l neutrons respectively. Because the time pick-off unit as described in section ( i i b) enabled the simultaneous fast timing and high resolution energy analysis of the He3 recoil particle i t was possible to establish a different "zero time" corresponding to He 3 particles of different energies. Figure (26) illustrates the effect with an example. Consider a reaction taking place at the target with a He3 recoil particle of 750 keV. From the kinematics of the reaction the associated neutron will have an energy of *+.L9 MeV. For flight paths of 26 cm for the He 3 and 83 cm for the neutron the arrival times for the two^particles will be t H e3 = 37-1 nanoseconds and t n. = h2 nanoseconds respectively. These times are marked on a time scale in figure (26) using the time at which the reaction takes place as an arbitrary zero reference with an appropriate delay placed in the neutron channel. The resulting output from the time-to-pulse-height converter (TPHC) is indicated in the diagram as corresponding to the energy of the He3 particle, Ejj e^: Similarly, -the arrival times of t H E 3 = ^0.3 nanoseconds for a He3 particle of 6 5 0 keV and t n 2 = *+l nanoseconds for its associated neutron of K . 5 9 MeV are shown. Thus the 6 5 0 keV He3 particle starts the time-to-pulse-height converter 2.8 nanosec-onds later than the 650 keV He3, i.e. At H E3 = 2 . 8 nanoseconds and its associated neutron, n 2 stops the TPHC one nanosecond earlier than the neutron, n^, i.e.Atn = 1.0 nanosecond. This produces a TPHC output corresponding to the He3 particle, %e^» "that is 3.8 nanoseconds less than for the He3 particle, r DEUTERON BEAM FIGURE 26 ESTRBL/£WMEA/T OF R ""ZERO TIME" CORRESPONDING* TO THE He 3 ENERGY. .1+6-E H e3 0 if both the energy of the He3 particle and the output of the TPHC can be recorded simultaneously then a different "zero time" can be established for each He3 energy. This is the function of the dual parameter multichannel pulse height analyser. The analyser is gated by a coincidence in the slower side channels as shown in figure (23). The signal from the TPHC is sent to one of the analogue to digital converters (ADC) and the signal from the linear amplifier of the semiconductor detector is sent to the other ADC. A typical spectrum is shown in figure (27). By integrating the counts over al l energies for each time channel a single parameter time-to-pulse-height spectrum can be obtained. This spectrum can be compared to time-to-pulse-height spectra for individual energy channels. Such a comparison for two energies = 550, keV and Ejje3 = kOO keV is shown in figure (28);" The FWHM for the integrated time-to-pulse-height spectrum was 7*L nanoseconds. For He3 recoil energies falling in the 550 keV channel the FWHM was 5*1 nanoseconds with the largest count in the same time channel as the integrated peak. This was approximately the maximum width of a time spectrum for any individual energy. For ljj e3 = k00 keV the TPHC peak was shifted 3*2 nanoseconds to the left and had a FWHM of k.6 nanoseconds. The gain in time resolution is achieved only at the expense of rather laborious analysis of each spectrum. There is the possibility however of automating this analysis with a computer. Additional information can be gained from 8 09 — I — OS — ( — 0£ 02 0 0 O O O O O 0 o 01 0 -4 o o o o o 00 o 0 o 0 0 0 00 0 0 o o o 0 0 O 0 0 ,° 0 0 1 o o o 0 o 0 o e P o o 0 o o e 0 0 o e 0 o 0 o e o o o o o o o e © © o o o O O 0 8 , o e © o o o e o e o e o o © o © o © o o o o o o o o o o o o o o © © o 0 0 © © o © © © o o © © © o o © © © o © © © © © © © 0 0 © © © o o © © © o o © © © o © © © o o © © © 0 0 © © © o o © © © o o © © © o o © © © o o © © © © © © © © © © © o © © © o o © © © o © e © o © © © o © ©-© o © © © o © © © © © © © e © © © © © © o o ©© o o o o o o o o o o o o o o o o o o o o o o o o O 0 0 o O 0 0 o o o o o o o o o o o o o © © o II II It 8 8 o -*7-the spectrum about the angular distribution of the associated neutrons which will be discussed in section (I). G. Charged Particle Spectrometry In employing the associated particle technique with the D(d,n)He3 reaction the principal problem is the copious number pf deuterons elastically scattered by the Coulomb field of the target nuclei which bombard the He3 detector. Several techniques can be used to overcome this problem, the choice depending on the deuteron bombardment energy required* 1/ Thin Foils in Front of Detector If the deuteron bombarding energy is sufficiently low a thin fo i l of carefully chosen thickness can be put in front of the He^  detector such that the undesired deuterons will be stopped by the foil whereas the He^  will be transmitted. This technique has been successful employed by other experimenters (7)3*+)* The main disadvantage with the f o i l is that i t seriously degrades the energy of He3 particles before the particles are detected and straggling causes a further spread in the energies of the He^ . At higher deuteron bombarding energies any foi l which would stop the deuterons would also stop the He^  because of the large stopping cross-section for doubly charged particles compared to singly charged particles of the same velocity. i i / Electrostatic Analyser An electrostatic field has been successfully employed for the discrimination'of He^  particles and deuterons (35,39). ,1+8-Their choice of electrostatic deflection in preference to magnetic deflection was made on the basis of the following analysis. For particles with charge q times the electron charge e, a mass m and an energy E we find for a radius of curvature ^ in a magnetic field with a strength B: ^ = /2mE qeB Therefore in a given field deuterons with energy E d and He3 particles with energy E^ e 3 = 8 / 3 Eg will be deflected along the same path. For an experiment in which the deuterons will be scattered with energies E^<Eg (generator), the following condition holds for complete discrimination1 E j j e 3 > 8 / 3 Eg (generator). Similarly for an electrostatic field of strength F P = 2J__ qeF and the condition for complete discrimination is EH e3>2Ed (generator). It was therefore concluded that the latter would give the best discrimination. Other reasons for the choice of electrostatic deflection rather than magnetic included comparative ease of construction and the sizeable difference in mass of material in the target vicinity contributing to background scattering. The most serious dissadvantage to the use of an electrostatic field is the large flight path of the He3 necessitated by electrostatic deflection. For Put's experiment ( 3 5 ) the flight path is estimated to be about 3 0 cm. His time - i r -resolution was 27 nanoseconds FWHM largely as a result of the time uncertainty in the arrival of the He3 particle. 111/ Magnetic Analyser When the bombarding energy becomes greater than half the energy of the He3 particle i t is no longer possible to achieve complete discrimination of the two particles by either electrostatic or magnetic deflection alone. However complete discrimination can be achieved as was demonstrated in Chapter II by using a combination of magnetic deflection and semi-conductor detector spectrometry. At higher bombarding energies magnetic deflection is to be preferred over electro-static deflection because large deflections can be achieved in a shorter distance with a magnet. The best discrimination can be achieved by deflecting the particles in the reaction plane since the He3 beam is compressed in this plane i f the particles are deflected in the correct sense. This is caused by the different values ,,pf energy and by different directions of the He3 particles from reactions at different depths in the target. This point was not realized during the design of the spectrometer for the experiment described in Chapter II. Therefore the He3 beam was defocussed rather than focussed by the spectrometer in the reaction plane contributing to the rather poor transmission efficiency of that spectrometer. The pole pieces of the spectrometer for this experiment were designed by graphically tracing the trajectories of He3 particles expected from a target that was 100 keV thick -50-to.700_keVHe3 particles such that the trajectories would focus in the reaction plane. One additional design goal was to impose some second order focussing on the He3 particles in the plane perpendicular "to the reaction plane. Second order focussing is the term used to describe the effect of the fringing fields of the pole pieces. This effect has been discussed extensively by W.E. Stephens (36) and W.G. Cross (37). The curvature of these fringing fields has the effect of exerting a force towards the center of the gap on any particle incident at an angle to the edge of the pole faces. The net result is that, for proper geometrical arrangement, the particles are focussed in the plane perpendicular to the reaction plane. Figure (29) shows the experimental arrangement of the magnetic spectrometer. The magnet box of the spectrometer, shown as a dashed curve in the diagram, was attached to the reaction chamber by a bellows assembly which could be adjusted for alignment. The semiconductor detector was mounted in a housing with Jflttings which permitted external positioning of the detector over a plane parallel to the exit flange of the magnet box. This feature enabled measurements of the He3 beam profile and positioning of the detector for best focussing. Figure (30) shows semiconductor spectra for various spectrometer currents, I g . The He 3 + + peak is clearly separated from the deuterons which have been degraded in energy by the target and elastically scattered into the spectrometer. Two obvious disadvantages to this method of spectrometry are NEUTRONS DEUTERON TARGET DEUTERON ' BEAM SEMICONDUCTOR DETECTOR MAGNETIC SPECTROMETER He5 COLL/flATOR FIGURE 29 E X P E R ) M E N T A L ARRANGEMENT OF MAGNETIC MASS SPECTROMETER PARTICLE ENERGY (keV X /Oo) F / S U R E 3 0 SEMICONDUCTOR SPECTRA FOR VARIOUS MASS SPECTROMETER CURRENTS. - 5 1 -evident from inspection of figure ( 3 0 ) . First, the charge states He3° and He3+ are not detected and second, the analysing power of the spectrometer is discriminating against He3++ particles of energy less than 500 keV and greater than 700 keV when the current is set to 15 amps. Thus, a considerable fraction of the He3 particles are not detected using this method. The relatively small deuteron peaks found in these measurements led us to consider the fourth possibility i.e. using no spectrometer and no f o i l . iv/ Thin Deuterium Targets Placing the semiconductor detector to look at the reaction target with no foil in front, or no spectrometer to discriminate against deuterons would have been impossible with the deuterium targets available up until now. The detector would have been swamped by the elastically scattered deuterons. Using the thin film deuterated polyethylene targets described in section (E) has made possible this method. Figure (3D shows a typical spectrum for the semiconductor detector. The "reaction protons" peak contains protons of two energies but they are unresolved because the post amplifier was saturating during this measurement. The He3 particles are obscured by the elastically scattered deuterons which have a fairly continuous energy distribution over that region. The only way the He3 particles could be identified uniquely was to gate the multichannel pulse height analyser with coincidences between the semiconductor detector pulses and the neutrons, therefore the He3 detector could no longer be used as a NUMBER OF COUNTS (ARBITRARY UNITS) -52-monitor for determination of the number of neutrons in the neutron, beam. Moreover i t was expected that the high count r.a.te_..in the detector ( 5X1G*4" counts/second) would cause a broadening of the He3 energy peak. Figure (32) is a He-J spectrum produced by gating with neutron -He3 coincidences. This last method was chosen for the experiment because i t gave a count rate approximately three times higher than when a mass spectrometer was used and better time resolution because of the shorter flight path for the He-3 particles. H. Shielding In using the associated particle technique careful consideration must be given to the type of shielding used and in some cases i t is necessary to decide if shielding is even advantageous. In a differential scattering experiment the use of shielding requires placement of the scatterer at a much further distance from the source with a resulting large decrease in the specific intensify. Placing the scatterer further from the source means also that the scatterer must'be larger, perhaps considerably more expensive, and for the same angular resolution the neutron detector must be placed at, a much greater distance. With a scaling up of distances additional background from air scattering may become serious. Therefore, if shielding is to be used, its size must be a comprimise between disadvantages caused from scaling-up and the increase in attenuation of direct radiation caused by F I G U R E 3 2 PARTICLE, E N E R G Y ( l - leV) -53-thicker shielding.. Measurements of the background counting rate were made with the experimental arrangement as shown in Figure (19) but without the wax shield or the concrete shield and collimator. With the neutron detector in the beam the ratio of random to true counts was 1/300 which was entirely inadequate for the proposed small angle scattering experiments. The large random coincident rate was due to the high count rate in the neutron detector caused by neutrons from the deuteron beam collimators, the deuteron beam catcher and scattering from the floor, walls, and air, in addition to the ones directly from the target source. There was also a large back-ground of X-rays and tf-rays from the high tension terminal of the Van de Graaff and from neutron induced reactions in the vicinity of the target chamber. The shielding was designed with these sources of background in mind. A wax wall was erected between the switching magnet and the target chamber to attenuate the neutron flux arising from the magnet box of the Van de Graaff analysing magnet and the sniffers for the corona probe stabilizer. An open ended room was constructed from solid concrete blocks 19.k cm x 19.L cm x 39»k cm to house the neutron scatterer and neutron detectors. This provided support for a wax and lead ceiling to shield against X-rays from the Van de Graaff and from air scattering above the target chamber and detectors. It consisted of a .635 cm thickness of lead below 20.3 cm of wax. The concrete wall also attenuated the direct neutron flux from the target chamber collimators and the Faraday cup beam catcher. Additional .lead_ was placed around the beam catcher and a .635 cm thickness of lead covered each side of the wal l perpendicular to the target chamber flange through which the neutron beam emerged. A 1*+ cm x 19.1 cm hole was l e f t i n the w a l l to allow the placement of a borated wax i n s e r t . The wax in s e r t was placed i n the w a l l a f t e r the neutron beam p r o f i l e had been measured so that the 5 cm diameter hole through the wax could be positioned properly with respect to the neutron beam. The s i z e of the hole through the wax was i n t e n t i o n a l l y larger than the associated neutron beam so that there would be no contribution to background at small scattering angles caused by associated neutrons in t e r a c t i n g with the outer end of the wax i n s e r t . The addition of t h i s shielding reduced the r a t i o of random to true counts from 1/300 to 3/10,000 with the neutron detector i n the beam and to 1/10,000 with the detector out of the beam at an angle of 7 degrees with respect to the scatterer. I. Beam Characteristics i / Beam Size and Divergence The q u a l i t y of an associated neutron beam i n terms of i t s s i z e and divergence depends on several factors. The incident deuteron beam should be as nearly p a r a l l e l as possible. Therefore, the necessary incident beam focussing was done as f a r from the reaction chamber as allowed by other r e s t r i c t i o n s of l o c a t i o n and space. The diameter of the deuteron beam at -55-the target restricts the angular resolution achievable for a recoil particle detector subtending at the target a fixed solid angle. For example, consider a detector .635 cm in diameter placed.19.1 cm from the target subtending a solid angle of .875 x 10"^  steradlans. As shown in figure (33) an angle 6 can be defined which is a measure of the angular resolution that will be achieved for the associated neutrons. For an infinitely small beam spot 6 = 1 degree and for a .318 cm beam spot 6 = 1.5 degrees, a 50% increase. The finite size of the beam spot can be partially compensated for by placing the recoil particle detector further from the target. For example, for a detector 1.27 cm in diameter placed 38ol cm from the target, the same solid angle would be subtended as in the previous example but 6 = 1 1 / 6 degrees. However, this .gain would be made only at the expense of increasing the divergence in flight times of the He3 particles and increasing the size of the detector with an accompanying increase in noise and detector capacitance. Figure (33) also illustrates a further increase in the divergence of the neutron beam caused by the kinematics of the D(d,n)He3 reaction. Using the same illustration of a detector at 19.1 cm from the target and at a lab angle of 75 degrees, the detector will accept He3 with lab angles of from 75 + 1.5 degrees to 75 - 1.5 degrees. The associated neutrons will emerge from the target with lab angles of 38.8 degrees and h2,2 degrees respectively. The 3.0 degree divergence of the He3 particles increases to a 3»^  degree of divergence of FIGURE 3 3 DIVERGENCE O P T H E N E U T R O N B E A M C A U S E D B y T H E K W E M A T / C S O F THE D ( d , h ) W e 3 REACTION. COLLIMATOR: DEUTERON BEFM DEUTERIUM TARGET H e 5 R E C O I L D E T E C T O R { D I A M E T E R « NEUTRONS -56-the neutrons. The i n i t i a l width and height of the neutron beam w i l l be determined by the si z e of the incident deuteron beam spot and the orient a t i o n of the target. The i n i t i a l width of the beam S i s : S = d co soc COS0 where d = diameter of the deuteron beam oc = the lab angle of the outgoing neutron beam 0 = the angle between the deuteron beam and the perpendicular to the target plane. For the configuration shown i n figure (33) > S = .^ O^  cm. The i n i t i a l height of the beam, h, i s simply the deuteron beam diameter or .318 cm. These calculations enabled us to .predict the maximum si z e of the neutron beam at the scatterer so that a scatterer could be selected which completely covered the.neutron beam. The neutron scatterer was placed at a distance D = *+2.9 cm from the reaction target. At t h i s point the maximum width, W, of the beam was: W = S + D s i n (angle of divergence) W = .k-Ch cm + **2.9 s i n (3.^ degrees) W = 2.95 cm The maximum height, H, of the beam was: H = h + D s i n (26) H = .318 + *+2.9 s i n (3.0 degrees) H = 2.57 cm -57-The scatterer.chosen was 3-18 cm in diameter. i i / Beam Profile The vertical neutron profile was measured by a simple movement in the vertical direction of the 5-08 cm diameter detector at a distance of 59-2 cm from the neutron source. The purpose of this measurement was to locate experimentally the center of the neutron beam. Figure (3k) shows the results of this measurement. The FWHM was 2 1/6 degrees. Measurement of the horizontal profile was not nearly as simple since the pivot point about which the neutron detector rotated in the horizontal plane was not beneath the neutron source but neneath the place where the scatterer was to be located. A second pivot point located beneath the neutron detector was necessary so that the detector could be pointed directly at the neutron source for each angle of the profile measurement. A simple computer program was written which would tabulate for each angle required in the neutron profile measurement the necessary settings for the two pivot points and the solid angle correction resulting from the variation in distance from the source. Figure (35) shows a horizontal neutron beam profile with a FWHM of 3 degrees. As expected, the angular resolution of the vertical profile is better than the horizontal profile as predicted by the geometry and kinematics. This would make a scattering experiment in the vertical direction a better choice i f one were interested in the best possible angular resolution. Unfortunately the left-right scattering asymmetry expected in FIGURE 3 4 O I 1 1 1 1 1 (--2 -I 0 4 1 +2 +2 ANGULRR HEIGHT IM DEGREES -58-Schwinger scattering is in the horizontal plane, i i i / Possible Improvement in Angular Resolution As described in section (Yb), He3 particles of different energies detected by the semiconductor detector will have associated with them neutrons which will produce counts., falling into .different time channels of the two parameter pulse height analyser. The 'simultaneous energy measurement .gives us information not only about the flight times of the particles but i t also gives us, within limits, the angle of emission of the neutron from the deuteron target. The limits depend primarily on the thickness of the target, which will cause variations in the detected He3 energies without varying the angle of neutron emission, and the energy resolution of the He3 detector and amplifiers. As shown .in figure (33) the neutron associated with the 6k0 keV He3 particle is emitted at a lab angle of L2.2 degrees and the neutron with the 7L0 keV He3 particle, at 38.8 degrees. To verify this prediction two dual parameter multichannel pulse height spectra were taken, one with the neutron detector located well on one side of the beam and the second spectrum with the detector on the other side. With the detector on the side detecting neutrons emitted at smaller angles, the events within the allowed time channels all f e l l in energy channels above 600 keV and on the other side the events al l f e l l in energy channels below 600 keV. Further experimental investigation needs to be made to determine - 5 9 -quantitatively how much improvement in the horizontal beam angular resolution can be made with this type of analysis. The two measurements made indicate that the improvement could be extremely significant but the analysis may be laborious. Iv/ Beam Intensity The measured neutron beam Intensity averaged 20 colnc/sec/mlllisteradian with an incident deuteron beam of 1.5 microamperes. Since the neutron detector used had an efficiency of approximately 30% this meant that the neutron flux 0* the beam was approximately 70 neutrons /sec/millister-adlan. This intensity could be increased in two ways. The ..incident deuteron beam could be increased or the solid angle of the He^  recoil particle detector could be increased. Both methods would increase the random coincident count rate. Increasing the deuteron beam would not gain much because this would require more frequent target changing, a time consuming task. The latter method has possibilities in that the size of the He3 collimator could be increased_Jn. -the vertical direction without seriously altering" the jangular^res^ution of the beam in the horizontal direction. ^:In;cTjea£es..-l&- beam intensity by factors of two or three might be achieved. CHAPTER IV SCATTERING OF ha55 MeV NEUTRONS FROM LEAD A. Introduction Using the neutron beam produced as described i n Chapter I I I , the d i f f e r e n t i a l e l a s t i c scattering cross-section ofJ+956 MeV neutrons on lead was measured at f i v e degree in t e r v a l s from ho degrees to 10 degrees« This chapter describes the experiment and the results after making the necessary corrections for .geometry, absorption, and multiple scattering,, The results of t h i s kind of experiment can be used to establ i s h the form of the d i f f e r e n t i a l cross-section at these angles i n order to extrapolate to smaller angles that part of the cross-section due to purely "nuclear forces". Improvements i n the angular resolution of the experiment are required before the smaller .angle measurements can be made. These modifications are also described i n t h i s chapter. B. Scatterer and Detector Arrangement Figure ( 3 6 ) shows the experimental arrangement of the target chamber, mechanical collimator, scattered,, neutron scattering table, and detector. The scatterer was placed k2.9 cm from the source and 10 cm from the exi t of the / collimator. I t was mounted i n an aluminum r i n g 15 cm i n diameter with four small aluminium spokes. The scattering sample could be removed from the beam by l i f t i n g the r i n g from i t s mounting on the scattering table and replacing i t by a dummy ri n g and spokes f o r background measurements. The scatterer used f o r the d i f f e r e n t i a l scattering cross-section measurements F'GURE 36 &x PERI MEN TAL. ARRANGEMENT OP T H £ C H A M B E R ; MECHANICAL COLLIMATOR SCATTERER ^ NEUTRON TABLE AND DETECTOR, - 6 1 -was 3 » 1 7 5 cm i n diameter, s u f f i c i e n t to cover the neutron beam, and 2 cm i n thickness, which was eh71 of a mean free path f o r scattering or absorption of a k . 5 6 MeV neutron. The scattering table consisted of a large s t e e l plate on which a three centimeter s t e e l rod was mounted. Two ^aluminium I - .beams supporting the neutron detector assembly were allowed to rotate about the s t e e l rod. The angle of rot a t i o n was measured by reading the po s i t i o n (on a graduated c i r c l e marked on the f l o o r ) of a pointer located at the end of the I'- beams. The neutron detector assembly, also constructed from aluminium, permitted the detector to be moved v e r t i c a l l y or i n a d i r e c t i o n p a r a l l e l to the I - beams. The detector could also be rotated i n the horizontal plane about an axis through the body of the detector probe, t h i s angle of rota t i o n being measured by a graduated c i r c l e on the detector assembly. Because the dimensions of the scatterer were kept as small as possible to reduce multiple scattering corrections i t was necessary to accurately a l i g n the scatterer with respect to the neutron beam. The v e r t i c a l alignment proceeded as follows. F i r s t , a rough v e r t i c a l alignment was made by simply positioning the scatterer and neutron detector by eye i n the same plane as the He J detector, target beam spot, and deuteron beam collimator. This alignment was not p a r t i c u l a r l y accurate because that part of the deuteron beam collimator v i s i b l e was rather close to the target spot. Then the v e r t i c a l -neutron beam p r o f i l e was measured as described i n Chapter I I I . From t h i s p r o f i l e measurement the neutron detector could be -62-positioned accurately in the center of the vertical profile. The detector probe was removed from the assembly and replaced with two aluminum discs with 1.27 cm diameter holes in their centers. With one flange removed from the target chamber, the target beam spot on the deuterated polyethylene target could be sighted through these two discs. The lead scatterer was replaced by a lucite disc with a small hole through the center. This lucite disc could then be aligned in the vertical direction by sighting the target beam spot through the three holes. Alignment of the scatter in the horizontal direction was done in a similar fashion but with an added complication. The scatterer had to remain positioned directly above the center of rotation of the neutron detector, therefore to change the position of the scatterer in the horizontal direction the scattering table from the steel plate up had to be moved. Unfortunately any movement of the scattering table would result in a change in the calibration of the graduated circle marked on the floor. Therefore any small shift in the position of the scattering table had to be accompanied by an appropriate shift in the position of the pointer at the end of the I -beams. This method was very sensitive to small changes in the scatterer position. For example, with the geometry used, a 3 millimeter misalignment in the scatterer would result in a reading of 0 .8 degrees for the center of the horizontal neutron profile. After the necessary changes in scatterer position were made the profiles were rechecked. -63-C". Flux Monitors and Detector E f f i c i e n c y One of the important advantages normally available to the experimenter using the associated p a r t i c l e method i s a simple and accurate way of determining the absolute neutron f l u x . I f the associated charged r e c o i l p a r t i c l e s can be detected and i d e n t i f i e d uniquely with 100$ e f f i c i e n c y , then the number of r e c o i l p a r t i c l e s detected i s the number of neutrons emitted into the s o l i d angle defined by the kinematics and geometry. However, without the use of a magnetic spectro-meter to eliminate e l a s t i c a l l y scattered deuterons of the same energy as the He 3 r e c o i l p a r t i c l e s , t h i s method could not be used. This necessitated the use of a second neutron detector placed i n the primary neutron beam to monitor the neutron f l u x . Using a conventional long counter the absolute neutron f l u x i s unknown and a subsidiary experiment would have to be performed to determine the absolute cross-section ( L0). This can be done f o r example by measuring the scattering from hydrogen and f i x i n g the cross-section scale to the well - known H(n,n) cross-section (^1). With t h i s method errors are introduced not only from s t a t i s t i c a l uncertainties i n making the c a l i b r a t i o n , but also from the long counter monitoring which may be sensitive to neutrons o r i g i n a t i n g from sources other than the target beam spot. With the additional detector used i n the associated p a r t i c l e experiment, i t was s t i l l possible to determine the e f f e c t i v e neutron f l u x by measuring the r a t i o of the counting rates of the two detectors i n the neutron beam. Subsection (F i i i ) of Chapter I I I describes the experimental arrangement of the neutron monitor,. The monitor was placed 212 cm from the scatterer so that the 11 cm diameter .liquid scintillator would adequately cover the neutron beam and yet be far enough away from the scatterer and the other detector to avoid contributions to the background. The major problem in measuring the ratio of the counting rates of the two detectors is that two separate runs are required during which time the target yield will change and there will be small variations in the deuteron beam inten-sity. This problem was alleviated by incorporating a second monitor to measure the total proton yield of the reaction D(d,p)T enabling a correction to be made for deterioration of the target. The proton monitor was expected to provide a better normalizing factor between the two runs than a measure of either.the time or the integrated current collected on the deuteron target. The proton monitor was not satisfactory as a neutron flux monitor over long periods because i t was insensi-tive to changes in the deuteron and He3 counting rates in the recoil particle detector which in turn Influenced the efficiency of the recoil particle detector to the He3 particles. The electronics used for detecting the reaction protons has been described in Subsection (F i ) . The proton detector was placed at a laboratory angle of 50 degrees with respect to the deuteron beam at a distance of 6.55 cm from the target spot and k,lk cm below the reaction plane defined by the deuteron beam and He3 recoil particle detector. It subtended a solid angle of 1.^ 3 millisteradlans at the target. -65-I f £ d i s the e f f i c i e n c y of the scattered neutron detector, and € n that of the neutron monitor, then i n any given scattering measurement the counts registered i n the respective detectors w i l l be n d = K o i 2 E F F dene) e d N p b ( i f - D dSL % = No TSm ) where No i s the t o t a l number of neutrons incident on the scatterer,_Q„__ i s the e f f e c t i v e s o l i d angle-subtended by the 7 EFF " scattered neutron detector at the angle 6 with respect to the incident beam, N p b i s the number of scattering n u c l e i per cm2, and dCT(0)/d/lis the d i f f e r e n t i a l cross-section* The s o l i d angle subtended by the monitor at the CD2 target was large enough to ensure complete coverage of the associated neutron1 beam whose attenuation by the scatterer i s represented by the transmission f a c t o r , T. From (^-1) and (k-2) the d i f f e r * e n t i a l cross-section i s then dcr(e) = n d T e m N p b (^ -3) d-Q. n m i l ^ F F G d The transmission fact o r , T, is obtained by comparing the normalized yields i n the neutron monitor f o r the scatterer i n and then out of the associated beam, the protoh detector providing the normalization fa c t o r . T i s calculated from T = n m x p m* (k-k) Pm nm' -66= where p m Is the number of proton counts for a count of n m in the neutron monitor and the primes indicate a measurement with the scatterer removed. The measurement gave T = ,6179 (+ ,0.0O7)» The ratio of the efficiencies € m / e d was found by removing the scatterer and comparing in separate runs the normalized counts obtained in the monitor and scattered neutron detector when each was placed alternately at zero degrees, completely covering the neutron beam. Then e m = V x pd» 6d Pm8 V where nm'- nd' are the neutron yields in the respective detectors and pm', pd' the corresponding counts in the proton detector. The ratio 6 3 / ^ was found to be 1. 1+925 ( I ± 0.007) During each of the measurements mentioned above, care was taken to check that amplifier gains and the discriminator bias levels did not change. D. Effective Solid Angle of the Neutron Detector Because the sensitivity of the neutron detector is not uniform over its entire volume, the effective solid angle of the detector subtending the scatterer cannot b© ovulated''-by-simple integration over the volume of the detector. If the neutron detector were 100$ efficient the solid angleH^oo o f t n e detector subtended at the center of the scatterer would be •0*100 = Area of detector - 6 7 -where r-^ i s the distance from the center of the scatterer to the front face of the detector. The other extreme i s to assume uniform s e n s i t i v i t y of the detector over i t s entire volume. In t h i s case a simple Integration gives -^•UNIFORM = Area of detector " r l r 2 where r 2 i s the distance of the back face of the detector to the center of the scatterer. For a detector with r-^ = 4-0.5 cm and r 2 = 4-8.1 cm, a large difference i s apparent i n "^UNIFORM = o8lf-^L00 I f the absolute e f f i c i e n c y , 6 , of the detector i s known then the mean free path,A, f o r a detectable c o l l i s i o n of a neutron i n the detector i s given by 6 = l - < T t / A (^ -5) where t i s the thickness of the detector. Using the attenuation of the neutron f l u x impinging on the detector to weight the integrand, an integration s i m i l a r to that used to calculate "^"UNIFORM c a n u s e d t o calculate the ef f e c t i v e s o l i d angle i l E F F = A r*e~' dx (*+-6) <r2~ri> ^ r i p 2W Where A i s the area of the detector. Equation (4—6) was solved numerically using a computer. For an assumed e f f i c i e n c y of 30 percent: -^•EFF = o89 Area of detector (4—8) r i 2 -68. Over the range of efficiences 20-4-0 percent-&EFF changes by + 1.7 percento The effective solid angle can also be found experimentally by measuring the counting rate with the detector at two distances from the scatterer, one distance approximately equal to the usual scatterer-to-detector distance and the other distance much larger than the dimensions of the detector. The ratio of the two counting rates then gives the ratio of the squares of the effective distances, and since the larger distance is well known, the sample-to-detector length can be found. The disadvantage with this method is that very long counting times would be required to obtain a statistically significant measurement, especially since the background to true coincidence count increases rapidly with distance. E. Multiple Scattering and Absorption Corrections  1) Introduction In order to distinguish scattered neutrons from background, and also to obtain data at a reasonable speed, It is necessary to employ, within limits, a large scattering sample. These limits are Imposed by two effects, multiple scattering and flux attenuation, for which corrections to the data have to be applied. By tracing neutron histories by the Monte Carlo method, the effects of flux attenuation and multiple scattering may be taken into account. In the past, Monte Carlo multiple scattering -69-programs have served their .purpose as a useful tool for calculating corrections to experimental data, but their utility has been greatly restricted by the large computing effort required. Neutrons are tracked from a source either conventionally or by the "forced first collision" technique (^ 2), a device that forces every neutron started to interact with the sample and hence contribute to the results. The detectors, imagined as a series of abutting regions lying on the detector circle, are replaced by a band in the scattering plane of interest whose height is equal to the diameter of the detector. The band is divided into zones corresponding to the different scattering angles, and when a neutron hits the band i t is classified by zone and collision type (e.g. single, double, etc.) Since the detector diameter is very small when compared with the radius of the detector circle, the solid angle subtended by the band is small and a large initial sample of neutrons must be run in order to obtain reliable statistics; this drawback is alleviated (at the expense of some error) but not overcome, by increasing the band height beyond the detector dimension. Monte Carlo multiple scattering programs have been used recently (^j1*1*) to make corrections to results of neutron scattering from lead. A listing for one of these programs was made available to us by R.O. Lane and W.F. Miller 0*h). However i t has not yet been used since a considerable number of revisions would have had to be made in the program to adapt i t to our particular problem. Their experimental - 7 0 -arrangement included a square f l a t plate scatterer at an angle of 4-5 degrees to the incident neutrons. Also t h e i r incident neutron f l u x was uniform over the scatterer. Our scatterer was a cylinder with axis p a r a l l e l to the neutron beam and the neutron f l u x was not uniform over the scatterer but peaked at the center of the cylinder. Additional d i f f i c u l t i e s would be involved i n changing the program.language to one suitable f or *he IBM. 7Q4-0 computer .available to us. The alt e r n a t i v e was to write a program for a PDP-8 (from D i g i t a l Equipment Corporation) computer which offered p r a c t i c a l l y unlimited computing time and on-line program debugging. Unfortunately the PDP-8 i s comparatively slow, has a very l i m i t e d memory (4-9 K b i t s ) , and requires machine language programming to conserve memory space. A Monte Carlo multiple scattering program was wr i t t e n using the flow chart given by Amster, Leshan, and Walt (4-2) as a guide with modifications to accomodate our experimental arrangement and to decrease the computing time. A description of t h i s program i s given i n Appendix B. 11) Input and Assumptions Various facts about the geometry were required as input data f o r the computer program. This information included: 1. thickness of scatterer = 2 cm 2 . diameter of scatterer = 3«l8 cm 3 . distance between scatterer and detector band = 4-0 cm - 7 1 -ho width, of detector band = 5»08 cm 5. number of detector zones =32. The detector zones were chosen to give the most information possible over the region of i n t e r e s t . From G-1G degrees the zones were at one degree i n t e r v a l s , from 1QJ+6 degrees the zones were at two degree i n t e r v a l s , and f o r the larger angles 30 degree zones were used. The c r u c i a l assumptions involved i n the multiple scattering calculations were the reaction cross-sections and the e l a s t i c scattering cross-sections. The o p t i c a l model provides a well-established way of c a l c u l a t i n g e l a s t i c cross-sections i f the o p t i c a l model parameters are known. Values of these parameters can be found by f i t t i n g the cross-sections obtained experimentally u n t i l optimum agreement i s obtained. The o p t i c a l model of e l a s t i c nuclear scattering represents the i n t e r a c t i o n between an incident neutron and a target nucleus by a complex p o t e n t i a l of the form V(r) = VREf(r) + iVIMg(r) where VRE and VIM are the magnitudes of the potentials and f ( r ) and g(r) t h e i r r a d i a l shape factors. A convenient form f o r f ( r ) and g(r) that has been widely used i s the Saxon-Woods form f ( r ) = 1  1 + exp (Cr-E)/a) where R Is approximately the nuclear radius and a i s the surface diffuseness. Using the ABACUS - 2 program (^ 5) an o p t i c a l model f i t was done on the d i f f e r e n t i a l scattering cross-section data -72= f o r 4-.1 MeV neutrons on lead measured by Mo Walt and J.R. Beyster (4-6). This f i t yielded the following parameters: VRE = 4-2.7 MeV VIM = 5.1 MeV R = 7.7025 fermis a = .65 fermis These parameters were then used to predict the cross-sections f o r scattering 4-.56 MeV neutrons on lead. The calculated d i f f e r e n t i a l scattering cross-sections f o r 128 di f f e r e n t angles were used by the multiple scattering program to trace i n d i v i d u a l neutron h i s t o r i e s . The t o t a l reaction cross-section, Oj., was used to calculate the mean free path,X, of a 4-.56 MeV neutron i n lead from the formula A= 1/(N x c r t ) where N i s the number of lead atoms per cm2 (N = .3199 x 102^ atoms per cm^). From the ABACUS - 2 program Ol = 7.3623 barns therefore z X = 4-.24-58 cm Also required f o r the multiple scattering program was the r a t i o of the absorption cross-section, Og as calculated by the ABACUS - 2 to the t o t a l cross-section OJ. C V ^ t = - ^989 For s i m p l i c i t y the program used the assumption of a vanishingly narrow neutron beam, i . e . each neutron h i s t o r y was traced s t a r t i n g from a t r a j e c t o r y perpendicular to the scat t e r e r , at the center of the scatterer. i i i ) Results of Monte Carlo Calculation The result s of the Monte Carlo c a l c u l a t i o n are - 7 3 -expressed in terms of N(i , 6 ) , the number of neutrons scattered i and only i times into the detector zone 6 + A 6 . N(i , 9 ) is usually not an integral number because each neutron is weighted by the probability of its being absorbed or rescattered before i t leaves the scattering sample. For a very thin target with negligible attenuation and multiple scattering the differential scattering cross-section can be calculated from the formula J ? * 6 > thin = »(l»»>tfaln (^-8) dSL n NpbJL where n is the number of incident neutrons,XI is the solid angle of the detector, and N p b is the number of scattering centers per cm . What is usually measured however is OO d C 3 W t h i c k = , E N ( i , e ) t h i c i £ i s I (•*-9>-dSL n Mpb SL Combining (^-8) and (*t-9) gives d C 7 1 ( e )thin = d a t e ) t h i c k x W ( 1 ' e ) t h l n (>f-10) d-fi dSL ^ ^ ' ^ t h l c k It Is the ratio, J^je^thin » w n i c n i s used to correct g K ( i , e ) t h i c k the scattering- data since i t takes, into account both the attenuation, and multiple scattering of the;neutrons. N ( l , 6 ) t h i n is calculated from, equation 0+-Q) using as a first approximation, the differential, scattering cross-section predicted by the optical model calculation. The -7k-denominator is provided by the Monte Carlo calculation. Sixteen hours of computing time were required to process the 8,000 neutron histories used in this study. Table (2) shows the results of this calculation. Neutron histories were not traced beyond three collisions since this would have given a negligible contribution to the results. Each detector zone subtended solid angles corresponding to + 3 degrees about the angle 6 shown in the table. Figures (37-39) are graphs of the single, double, and triple scattering as a function of angle. The same arbitrary units for the number of neutrons entering a detector zone are used for each graph. It can be seen from these graphs that the higher order scattering is more isotropic. This tends to lower the peaks and f i l l in the valleys of a differential scattering cross-section curve. This is illustrated in figure (4-0) showing the shape of the cross-section as calculated for a thin target compared the dashed curve for a thick target distorted by multiple scattering. F. Inelastic Scattering Because the energy resolution of the neutron detector was so poor, i t was impossible to distinguish between elastic and inelastically scattered neutrons simply by examining the energy spectra of the neutrons detected. Some authors make corrections to their measurements (9,4-7) by using inelastic scattering data provided by other experi-ments. The difficulty with such corrections is that assump-TABLE 2 MONTE CARLO CALCULATIONS ^ e+3° N l N 2 N3 fx H ( i , e ) t W n - N(l,e) w -3 33.0 1.86 • 12 35.0 52.6 1.511 1.0 2?.7 1.60 .10 29.4- 44.4- 1.510 15 21.9 1.4-0 .09 23.1+ 35.1 i.5oo 20 15.5 1.21 .08 16.8 24-.8 1.^ 79 25 9.2k 1.02 .07 10,3 14-.8 1.^ 38 30 5.29 .83 .07 6.19 8.4-8 1 1.370 35 2.38 .64- • 06 3.00 3.82 1.271 ko .79 M .05 1.30 1.27 0.974-3 > h 5 or 20 4 /04 FIGURE 3 7 SINGLE SCATTERING AS A FUNCTION OF ANGLE 6, 'CM 20 30 (DEGREES) 2 2-i 25 F I G U R E 3 9 TRIPLE S C A T T E - R I N G AS A FUNCTION OF A N G L E . .1 + o /0 20 3 0 40 5 5 0 } 4 0 f 304-20f / 0 + FIGURE-4-0 T H / N COMPARED TO THICK TARGET SCFTTTIERING, N(i)Q) FOR A THIN TARGET Tl M ( t ; e) FOR A i = 1 T H I C K T A R G E T 0 o /O 20 3 0 9CM ( D E G R E E S ) 4 0 - 7 5 -tions often must be made about the angular d i s t r i b u t i o n of the i n e l a s t i c a l l y scattered neutrons. This i s especially undesirable f o r corrections to small angle scattering data where angular d i s t r i b u t i o n s have not been measured f o r i n e l a s t i c a l l y scattered neutrons. The problem i s not as severe i n the case of Pb 2 0® because i t has a very high f i r s t excited state of 2.61 MeV and r e l a t i v e l y wide spacing of the lowest excited states (4-8) compared to other heavy n u c l e i . For t h i s reason lead was chosen as the scatterer rather than Uranium which, f o r example, although i t has a higher atomic number to enhance Schwinger scattering, also has cl o s e l y spaced, low l y i n g , f i r s t excited states. Unfortunately i t i s d i f f i c u l t and very expensive to obtain i s o t o p i c a l l y pure samples of lead. Naturally occurring lead having an ls o t o p i c 208 composition of Pb has been studied with neutrons of energy up to k,5 MeV, using a ti m e - o f - f l i g h t technique (4-0). These measurements (made with lead scattering samples; one containing 71.3$ P b 2 G 8 , and the other, 88.3$ P b 2 0 6 ) were made to estimate the scattering due to 99% pure Pb 2 0^ by car e f u l subtraction of the respective spectra. The r e s u l t i n g spectrum indicated that the i n e l a s t i c scattering of neutrons 208 from Pb up to t h i s energy i s i s o t r o p i c to 20 degrees and only 1-2$ of the e l a s t i c scattering cross-section over the range of angles from 20 to 14-0 degrees. Nevertheless an attempt should be made to make a measurement of the i n e l a s t i c s c attering at smaller angles i f one i s to have any confidence -76-the in t e r p r e t a t i o n of result s at these angles. As described i n Chapter I I I , t i m e - o f - f l i g h t spectrometry can be used to measure the energy of the detected neutrons provided the time resolution and f l i g h t path are adequate. For a 4-.56 MeV neutron, the f l i g h t time over a distance of k-0 cm i s 13.6 nanoseconds. A neutron which has been i n e l a s t i c a l l y scattered from the 2„6l MeV f i r s t excited state of Pb would have an energy of 1„95 MeV. I t s f l i g h t time over the same distance would be 20.7 nanoseconds giving a time separation f o r the two neutrons of 7.1 nanoseconds. This time separation would be s u f f i c i e n t to resolve the two time-to-amplitude converter peaks of equal amplitude but i n s u f f i c i e n t to i s o l a t e peaks with a very large difference i n amplitude. Increasing the f l i g h t path to 80 cm, improves the energy resolution considerably at the expense of reducing the s o l i d angle of the detector by a factor of four. Although t h i s makes the energy resolution adequate, very long counting times would be required to separate a l i k e l y 2% effect from the back-ground. One long measurement made with the detector at 50 cm showed no s t a t i s t i c a l l y s i g n i f i c a n t increase i n the number of counts i n the region where i n e l a s t i c events would be expected to occur. G. E l a s t i c Scattering Results from Lead The d i f f e r e n t i a l e l a s t i c scattering cross-section of h.56 MeV neutrons on lead was measured at f i v e degree i n t e r v a l s from 10 degrees to ho degrees using a scatterer -77-of thickness A? of a mean free path. The d i f f e r e n t i a l cross-section, dot8)/dfl(UNCORRECTED), uncorrected for multiple scattering and attenuation was determined from equation 3) dctO)(UNCORRECTED) = N ( 0 ) T N p D d-Q_ n m -^ -EFF ^ d with the parameters as defined i n section C and N ( 6 ) = n d i s the number of scattered neutrons detected at the angle 6 . N ( 6 ) was obtained a f t e r making the necessary corrections f o r background. Depending on the angle, there were two possible types of background; random and beam dependent. The random background was determined by i n t e -grating the number of events i n an area of the time sorter spectrum beyond the region of expected true coincidence events. The beam dependent background, which was not n e g l i g i b l e at 10 degrees had to be determined i n a separate run. The result s of these measurements are tabulated i n table 3» Also included i n table 3 are the d i f f e r e n t i a l cross-sections, d<T(e)/&fl, corrected for multiple scattering and attenuation as outlined i n section E. These results can be compared to those of other workers by examining figure (**1). Scattering measurements have been made at lower and higher neutron energies. M. Walt and J.R. Beyster (*+6) measured the d i f f e r e n t i a l scattering cross-section of ,^1 MeV neutrons from lead using a biased s c i n t i l l a t o r detector and mechanical co l l i m a t i o n . Their r e s u l t s are shown as squares i n figure (*+!). TABLE 3 ELASTIC SCATTERING RESULTS FROM LEAD 6 NEUTRON COINC BACKGRND N(0) dpi UNCORR.) dg-d-O- d-O, MONITOR COUNT COUNT 10 25.5K 503 273 230 5.31 8.02 + .96 15 26.9K 268 91 177 3.88 5.86 + .62 20 *+2.3K 298 (h 231* 3«26 4-. 86 + .39 25 i+8.7K 308 &V 224- 2.71 3.90 + .35 30 52.3K 232 106 126 1.4-2 2.04- + .37 35 66.8K 197 106 91 .802 1.02 + .16 1+0 74-.4-K 14-0 90 50 .396 .39 ± .12 F I G U R E 4-1 NEUTRONS o d .2 cl 13 IB SCATTERING OF ON LEAD. PRESENT WORK WiTH 4 . 5 6 MeV NEUTRONS C 5 0 R L 0 V ET. AL. (9) W I T H 4.0 MeV N E U T R O N S A 8 R C U S 2. C A L C U L A T I O N FOR -4.5<o MeV NEUTRONS M. W A L T ET.PtL.QG) W I T H 4.1 MeV NEUTRON/£ . W.T. TiHElN (±15%) (So) \NiTH 5,0 Mel/ NEUTRONS 20 30 QCM (DEGREES) -78-W.J.. Rhein (50).measured the d i f f e r e n t i a l cross-section of 5 MeV neutrons from lead using a r i n g shaped scatterer and biased,detector. His re s u l t s are shown as c i r c l e s . In both cases no timing was used to discriminate against background and no estimate of the error i s indicated i n t h e i r published papers. The work of Gorlov et. a l . (9) with h MeV neutrons Is also included (marked with crosses) since i t i s the most recent r e s u l t . Their paper includes no description of t h e i r neutron source or scattering technique. The results of the e l a s t i c scattering of ^.1 MeV neutrons from natural Pb obtained by Towle and Gilboy (*+0) using t l m e - o f - f l i g h t are not included since quantitative values of the d i f f e r e n t i a l cross-sections could only be estimated from t h e i r graph with considerable uncertainty. Moreover t h e i r measurements were made to 20 degrees only. The s o l i d curve i s the d i f f e r e n t i a l cross-section predicted f o r *+.56 MeV neutrons by an o p t i c a l model f i t to the results of M. Walt and J»R. Beyster (*f6) as described i n subsection (E i i ) . These measurements enable one to make a reasonable extrapolation of the "nuclear part" of the d i f f e r e n t i a l s c a t t e r i n g cross-section to smaller angles. The shape of the curve compares favourably with that predicted by the Abacus 2 c a l c u l a t i o n and with those of the other measurements at h and 5 MeV. I t i s d i f f i c u l t to make a meaningful compar-ison of the absolute cross-sections since most of the measure-ments from h to 5 MeV were made at one energy only with an accuracy of less than + 10$« Considering the large corrections made f o r multiple scattering i t would be d i f f i c u l t - 7 9 = to claim better than + 10% for the absolute value of this measareamt. H. Projected Experiment Using a Thin Slab Detector The results of the preliminary measurements of the differential scattering cross-section indicated that two general Improvements in the experimental arrangement were required to make measurements at smaller angles. First, the angular resolution of the scattered neutron detector must be improved. This could be done both by moving the detector further from the scatterer and by decreasing the size of the liquid scintillator. Second, the detector probe needs to be reoriented such that the body of the probe will not be partially in the primary neutron beam when the detector is positioned for a small angle measurement. With the main body of the probe being 11,k cm in diameter, even at a 1 0 degree scattering angle, part of the probe was partially in the neutron beam. This accounted for the large beam dependent background associated with the 1 0 degree measurement. By mounting the probe perpendicular to the scattering plane, this problem is. eliminated. A mount which will support the detector vertically is now under construction and a smaller liquid scintillator 1.27 cm x 7.62 cm x 2.5 1* cm deep is already available. A temporary vertical mount was used to position the small detector at + 7 degrees. The results of this measurement are described in Chapter I I I , but i t is essential to note here that the beam dependent background was even smaller than for =80= t h e l a r g e d e t e c t o r . The m a j o r p r o b l e m w i t h t h e s m a l l d e t e c t o r i s t h e d e t e r m i n a t i o n o f i t s e f f i c i e n c y . I t s s m a l l s i z e e x c l u d e s t h e p o s s i b i l i t y o f p l a c i n g i t i n t h e n e u t r o n beam such t h a t i t w o u l d c o v e r t h e e n t i r e beam u n l e s s a l l o f t h e s h i e l d i n g were removed so t h a t i t c o u l d be p l a c e d r i g h t a t t h e e x i t f l a n g e on t h e t a r g e t chamber . The o t h e r p o s s i b i l i t y i s t o c a l i b r a t e i t s e f f i c i e n c y r e l a t i v e t o t h e l a r g e d e t e c t o r by p e r f o r m i n g s c a t t e r i n g e x p e r i m e n t s a t 20 degrees u s i n g t h e two d e t e c t o r s and compar ing t h e i r r e l a t i v e c o u n t i n g r a t e s . T h i s w o u l d r e q u i r e a l o n g c o u n t i n g t i m e t o o b t a i n adequa te s t a t i s t i c s . One a d d i t i o n a l improvement t o t h e t e c h n i q u e may make f u r t h e r r e d u c t i o n s i n t h e random backg round w i t h l i t t l e s a c r i f i c e i n d e t e c t i o n e f f i c i e n c y . Neutron-gamma d i s c r i m i n a t i o n sys tems a r e now a v a i l a b l e ( 8 2 ) w h i c h a r e n o t as i n e f f i c i e n t as t h e d i s c r i m i n a t o r d e s c r i b e d i n Chap te r I I and w h i c h have h i g h c o u n t r a t e c a p a b i l i t i e s (2 x 10 c p s . ) . N e v e r t h e l e s s , t h e s i g n a l t o backg round r a t i o i s now s u f f i c i e n t t o e n a b l e a s m a l l a n g l e s c a t t e r i n g e x p e r i m e n t t o be p e r f o r m e d down t o as l o w as h o r 5 degrees w i t h v e r y l i t t l e change t o t h e p r e s e n t a r r a n g e m e n t . The measurement o f t h e .39 ba rns p e r s t e r a d i a n c r o s s - s e c t i o n a t 4-0 degrees d e m o n s t r a t e s t h a t s m a l l c r o s s - s e c t i o n s can be measured w i t h t h i s t e c h n i q u e i n a r e a s o n a b l e l e n g t h o f t i m e . T h i r t y p e r c e n t s t a t i s t i c s were o b t a i n e d i n 3 h o u r s f o r t h i s a n g l e . CHAPTER V A RESUME OF THEORY AND EXPERIMENTS LEADING TO AND INVOLVING SMALL ANGLE SCATTERING OF NEUTRONS A. Introduction Several interactions i n addition to that due to a simple o p t i c a l model p o t e n t i a l have been proprosed to explain small angle scattering of neutrons. Some of the theory involved i n these interactions w i l l be discussed together with the related experiments. Of special interest i s the anomalous increase i n the d i f f e r e n t i a l cross-section observed at .small angles. Measurements have been made at small angles for several heavy and medium-weight n u c l e i at a few neutron energies between .57 and ^-.0 MeV, and at lh.2 MeV (M-7,51-56). Many of these measurements show an increase i n the d i f f e r e n -t i a l cross-section as the angle decreases to small values that cannot be r e a d i l y a t t r i b u t e d to the nuclear force or to,the spin-orbit i n t e r a c t i o n a r i s i n g from the motion of the neutron magnetic moment i n the nuclear Coulomb f i e l d (Schwlnger scattering). One possible interpretation of t h i s r e s u l t i s that since the neutron has a charge structure, as demonstrated by electron scattering (83), then there can be an inter-action between an Induced dipole moment of the neutron and the external e l e c t r i c f i e l d of the scattering nucleus. A comparison i s made of the predicted values pf the neutron p o l a r i z a b i l i t y with the value estimated by making use of data on the photoproduction of pions from protons and with the value calculated from the meson theory (57-58). —82*r B. The Optical Model Early attempts to explain the interaction of neutrons with the atomic nucleus by means of a potential model met with only partial success (59). It was not until 1952 that a systematic analysis of neutron total cross«*section measurements between zero and 3 MeV by Barschall (60) showed regular maxima and minima indicating that these cross-sections did not depend on the internal structure of the nucleus as much as on the average? field of all the nucleons. Feshbacjkj Porter»V and Weisskopf (61-62) were then led to interpret these^  results in terms of a model of nuclear reactions called the optical model in analogy with the interaction of light with a semi transparent glass sphere. The neutrons are considered as being diffracted, refracted, and absorbed by the spherical nucleus. These optical properties are provided by introducing a complex well into the wave equation of tlie form V = U + 1 W .where jj and V .are the strengths of the real and imaginary parts of the -potential respectively. The imaginary part of the potential is related to compound nucleus formation by including a l l nuclear reactions, inelastic scattering, and even part of the elastic scattering in the absorption cross-section, o£» It has been shown that the elastic scattering cross-section can be decomposed into a shape - elastic term and a compound - elastic term (62,63) - se T ce -83-The shape - elastic cross-section, (Js"e, represents elastic scattering which does not involve compound nucleus formation. Energy is conserved, and the exit channel coincides with the entrance channel. The compound - elastic term, <T" , denotes c© elastic scattering produced first by the formation of a compound nucleus and then by its subsequent decay through the entrance channel. The only distinguishing feature between these two modes of scattering is the time for their occurence. Shape - elastic scattering takes of the order 10~22 seconds, the transit time of the neutron across the nucleus, whereas compound - elastic scattering requires the decay of the -15 compound nucleus with a lifetime of approximately 1G ' seconds. Therefore part of the elastic scattering can be included in the absorption cross-section, which is preferrably called the cross-section for compound nucleus formation. Hence the sum .<£ '+ %e * <5 ( = ^[ ) gives the cross-section for compound nucleus formation, where cr^  denotes reaction processes such as (n,p), (n,oO, and (n,n' ). For their original calculations Feshbach, Porter and Welsskopf used a very simple, spherically symmetric, square well potential which depended only on the nuclear radius, R = H0A,/k , where RQ = loM-2 fermis. With this potential, the authors were able to explain the cross-sections reported by Barschall (60). However, poor agreement was given for differential elastic cross-sections at large angles for heavy n u c l e i (6*+, 65)., A p h y s i c a l l y more reasonable p o t e n t i a l was then suggested .by Woods and Saxon (66) providing a smooth v a r i a t i o n of the potential at the nuclear radius. The r a d i a l v a r i a t i o n f ( r ) of t h e i r ' p o t e n t i a l was of the form f ( r ) = (1 + exp ((r-RVa ) ) " 1 where a i s the. surface diffusenesso ; A further refinement to the o p t i c a l model p o t e n t i a l has been the in c l u s i o n of a spin - o r b i t term (6?) which enables the p o l a r i z a t i o n of the e l a s t i c a l l y scattered neutrons to-be calculated,* As f a r as the d i f f e r e n t i a l scattering cross-section i s concerned t h i s term makes only a minor contribution to the cross-section mainly i n the regions of the d i f f r a c t i o n minima' (68)„ One of the recent attempts to put the o p t i c a l model on a less empirical basis has bean made by Perey and Buck (69)0 They have analysed neutron scattering using a non - l o c a l potential,, The non - l o c a l potential.,, by taking into account the f i n i t e s i z e of the incident neutron i n the nuclear f i e l d of the target nucleus, i s independent of the incident neutron energy within, the range of v a l i d i t y of the o p t i c a l m o d e l o By i n i t i a l l y determining the non - l o c a l parameters by f i t t i n g them to neutron scattering from l e a d 9 excellent agreement was obtained f o r other n u c l e i at neutron energies from 1 to 25 MeV. Unfortunately solution of the Schroed.inger wave equation f or a non - l o c a l p o t e n t i a l requires considerable computing f a c i l i t i e s . - 8 5 -C. Schwinger Scattering In 1 9 ^ 8 , with the intention of suggesting a new method for obtaining polarized neutrons, Schwinger (70) described a spin - orbit interaction arising from the motion of the neutron in the nuclear Coulomb field. Since neutrons possess a magnetic moment, they may be appreciably scattered by the intense electrostatic fields of heavy nuclei. The relationship between the magnetic moment and spin of a neutron can be written as where M* is the magnetic moment vector in erg gauss"1, [ytLj is the magnetic moment of the neutron = 1.9135 nuclear magnetons, eft 2mc l s * n e n u c l e a r magneton = Oo50505 ± 0.00002 x 10~2^ erg gauss"1 and is the Pauli matrix. The magnetic field strength if in the frame of reference of a neutron moving with velocity 7 produced by the approaching electric field it of the nucleus Is H = -c-E x V (5-2) The potential energy of the neutron's magnetic moment in the magnetic field B* can be expressed in the Hamiltonian for the neutron in its own frame of reference as 9/=-M-H (5-3) With (5-1) and (5-2), (5-3) becomes 9/ = - M • (E x f) (5->0 -86= Transforming the Hamiltonian to the frame of reference of the nucleus gives ty-W+g (5-5) where P = mV* is the momentum of the neutron relative to the nucleus. Combining (5-D> (5-4-), an4 (5-5) gives , + £ (5-6) Using the following relationships s - . R 3 5 * • ± * - -where 2: is the atomic number of the nucleus L* and S* are the orbital and Intrinsic angular momenta of the neutron In units of 71 respectively. Equation (5-6) may be written The Schroedinger equation describing the motion of the neutron is then -it V 2^ + U J Z e 2 t ) 2 -V - c> /* 7 N 2 m y m*cx r 3 " c r Schwinger ( 7 0 ) obtained the Born approximation pf the Schroedinger equation (5-7.) resulting in a differential scattering cross-section of the following form. crfe,FT)«|4v,(©)|a+'6a'cotxt>i + G I»,T>)co"te£ (5-8) where f c(6) is the amplitude of the nuclear scattering, -6 = 2 Leg ^ 4 P is the polarization vector of the incident beam, 1? is the unit vector normal to the plane of - 8 7 -•;• the reaction, and Im denotes "imaginary part of." Consequently the differential scattering cross-section for the scattering of a neutron beam will be modified at small-angles and will be sensitive to the polarization of the incident neutrons. In order to make an estimate of the magnitude of; the differential scattering cross-section for M-.56 MeV neutrons on lead at small angles resulting from this inter-action, the amplitudes of the nuclear scattering were deter-mined from the optical model potential. Using the optical model parameters derived.as outlined in section (G) of Chapter IV, the phase shifts describing the scattering from this complex potential were obtained.with the ABACUS - 2 code ( ^ 5 ) . The phase shifts, 5^ , were given as for the A.tii partial wave, or R e ) - c o s 2.d^ I m ( ^ ) = Sin where RE denotes "real part of." The nuclear scattering amplitude can then be expressed in terms of the phase shifts £(©) = A E (2.*+i)e c <k Sin 4 ft (cose) ( 5 - 9 ) where A - (2rr\E./h*) and r\(cose) are Legendre polynomials. A computer program was written by the author to calculate the cross-sections, CT(6,n), for neutrons 100 percent polarized in the scattering plane using equations ( 5 - 9 ) 7 ( 5 - 8 ) , -88-and the phase shifts provided by the ABACUS -2 program* Figure ( ^ 2 ):shows the results of this computation. The divergence of the cross-section at zero degrees scattering angle resembles that in Rutherford scattering, and may be removed in the same way, by taking into account the screening by atomic electrons. It can be seen from this figure that the interaction is sensitive to the polarization of the neutrons only at small angles. It was not until 1956 that a successful attempt was made to detect.Schwinger scattering, Aleksandrov (53) published some convincing results from his experiments with fast neutrons emerging from a reactor. They were collimated with a steel collimator to 0.9 x 3.6 mm thick. After collimation the width of their neutron beam at half maximum was about ,75 degrees. The measured angular distribution for the elastic scattering of neutrons compared favourably with Schwinger's theoretical calculation. Although other workers (51-5^ 0 imply the detection of Schwinger scattering by claiming to subtract this contribution to the cross-section in looking for anomalous Increases at small angles, the best demonstration of Schwinger scattering was made by A.J. Elwyn et. al... (^ 7) in their small-angle scattering of .83 MeV neutrons by Uranium. This work also included a measurement of the polarization, P(6), of the scattered neutrons. : The magnitude of the neutron polarization is defined as P(6) = N*- N~ (5-10) N++ N" -89-where; ;N and IT are the numbers of neutrons with spin parallel and antiparallel to a perpendicular to the scattering plane. If the incident neutrons are polarized in the scattering plane with magnitude PT, then the scattering of the neutrons will be characterized by a left - right asymmetry e = P(e )P T = IR - I L (5-11) I R + I L where 1^  and 1^  are the intensities measured by neutron detectors placed at a fixed scattering angle 6 but with azlmuthal angles equal to zero and TT, respectively. For their determination of P(6), A.J. Elwyn et. al. (T7) used a previously determined value for the polarization, Pi, of the incident neutrons emitted at 51 degrees in the Li?(p,n)Be7 reaction. To minimize..errors arising from variations in efficiency, geometrical effects, and background effects, an effectlve; Interchange of detector position from left to right was accomplished by processing the neutron spin through 180 degrees. Unfortunately the statistics on these measurements were not sufficiently good to verify the prediction pf the polarization P(6) by Schwinger (70) Pie) = z l w ^ ( e ) Ycot(Q/2) -,2) where ^ =6/4. If i t were possible to verify equation (5-11) then small - angle neutron scattering could be used as a "polarizer" or "analyser" of fast neutrons from the D(d,n)He-^  reaction in addition to the present, commonly used C 1 2 and Re*, Large discrepanies appear i n the measurements by various workers of the p o l a r i z a t i o n of neutrons from the D(d,n)He^ reaction forbombarding energies varying from 50 keV to 20 MeV. Small - angle neutron scattering may aid i n esta-b l i s h i n g the.correct values of the po l a r i z a t i o n s . An excellent review of this, problem i s found i n a paper by R.W. Fin l a y ( 7 1 ) . D. E l e c t r i c P o l a r i z a b i l i t y Scattering I t i s now w e l l known from scattering experiments with high energy p a r t i c l e s . t h a t the neutron has a charge "structure", presumably caused by a "cloud" of charged mesons around a central core, which i s d i s t r i b u t e d over a space region.of 10"^3 cm ( 8 3 ) . Therefore i n a e l e c t r i c f i e l d |f there may be induced In the neutron an e l e c t r i c dipole moment P* p a r a l l e l to the inducing f i e l d . p = OCET where c< i s the e l e c t r i c p o l a r i z a b i l i t y of the neutron. This should show i t s e l f i n an anomalous behavior of the d i f f e r e n t i a l cross-section at small angles ( 5 3 ) ° The perturbing Hamiltonian due to the in t e r a c t i o n of the induced neutron e l e c t r i c dipole moment with the external f i e l d i s then 61/' » - P> E\ = oc £ Z Thus i n the f i e l d of a heavy nucleus of charge 2", the perturbing Hamiltonian may be taken to be -91-where Q(R-r) Is a function depending on the charge distribution within the nucleus, and R is the nuclear radius equal to fermis. .One of the first attempts in the literature to separate the effects of different types of scattering was made in a theoretical paper by Barashenkov and Kaiser (72). Their: equation for the energy of interaction between the neutron and nucleus was 9/(r) - UM-/** /zm^&'irf - o c Z e V ^ f t - O (5-1^) The first term was determined by purely nuclear forces and by the assumption that the interaction was spin - independent. The second term describes the "Schwinger scattering" and the third term describes the "electric polarizability scattering". For simplicity Q was assumed to be a step function Q(R - r) = CO for r < R r; (.1 for r>R Using the Born approximation the following expression was obtained for the differential cross-section for elastic scattering of a beam of unpolarized neutrons by the nucleus djrte) = J ^  (e) W 4. -Pp Ce) Re 4n (e) + _ L ( 5 _ 1 5 } where fn(©) is the nuclear scattering amplitude, and •fi (S) = C€ cot eA)A and T p t e ) = o( ? V " / < R /s/w KR •+• cos K R + sm KR) are the amplitudes for Schwinger and polarizability scattering respectively where K = /8Em sin 6 /2. Figure (4-3 ) shows - 9 2 -the curves representing the calculations of Barashenkov and Kaiser for the differential cross-section of the elastic scattering of k MeV neutrons on with oL = 1G"^ ° cm^ ; <7i»(T2» G 3 are the cross-section of the nuclear, Schwinger and polarizability scattering: cr = 07 0 1 +- erf 3 ^ = o - > c£ Even for values of o£ as large as lO"1*0 cm^ , i t can be seen:that the scattering due to polarizability of the neutron alone is very small. The authors of this paper conclude that for comparison with experiment i t is necessary to have a good knowledge of the absolute value of the purely nuclear scattering since the slope of the curve CT(©0 constructed from the formula (5-15) is small and qualitatively the curves CT(6) and 0^.(0) are difficult to distinguish. Experiments on the elastic scattering of neutrons at very small angles were first performed by Y.A. Alexandrov (53)» Large increases in the differential cross-section for the scattering of reactor neutrons of average energy 2 MeV in the angular region 6 < 11 degrees were observed for the heavy nuclei Pu^ and IT?2 but not for Sn, PD, Bi, and Cu. In an attempt to interpret this anomalous scattering, the amplitude of pure nuclear scattering was estimated by extrapolating the experimental curves from the high angle regions into the small regions. . The discrepancy observed for the heavy elements was attributed to a contribution caused by a„ neutron polarizability oC= (8.0 + 3.5) x 10~ i f l cm^ . In a more recent paper (52) Alexandrov retracts his original -93-conclusions about the size of the polarizability of the neutron and cautiously concludes that "the detected phenomena were not yet satisfactorily explained." In 1961 Alexandrov et. al. (52) made small - angle scattering measurements of reactor neutrons from the elements Th, U, and Cu. For neutrons of average energy .8 MeV there was no anomalous increase in the cross-section. With neutrons of average energy 2.8 MeV, however, anomalous increases were observed for Th and U but not for Cu. In 1963 Dukarevich and Dyumin (5*0 used the associated particle technique with the T(d,n)Helf reaction to obtain a well collimated beam of 1^ .2 MeV neutrons. These neutrons were elastlcally scattered from W, Pb, Bi, Th, and U nuclei. Anomalous increases in the cross-section were observed only for Th and U. Fossan and Walt (55) In 196*f elastlcally scattered neutrons of energy .57 MeV with an energy spread of 50 keV from uranium. The neutrons were produced by the Li^(p,n)Be^ reaction and collimated with a borated - paraffin and polyethylene colli-mator. In 1966, Elwyn et. al. (**7) published a paper describing measurements of the polarization and differential cross-sections in the small - angle scattering of .83 MeV neutrons by uranium together with a very detailed and comprehensive theoretical treatment of their work. They observed an anomalous increase in the cross-section with decreasing angle similar to that reported by Alexandrov (52) for 2.8 MeV neutrons on U and Th but not as pronounced. No corresponding anomalous polarization effects were seen, however. Most recently, Gorlov et. al (9) -ab-used 4- MeV D(d,n)He^  neutrons to examine the scattering from U, Bi, pb,_Sn, In, and. Cu. They report no anomalous increases in the cross-sections butunfortunately they failed to provide any information about their experimental technique. One very recent attempt to measure the polariz-ability of the neutron using very low energy neutrons 1 keV to 26 keV from a pulsed reactor was made by Y.A. Alexandrov et. al. (73). In scattering these neutrons from uranium, they used time of flight techniques to measure the energy of the neutrons and the calculated interference between the polarizability and nuclear potential scattering to interpret their results. They obtained a value of (0.3 ± 9.2) x 10"h2o E. Theoretical Calculations of the Neutron Polarizability At present there exists no rigorous theory, which could allow for the calculation of effects connected with the internal.structure of the nucleons. Any contributions involving the internal regions must be made by extrapola-tions for which there is l i t t l e justification. Theoretical estimations of the electric polarizability must rely on the assumption that the main contributions arise from processes taking place at the peripheral regions. An order of magnitude estimate of the electric polarizability can be made using the equations of classical meson theory (72), z I*-^ -42 3 oc = & f a = |.6x/0 Cho - 9 5 -where f /tic = 0.08 is the meson nucleon coupling constant and a =Ti^uc = 1.-+1 x lO'^cm Is the characteristic dimension of the meson cloud in the nucleon. Several theoretical estimates have been made of oC to varying degrees of rigour (.7k - 76). Their estimates of oC give the limits -4- "5 1 - 4 2 3 2 x / o c m < c< < ZYIO c m ' Barashenkov, (77) however, has recently obtained a value of cXnear 8 x 10 cnr by including contributions from virtual excitations of positron and electron pairs. Other less usual effects have been discussed in the literature which may account for the observed anisotropy in neutron scattering. These include 1) Influence of the atomic electron shell. This can be discounted; from the fact that i t can be shown that the contribution would be significant only for scattering angles 0 < 1 degree (72) 2) Interactions with the electric quadrupole and magnetic dipole moments of the nucleus. Calcula-tions show that these would not explain the observed anomalies (78). 3) Inaccuracies in the calculations of the nuclear scattering and its interference with the polarization and Schwinger scattering. Comprehensive calculations were carried out by A.J. Elwyn et. al. (k7) using an optical model of the nucleus with diffuse boundary and spin orbit forces. It turns out that in the angular range ©<10 degrees, the results are -96-quite insensitive to the shape of the nuclear potential. Numerical calculations also show that the Born approximation can be used with good accuracy for the amplitudes of the Schwinger and potential scattering (72). *+) An interaction which may be associated with specific features of fissionable nuclei. Since the fission threshold for occurs at a neutron energy of approximately 0.6 MeV, a l l of the measure-ments with the exception of the measurements of Alexandrov (52) with reactor neutrons of average energy 0.8 MeV are consistent with this interpreta-tion. A. J. Elwyn et. al. 0+7) suggest that the energy spread of the beam may account for the decrease in the magnitude of their small angle results. 5) Redmond (79) has shown that a sufficiently strong spin-orbit force localized at the nuclear surface can give rise to enhanced small - angle scattering of neutrons although such an interaction seems unlikely. 6) A nuclear - potential (tail) longer than contained in the Saxon - Woods potential is indicated in the elastic scattering of 96 MeV and 136 MeV neutrons from carbon (80) which may account for some of the anomalous increases in the cross-sections observed. 1 -97-The first three effects are sufficiently well accounted for. Last two interactions require a more detailed theoretical treatment then is presently available before one could make any commitment about their ability to explain the present data. Number four may be true merely to the extent that the specific feature of fissionable nuclei is a high Z. Whether or not the anomalous increase is connected with the fission process would best be tested by a detailed study of the energy dependence of small-angle scattering of neutrons from fission-able and non-fissionable nuclei in the vicinity of the fission threshold. F. Conclusions As can be seen from this review, theoreticians have had considerable difficulty in explaining recent low angle scattering of neutrons simply because of the number of possible interactions involved and because of the fact that some of these interactions are not completely understood. In trying to isolate one type of interaction such as the electric polarizability scattering, one must make some unverlfiable assumptions about the magnitude of other inter-actions and the adequacy of optical model extrapolations to small angles. It is hoped that additional data in the neutron energy range 2.5 MeV to 5 MeV will help to isolate the contributions from the various interactions described. So far the information available from the measurements in this -97 b-energy region has been limited to a certain extent by the fact the neutrons used were neither monoenergetic nor polarized. The associated particle technique as described in this thesis provides a method of producing a well colllmated, monoenergetic, partially polarized neutron beam of h.56 Me? with sufficient intensity and low enough background to perform a small - angle scattering experiment. In order to obtain the 5 percent statistics required to determine the presence of an anomalous increase In the scattering cross-section or a left-right asymmetry due to Schwinger scattering approximately 8 hours per point would be necessary with the available neutron flux and angular resolution. Reprinted from T H E RE V I E W O F S C I E N T I F I C I N S T R U M E N T S , Vol. 37, No. 3, 316-318, March, 1966 Printed in U. S. A. Detection of Pulse Pile-Ups with Pulse Overlap to Pulse Height Converter* L. F. M O N I E R f AND G. E. T R I P A R D f Physics Department, University of British Columbia, Vancouver, B.C., Canada (Received 8 October 1965; and in final form, 1 November 1965) A new type of pile-up rejector, using a pulse overlap to pulse height converter, is described. It is operated at the output of a double delay line, clipped amplifier and has a resolving time better than 20 nsec. INTRODUCTION EX P E R I M E N T S which involve precision pulse height analysis suffer from spectral distortion when high count rates are used. If two or more pulses arrive within a sufficiently short time interval, the superposition of their waveforms results in ah incorrect amplitude measurement. This time interval may be referred to as the pile-up re-solving time of the system. To reduce the pile-up resolving time various pile-up rejectors have been bui l t . 1 - 3 Most pile-up rejectors require a system which can resolve the pile-up signal from the detector into two consecutive sig-nals. This can be done by R C shaping, delay line clipping, or through the use of a charge piekoff device before the preamplifier of a semiconductor detector. This paper de-scribes a pile-up rejector which examines the width of the positive going part of the output pulse from a 740 nsec double delay line (DDL) clipped linear amplifier4 by means of a "pulse overlap to pulse height converter" thereby distinguishing between single pulses and pile-up pulses with a pile-up resolving time as low as 20 nsec. Similar systems have been used by Alexander and Goulding 5 as a particle discriminator selecting neutrons in a background of y rays and by Sayres and Coppola 6 as a risetime dis-criminator for reaction particles in an ionization chamber. METHOD OF OPERATION A block diagram of the pile-up rejection system is shown in Fig. 1. Pulses from the D D L amplifier are sent to the input of a discriminating limiter. This circuit, as described by Sayres and Coppola,6 generates a square pulse about 2 V high, when the input pulse crosses the zero voltage level. The limiter can be adjusted to trigger just above the input noise level. The output pulses obtained have widths which are determined by the degree of overlap of the two consecutive pulses from the detector. The output * Research supported by a "grant from the Atomic Energy Control Board, Canada. t Recipient of a National Research Council of Canada Studentship. 1 S. Rozen, Nucl. Instr. Methods 11, 316 (1961). 2 M . G. Strauss, Rev. Sci. Instr. 34, 355 (1963). 3 J. D. McGervey and V. P. Walters, Nucl. Instr. Methods25, 219 (1964). 4 R. L. Chase and V. Svelto, IRE Int. Conv. Rec. Pt. 9, 106 (1961) (the amplier used was manufactured by Cosmic, model 901). 6 T. K. Alexander and F. S. Goulding, Nucl. InstR Methods 13, 224 (1961). 6 A. Sayres and M. Coppola, Rev. Sci. Instr. 35, 431 (1964), from the limiter could then be sent to a pulse width to pulse height converter and the subsequent output analysed with a pulse height analyzer which would generate a veto pulse if its input were too large. However, the incremental change in output height from the pulse width to pulse height con-verter is small for a small change in the input pulse width. For example, a 2 nsec change in a pulse width of 740 nsec would provide only a 0.27% (100%X 2/740 nsec) change in the output pulse height. Moreover, the outputfrom the pulse width to pulse height converter normally has a decay time at least an order of magnitude greater than its risetime. Therefore unless special R C shaping or delay line clipping is used at the output these pulses can also be involved in electronic pile-up and no advantage in pile-up rejection would be obtained. To overcome these two difficulties the circuit shown in Fig. 2 was used. This circuit which we call a "pulse overlap to pulse height converter" (POPHC) has an output which has a width of only twice that of the D D L amplifier output and a larger incremental change in pulse height for a small change in the width of the limiter output. A 2 nsec change in pulse width of 740 nsec pro-vided a 1.3% change in the output pulse height. The output from the pulse overlap to pulse height converter is then sent to a tunnel diode discriminator?'8 (discriminator No. 1 in Fig. 2) which is used to inhibit a fast linear gate (nor-mally open) in the event of a pile-up pulse. The two requirements placed on the'linear gate are a frequency response consistent with the D D L amplifier used and a very short recovery time, the latter preferably less than the width of the D D L amplifier pulses. - J — L ToBIL D I S C R I M -INATOR # 1 J L \ R £ £ . T U N N E L DIODE D I S C R I M -INATOR # 2 J L L I N E A R G A T E N O R M A L L Y O P E N FiG.-l. Block diagram of pile-up rejector. 7 G. Infante and F. Pandarese in Nuclear Electronics Conference Proceedings, Belgrade, 1961 (International Atomic Energy Agency, Vienna, 1962), Vol. Ill, p. 29. 8 G. Jones, Rev. Sci. Instr. 34, 938 (1963). 316 317 P U L S E P I L E - U P D E T E C T I O N TWO 0.5 f,i GENERAL RADIO DELAYS OUTPUT "A" p o o " ' T O TRIGGER « I ) .05»f OUTPUT B 220 ' ' I T 0 TRIGGER a 2 ) ,05^f F I G . 2. Pulse overlap to pulse height converter. PULSE OVERLAP TO PULSE HEIGHT CONVERTER The pulse overlap to pulse height converter is very-simple in design and operation. As shown in Fig. 2, two emitter followers at the input of the circuit isolate the discriminating limiter from the succeeding circuitry and they also match impedances at both ends of a 1 /jsec vari-able delay consisting of two General Radio variable delays (220 fl impedance, 0.5 /usee delay) in series. The pulse over-lap to pulse height conversion takes place at one of the center taps (output ' A ' in Fig. 2.) where the pulses from the emitter-followers have been delayed by times T\ and T2, respectively. The center tap is adjusted so that T\— T2 is equal to the width La of the limiter pulse for no pileup. Any small change AL in the width of the input pulse then produces a relatively large change AA in the amplitude of the output pulse. The leading and trailing edges of the limiter output pulse are superimposed in such a way that AA = AL/(tT+t.f), where lr+lf is the sum of the rise and decay times of the limiter output pulse. The maximum change AA in the amplitude of the output pulse is 50% of the maximum and constitutes a change from no overlap to complete overlap of the leading and trailing edges of the limiter output pulse. Therefore a 2 nsec change in the width of the D D L amplifier pulse would provide a 1.3% [50%X2 nsec/(/ r+//)] change in the output pulse height, where lT-\-tf= 70 nsec. As discussed in the section on performance the second center tap (output 'B') going to trigger No. 2 may not be required. Its use can extend the range of pile-up rejection to include pulses which arrive during the negative going part of the initial D D L amplifier pulse. The second center tap on the delay is adjusted so that for no pile-up the outputs from the emitter followers of the P O P H C are de-layed with respect to each other by a time L0+AI, where At is approximately 100 nsec. This causes a coincidence at the center tap whenever two D D L pulses arrive within 740 nsec to 1.5 jusec. This output is also sent to a tunnel diode discriminator7'8 (discriminator No. 2 in Figs. 1 and 2). The operation of this part of the circuit can be more easily understood by examining the last three wave-forms in Fig. 3 which represents the arrival of two con-secutive pulses separated by a time interval of 1 /xsec. PERFORMANCE To test the performance of the pile-up rejector, two pre-cision pulsers were used to send pulses into the preamplifier simulating the detection of two charged particles, one de-layed with respect to the other by a time T . The noise on the pulses as measured at the output of the D D L amplifier corresponded to 50 keV. Figure 4 (curve a) is a graph which shows the percentage of the pile-up rejected for two 1.4 MeV pulses as a function of the delay time T between the two pulses. With a delay of only 14 nsec, over 50% of the pile-up pulses were rejected, and with a delay of 22 nsec over 99% were rejected. When the delay became greater than the width of the positive going part of a D D L amplifier pulse the pile-up pulses were no longer rejected. The delay (of the order of 740 nsec) at which this occurred was such that there was negligible distortion of the positive going portion of the D D L amplifier pulse. This resulted in an over-all pile-up rejection efficiency (in the region of 0 to 740 nsec) of 98.4% for random, pulses of 1.4 MeV. This represents a decrease by a factor of 57 in the apparent pulse width, for pile-up considerations, over the D D L am-plifier without pile-up rejection. The major limitation to the pile-up resolving time, when using pulses which originate in fast detectors, such as or-ganic scintillators or semiconductor detectors, is the ac-curacy with which one can measure the initial time of the D D L amplifier pulse. This accuracy depends directly on the input noise level at the discriminator limiter. Therefore, a slightly poorer performance was obtained for test pulses simulating 350 keV with 50 keV of noise. Figure 4 (curve b) shows the pile-up rejection with a signal-to-noise voltage ratio of only 7. The over-all pile-up rejection efficiency for randorh pulses of 350 keV was 95%. A similar performance was obtained for large pulses simulating 2.8 MeV distorted by the addition of 224 keV pulses. Figure 4 (curve c) shows WITHOUT PILE-UP F I G . 3. Pulse >vave forms of pulse over-lap to pulse height converter. D0L OUTPUT POPHC OUTPUT (TO TRIGGER tt 2 ) WITH PILE-UP —u DDL OUTPUT POPHC OUTPUT (TO TRIGGER « 2) —I" [ — A t L . F . M O N I E R A N D G . E . T R I P A R D 318 the pile-up rejection for these pulses. However, the over-all pile-up rejection efficiency for random pulses of this kind was 95%. In the experimental arrangement described the amplitude of the voltage pulses at the input of the dis-criminating limiter was 180 m V / M e V . As pointed out by Strauss,2 if the pulses to be measured originate in fast detectors the signals from the subsequent slow amplifiers can be considered as virtually true ex-ponential pulses, and as such are most suitable for pile-up detection. If the pulses originate in slower detectors, such as N a l , random variations in the risetime cause statistical fluctuations in the pulse shape and therefore limit the efficiency of pile-up rejection. Depending on the type of pulse height analysis per-formed on the pulses it may. be sufficient to reject only the pile-ups involving overlap of the positive parts of two pulses. If necessary the region of pile-up rejection can be easily extended to include the entire width of the D D L amplifier pulse. Figure 5 shows the percentage pile-up re-jection for 1.4 MeV pulses over the two ranges, one using only the pulse overlap to pulse height converter and the other over the extended range using the additional delay center tap. This addition would be necessary if one were to use for example a Nuclear Data 160 multichannel an-alyzer which has a special input for doubly clipped pulses. In this case the improvement over the D D L amplifier that can be obtained with the addition of the pile-up rejector is even greater, since the effective width of the pulse, for EJECTED / -UP Rl - 8 0 I / O ' 1 GE PILE / •60 1 J 1 1 — • C . \ < ', \ z_ \ ' \ ° \ \ \ s \ ' \ I / - 4 0 / , 1 / / / / ' '' -20/ ;•• PILE-UP REJECTION REGION COVERED BY PULSE OVERLAP TO PULSE HEIGHT CONVERTER DDL ZERO CROSS OVER TIME ADDITIONAL — " ^ PILE-UP REJECTION REGION COVERED BY SECOND CENTER TAP (OUTPUT TO TRIGGER W 2) OVERLAP (NANOSECONDS) F I G . 4 Percentage of pile-up rejected: a—two equivalent 1.4 MeV pulses with 50 keV noise; b—two equivalent 350 keV pulses with 50 keV noise; and c—2.8 MeV-f 224 keV pulses with 50 keV noise. 2 0 0 4 0 0 GOO 8 0 0 1000 I: r OVERLAP (NANOSECONDS) F I G . 5. Pile-up rejection ranges. pile-up considerations, is reduced by a factor of 100 from 1.5 jusec to 15 nsec. Other types of analyzers may require an even longer range of pile-up rejection. It is relatively simple to use this pile-up rejector in conjunction with one which has a longer pile-up rejection period but which may not have as short a resolving time as that provided by the pulse overlap to pulse height converter. Figures 4 and 5 can be used to give a good estimate of line broadening effects of pile-up in any particular region of a spectrum. For example, if a very strong spectral line producing pile-up appeared at 1.4 MeV, then any weak line occurring between 1.4 and 2.8 MeV would tend to be ob-scured by the pile-up. With a knowledge of the amplitude of a pile-up pulse as a function of the delay r between the two single pulses producing the pile-up, one could deter-mine the pile-up rejection efficiency within any energy interval between 1.4 and 2.8 MeV. Therefore, using the pile-up rejector, the only energy interval where pile-up would cause substantial loss in resolution in this example would be within the immediate vicinity of 2.8 MeV where the delay T was less than 20 nsec and the amplitude of the pile-up pulse was indistinguishable from that of a single 2.8 MeV pulse. The most important advantages offered by this pile-up rejector are its high pile-up rejection efficiency even for small sigrial-to-noise ratios, the simplicity and uncritical nature of the setting-up adjustments, and the fact that it is used at the output of a D D L amplifier making it suitable for semiconductor detectors without affecting energy resolution. NUCLEAR INSTRUMENTS AND METHODS 45 (1966) 282-286; © NORTH-HOLLAND PUBLISHING CO. ACCURATELY DEFINED NEUTRON BEAMS FROM D(d,n)3He AT ED = 50 keV, USING THE ASSOCIATED PARTICLE METHOD* L . F . C. MONIER+, G . E . T R I P A R D and B. L . W H I T E Department of Physics, University of British Columbia, Vancouver, B.C. Received 14 April 1966 Accurately collimated fast neutron beams of small angular width and known absolute intensity and energy were produced by bombarding heavy ice targets with 50 keV deuterons and operating the neutron detector in coincidence with a semi-conductor counter detecting the 3 He recoil nuclei. The measured 1. Introduction A simple m e t h o d 1 - 8 ) o f producing accurately co l -l imated fast neutron beams of k n o w n absolute intensity is to produce the neutrons by means of a reaction such as D ( d , n ) 3 H e and then to operate the neutron detection system i n time coincidence wi th a spectrometer detecting the associated recoi l nuclei , i n this case 3 He. The recoil nuclei, being charged, are detected w i t h 100% efficiency, so that the number of associated neutrons is k n o w n accurately. The geometry of the neutron beam thus produced is defined by the geome-try o f the target spot and the recoi l detector and by the reaction kinematics. Depending on the part icular reaction chosen, on the bombard ing energy and on the target material , it may be necessary to take into account the scattering of the incident bombard ing particles while traversing the target and the scattering o f the recoil nuclei while leaving the target, i n calculat ing the * Research supported by a grant from the Atomic Energy of Canada Control Board. + Now with Hydro-Quebec attached to Atomic Energy of Canada Ltd. ( C A N D U - B L W D D ) , Ontario. beam profile agreed with the theoretically calculated profile. The beam was used to measure the absolute neutron detection efficiency and the scintillation pulse spectrum of a plastic scintil-lation counter bombarded by 2.55 MeV neutrons. resulting neutron direction. Such calculations are difficult and uncerta in; fortunately it has not been necessary to introduce such corrections to obtain agreement between theory and experiment i n the present experiment. Previous workers 5 ) using this method and using the T - d reaction were unable to obtain agreement between measured and calculated neutron beam profiles, probably because of scattering i n the target. A t the higher bombarding deuteron energies they used and wi th tritiated z i r con ium targets, the effects o f scattering were much more serious than i n the present experiment. A major reason the associated particle technique was not exploited in conjunction wi th the d - D reaction un t i l recently was the difficulty o f performing accurate spec-trometry on the recoil nuclei and at the same t ime per-forming fast coincidences between the recoil nuclei and the neutrons. Th i s difficulty has been removed by the development of semiconductor counters wi th th in windows and wi th adequate energy resolution and frequency response. F o r the present reaction D ( d , n ) 3 H e , wi th EA = 5 keV, the 3 H e recoil energy is only 185 k e V DEFINED NEUTRON BEAM SEMICONDUCTOR COUNTER Fig. 1. Target and beam arrangements, <XT is the angle between the normal to the target plane and beam; 9 H E 3 , the angle of the recoil detector with respect to the deuteron beam; and dn, the angle of the associated neutron with respect to the deuteron beam. 282 ACCURATELY DEFINED NEUTRON BEAMS 283 PHOTO MULTIPLIER PLASTIC SCINTILLATOR (NE-102) SEMICONDUCTOR COUNTER CHARGE SENSITIVE AMPLIFIER AMPLIFIER DISCRIMINATOR LINEAR GATE COINCIDENCE UNIT SINGLE CHANNEL PULSE HEIGHT ANALYSER IOO-CHANNEL PULSE HEIGHT ANALYSER Fig. 2. Block diagram of the electronic system used. different from the energy of the T recoil nuclei produced by the competing reaction D(d,p)T, so low window broadening and system noise is essential, in order to resolve the 3 H e and T groups. The work described in this paper consists of the measurement of the spatial distribution (the "beam profile") of a neutron beam produced using the associated particle method, the comparison of the measurement with a computed beam profile, and the use of the beam to measure the abso-lute neutron detection efficiency and pulse spectrum of a plastic scintillation spectrometer. 2. Beam profile measurement Fig. 1 shows the target and beam arrangements. The bombardment took place inside an aluminum reaction chamber from which the neutron beam emerged through a 0.18 mm aluminum window. A beam of 1.5 /iA of 50 keV deuterons passed through a collimator of diameter 1.033 mm just in front of the target. The beam incident on this collimator was parallel and diffusely distributed over a circle of about 5 mm dia., to snsure that the deuteron flux on the target was reason-ably uniform. The target was D 2 0 frozen onto a 0.795 mm copper backing maintained at liquid nitrogen temperatures and was thick to 50 keV deuterons. The angle between the normal to the target plane and beam was 35°, producing an elliptical target spot. At the recoil detector the target spot subtended an angle of 1.18° in the horizontal plane and an angle of 1.78° in the vertical plane. The recoil detector collimator was circular; it was placed at an angle of 105° with respect to the deuteron beam and subtended an angle of 1.35° at the target. The recoil detector was a R C A diffused junction semiconductor counter type A-3-75-2.0. The neutron detector was a 7.5 cm thick block of N E 102 scintillation plastic subtending, at the target, an angle of 0.87° in the horizontal plane and 6.5° in the vertical plane. Fig. 2 is a block diagram of the electronic system used. The pre-amplifier for the semiconductor detector had an equivalent input noise of ^ 6 keV. The coin-cidence resolving time was about 10 fisec. Fig. 3 is a typical ungated pulse spectrum obtained from the recoil detector under these conditions; it shows the two particle groups completely resolved, allowing coincidences to be made with the 3 H e recoils only. The beam profile was measured in the horizontal plane, by measuring the number of neutron-3He coin-cidences per unit incident beam charge as a function of the angular position of the neutron counter in the horizontal plane. The results are shown in fig. 4. The circles are the experimental results, with one typical experimental error flag shown and the solid line is the theoretical beam profile calculated as described below. The zero of the angular coordinate corresponds to the central angle of emission of neutrons produced by deuterons with 50 keV bombarding energy, where the central angle is that angle which would be obtained if the target spot and recoil detector were infinitesimal, located at the centres of their real areas. The skewness of the calculated curve about zero angle is due to the progressive reduction of the deuteron energy as it CD or C H A N N E L . N U M B E R Fig. 3. Response of semiconductor detector to D on D reaction with an incident deuteron energy of 50 keV and a semiconductor detector angle of 105°. 284 L. F. c. MONIER et al. 90 -2.0 -I.O o 1.0 2.0 3.0 4.0 5.0 N E U T R O N A N G L E U N D E G R E E S ) Fig. 4. Experimental and calculated neutron beam profiles. traverses the target. It can be seen that the agreement between experiment and calculation is good. 3. Calculation of the beam profile The calculation proceeded in three stages. First, the beam profile which would have been measured by a point neutron detector was computed, assuming an infinitely thin target. It was assumed that the deuteron flux was incident uniformly over the target spot. In this case the coincident neutron flux in a given direction was proportional to the area of the recoil detector which was seen from that direction to overlap with the target spot. Allowance was made for the centre of mass to laboratory coordinate transformation. The profiles in the horizontal and vertical direction obtained by overlapping the target and recoil detector areas are shown in fig. 5. Second, the finite target thickness was introduced. As the bombarding deuterons are slowed down in traversing the target, neutrons are produced with central angles and yields corresponding to E6 between 50 keV and 0 keV. The neutron profiles corresponding to the bombardment of thin targets with deuterons of kinetic energies 50 keV, 46 keV, 41 keV and 36 keV were calculated. Then, the profile for a thick target was obtained by summing and smoothing these thin target profiles. The thin target profiles are shown in fig. 6; the zero for the horizontal angle corre-sponds to the central angle for neutrons produced by 50 keV deuterons. Third, an integration over the finite sized detector was performed, the result being the calculated distribution shown in fig. 4. The agreement between experiment and calculation shows that the effects of beam and recoil nucleus scattering in the target are negligible in the present arrangement, and that the beam width does in fact depend only on geo-metry and kinematics. The count rates obtained were low, the order of i two neutron counts per second per millisteradian. Fig. 5. Calculated intensity of the neutron beam for a thin target. ACCURATELY DEFINED NEUTRON BEAMS 285 4. Neutron counter efficiency for 2.55 MeV neutrons The neutron beam was used to determine the abso-lute neutron detection efficiency of a cylinder of plastic scintillator N E 102, of 2.54 cm thickness and 5.08 cm dia. The neutron beam was incident normally at the centre of the plane face of the cylinder. The geometry was such that the beam was localised well within the area of the plane face of the scintillator, so that the efficiency £ was given directly by the ratio of the number of neutrons counted in coincidence with 3 H e recoils, Nc, to the number of 3 H e recoils, Nr. Nc was taken to be equal to twice the number of counts in the neutron spectrum above energy \E, where E is the maximum energy given up by the neutron to the scintillator. Fig. 7 shows the pulse spectrum from the neutron spectro-meter when it was operating in coincidence (solid line) and also when it was counting all neutrons incident on it, i.e. not operating in coincidence (dotted line). The measured efficiency was 0.297 (1 ± 0 . 0 3 ) ; this is com-pared in fig. 8 with the efficiency calculated using the approximation given by Swartz and Owen 9). The calculated efficiency ec is plotted as a function of LL the average distance travelled in the scintillator by a neutron which has collided with a carbon nucleus. Since double scattering of neutrons by hydrogen nuclei was not considered in the calculation of ec, and since O O - N O N C O I N C I D E N C E C O I N C I D E N C E 2 0 4 0 6 0 C H A N N E L N U M B E R Fig. 7. Pulse spectrum from the neutron spectrometer. 286 L. F. c. MONIER et al. 2 . 0 VALUE OF 3 . 0 4 , 0 IN CENTIMETERS Fig. 8. Calculated and measured efficiencies of a plastic scin-tillator. the scintillator is sufficiently thick to require a reason-ably accurate treatment of such scattering, it is not fruitful to try to compare the theory of Swartz7"and Owen with this result to a high degree of accuracy. Rather this technique could be used to provide the experimental results on which to base the derivation of a more accurate theory of scintillator efficiencies and spectra. 5. Conclusions This method produces neutron beams of energy near 2.5 MeV, with intensities which are accurately defined, and with accurately predictable geometry. The proper-ties are of use in making absolute measurements of neutron absorption cross sections and of scattering cross sections at small angles. We are grateful to the National Research Council of Canada for supporting two of us (L. F. C. M . and G. E. T.) with scholarship and to the British Columbia Telephone Company for supporting one of us (L. F. C. M.) with a bursary. References 1) V. I. Strizhak, V. V. Bobyr and L. Ya. Grona, JETP 13 (1961) 506. 2) Yu. V. Dukarevich and A. N. Dyumin, Zh. Eksp. Teor. Fiz. 44 (1963) 130. 3 ) D. Didier, J. Phys. Radium 22, Suppl. no. 11 (1961) 149A. 4) C. F. Cook, Nucl. Instr. and Meth. 15 (1962) 137. 5 ) J. Rethmeier, C. C. Jonker, M. Rodenburg, J. W. Hovenier and D. R. v. d. Meulen, Nucl. Instr. and Meth. 17 (1962) 273. 6) C. I. Hudson, Jr., W. S. Walker and S. Berko, Phys. Rev. 128 (1962) 1271. 7 ) B. L. White and L. F. Monier, Am. Phys. Soc. Ser. II 8 (1963) 119. 8) J. D. L. H. Wood, Nucl. Instr. and Meth. 21 (1963) 49. 9) C. D. Swartz and G. E. Owen, Fast Neutron Physics 1 (ed. Marion and Fowler, Interscience Publ. Inc., New York, 1960) p. 222, eq. (14). Reprinted from T H E RE V I E W OF SC I E N T I F I C I N S T R U M E N T S , Vol. 38, No. 3, 435-436, March, 1967 Printed in U. S. A. Preparation of Thin Film Deuterated Polyethylene Targets* G. E. T ^ I P A R D J A N D B. L. WH I T E Physics Department, University of British Columbia, * Vancouver S, B. C. (Received 21 September 1966; and in final form, 24 October 1966) I V H I N deuterium targets of about lOO/jg/cm2 were required for the production of monoenergetic neu-tron beams using the D(d,n) 3He reaction. White 1 has described the preparation of thin polyethylene films be-tween 900 and 2500 A thick by vacuum evaporation. The only disadvantage of this technique is that a large fraction of the evaporated. polyethylene is lost in the vacuum chamber. Another technique2 similar to the one described in this paper was used to prepare targets 1-20 mg/cm 2. The main difficulty with the 100/ig/cm 2 targets is their very poor stability in a charged particle beam due to their very low thermal and electrical conductivity. In the present work, it is shown that the evaporation of a thin film of carbon onto the polyethylene improves the target stability considerably. The targets prepared were capable of withstanding an incident 2 MeV deuteron beam of 200 nA through a 0.318 cm diam collimator for 1 h with only a 10% deterioration of the deuterated polyethylene. Polyethylene films were prepared by dissolving 0.01 g of deuterated polyethylene3 (C2D 4) n in 5 g'of boiling xylene. The solution was kept near the boiling point for 5 min to completely dissolve the polyethylene. While still hot the solution was poured quickly onto process clean micro slides4 76X25X1 mm. Five grams of solution were sufficient to cover 6 slides. The slides were set aside in a dust free environment to dry for 24 h. Using a carbon arc apparatus described by Dearnaley,6 a thin carbon film 10 ng/cm2 was evaporated,onto the polyethylene. The polyethylene film with its thin carbon coating was floated off the glass by lowering the slide slowly into the water at an angle of 30° to the surface. Before floating the film off, it is convenient to scribe the required target shapes with a sharp object. The films must be floated off very slowly to avoid tearing; therefore it is not recommended that this be done by hand. One successful method is to start the floating off procedure by hand at one end of the slide until about 2 mm of poly-ethylene has lifted. Then the slide is floated by surface tension in a pan of water about 3 slide thicknesses deep. Surface tension will float the remainder of the film from the slide with no damage to the film as the region of the slide uncovered by the film no longer supported by surface tension sinks beneath the surface. Only "process clean" 4 slides were successful in avoiding sticking. When the slides had been used once, they could not be reused. The films were picked up on flat metal frames with a ( d , p ) C ' 3 0(d,p)T 2.8 3.0 ENERGY IN MeV F I G . 1. Reaction protons from deuterated polyethylene targets. 436 N O T E S 0.318 cm diam hole by dipping the frames into the water and raising them slowly at a steep angle. Carbon targets5 were prepared separately,' usirig the same evaporation time as used in the carbon evaporation on polyethylene. The thickness, of the carbon targets was measured by elastically scattering protons from the carbon. This measurement was used to estimate the thickness of the carbon film on the polyethylene. The carbon films were found to be 10 Mg /cm 2 ±3/ig/cm 2 or about 2.5 keV thick to 870 keV protons. The thickness of the combined carbon and polyethylene films was de-termined by measuring the shift of the 873 keV resonance of 1 9F(p,a,7) 1 60 reaction after the film was placed in front of a thin calcium fluoride target. .The measured shift in the resonance for the combined films was 28 keV. To measure the target deterioration, reaction protons from bombarding the targets with 2 MeV deuterons were counted with a semiconductor counter placed at a lab angle of 60° with'"respect to the incident deuterons. A 0.05 mm aluminum foil was placed in front of the detector to completely degrade the 3He, T, and scattered deu-terons. Figure 1 is an energy spectrum of the reaction protons from the reactions 1 2C(d,p) 1 3C and D(d,p)T. By monitoring the ratio of the number of counts in the two peaks, it was possible to detect any deterioration in the deuterated polyethylene resulting from possible melting or sublimation. With an incident deuteron beam of 100 nA through a 0.318 cm diam collimator, there was no detectable deterioration of the target after 1 h of bom-bardment. With 200 nA, there was about a 10% decrease in the d on d proton yield with respect to the 1 2 C proton yield after 1 h of bombardment. The targets are very fragile, and have a tendency to tear along the edge of the target mount at the time that the bombarding beam is removed. This tearing may be caused-by the-sudden change in the thermal and electro-static equilibrium between the target and mount. * Research supported by a grant from the Atomic Energy Control Board of Canada. f Recipient of a National Research-Council of Canada Studentship. 1 M. White, Vacuum 15, 449 (1965). 2 G. T. J. Arnison, Nucl. Instr. Methods 40, 359 (1966). 3 (C2D4),, from Merck Sharp and Dohme of Canada Ltd., Montreal, Canada. 4 Micro slides "process clean" from Corning Glass Works, Corning, N. Y. 6 G. Dearnaley, Rev. Sci. Instr. 31, 197 (1960). APPENDIX B MONTE CARLO COMPUTER PROGRAM FOR MULTIPLE SCATTERING CORRECTIONS A computer program was written to calculate the multiple scattering corrections to the scattering data of "+o56 MeV neutrons oh lead as described in Chapter IV. A flow chart similar to the one in the article on "Computer Techniques" by Amster, Leshah, and Walt in Fast NeUtrott Physics (^2), was used with some variations to improve the computation time and to adapt to the different geometry. The idealized geometry for the Monte Carlo calculation is shown in figure (hk)a Neutrons are incident along the Z axis and are assumed to impinge on the center of the scatterer. Scattered neutrons which leave the sample and pass through a cylindrical band coaxial with the Z axis are tabulated. This band simulates the actual neutron detector placed in various positions to observe the angular distribution of the scattered neutrons. Table (h) lists the definitions of the quantities used, and the flow diagram for the computer code is shown in figure 0+5) 0 The cross-sections for the scattering material are specified for the energy of the neutron being scattered. The printed output of the calculation gives T, the number of neutrons leaving the sample; A, the number of neutrons absorbed; C, the number of neutron scattered more than three times; and N^  £ the number of neutrons hitting the band in angular interval i after having )) collisions. The first three TABLE h DEFINITIONS OF QUANTITIES USED IN FIGURE f>5) Quantity Definition N Number of neutrons which have been processed since the last print cycle N* Selected number of neutrons to be processed per print cycle T Number of neutrons which emerge from the sample A Number of neutrons which are captured in the sample C Number of neutrons which have been scattered more.than three times I., • Number of neutrons which hit the detection band segment in interval i after having )) collisions in the sample R Random number between zero and one x,y,z Coordinates of particle u,v,w Direction cosines in laboratory system ~h<$ Total mean free path ~t Probability of a particular neutron leaving the sample without a subsequent collision S Distance along neutron path from collision to edge of sample s' Distance along neutron path from collision to cylinder y 2 + z 2 = B2 ¥ Neutron Weight 1 Distance to next collision f - Ratio of <£ to Cl~ FIGURE '4-4- IDEALISED GEOMETRY FOR A DlFFENTlRL CROSS-SECT/ON MEASUREMENT: - 99 -quantities are recorded primarily to make sure the code is correct and that the computer is running properly. Some of the less obvious steps in the flow chart need clarification. The quantity t, which is the probability that a neutron will leave the sample before the next collision, is computed before each collision and the neutron weight reduced by the factor (1 - t). The distance to collision is set to — "Aj In 0 - 0 - t ) R j rather than-/^/nR , so that each particle is forced to make a collision within the sample. To show this let S be the distance to the edge of the sample and 1 the distance to the point of forced scattering. Then we want S . ^ & } Therefore / - exp ( - S /Xj) ^ » - e x p ( - 4 / A j ) . Given t = exp(-S/X3) ) then for some R, where O ± R 4*. \ R ( l - b ) = / - e x/of - ^ A P yielding - A 3 In ( j - C l - t ) R J = L The escape probability multiplied by the particle weight is considered to be the fraction of the particle which escapes and is tabulated as a successful event i f the trajectory intersects the detector band. The closed loop in the line starting (^defines a rejection technique for choosing the scattering#angle from a probability distribution determined by the differential - 1 0 0 -cross-sectionso The new direction cosines are chosen at random by selecting a direction from a distribution which is uniform over a sphere, and the scattering angle is computed by taking the scalar product of the directions before and after collision» This choice of angle is accepted in a fraction of the cases, that fraction being proportional to the differential cross-section for scattering into the selected angle. Random Cosine Generator (Refo 81) The problem is to choose a point (u,v,w) uniformly 2 2 2 on the unit sphere u + v + w = 1. The element of area for this sphere in spherical coordinates if , 0 is Sin X c\X d0 « - o W v y where <P is the longitude and w = cos ft . The probability density function p(w) is therefore given by For w w For <|> ^ f<j> r$ •7T Defining Q - </(uV v 7) = /6 -w' 1-) } the random cosines are then given by W = 2#, - / O £ R, £ / where R^  is one random number, and u = ^>cos<j> ^ V = ^cos <p - 101 -where fj) = ir(2 R x - /) O £ R v ^ I with ft} being a second random number* Table Searching Subroutine ...A table searching subroutine was required to look up the differential cross-section <T(/*) corresponding to one of 128 direction cosines. If the list were to be searched consecutively, an average of 6k comparisons would be required for each search. A subroutine was written which made the search using successive approximations thereby reducing the number of comparisons required to seven (since 2? = 128). This subroutine was also used to incre-ment corresponding to the cosine 0t* whenever a neutron hit the detection band. Three Dimensional Geometry to Determine S Three dimensional geometry was used to calculate the distance S of the scattering point (x, y, z) to the intersection of the trajectory of the scattered neutron with direction cosines (u,v,w) to the surface of the sample. The sum of the squares of the direction cosines is unity there-fore S a = S^iu^+v^^) (A-l) From the right angle triangle produced by the projection of the trajectory on the (x,y) plane through Z R c z= (y+Sv)V (x+Sv ) z (A-2) - 1 0 2 -Subtracting equation (A-l) from (A-2), S ' - ^ w ^ S V ( S v ) V S u ) M y + S v / ) * - ( x * S u ) z (A-3) which reduces to ( , _ w ^ ) Sz - f 2 ( v y 4 - u x ) S + (y2 + x2-R^)^0 Solving the quadratic (k-k) for S, S = -e -K- /e x-ar U-5) a where a = ( r - w 1 ) p e = {vy+ wx) and r = yx+ X 1-^ 1 . REFERENCES 1 . A. Wattenburg, Photo-Neutron. Sources and the Energy of Photoneutrons, Phys. Rev. 7 1 , ^ 9 7 ( 1 9 ^ 7 ) . 2 . E.W. Vogt (Private Cummunication). 3 . Hanson, Taschek, and Williams, Revs. Modern Phys. 2 1 , 6 3 5 ( 1 9 ^ 9 ) . h. J. T. Sample, PhD Thesis, University of B.C. ( 1 9 5 5 ) * 5. W. G. Cross and R. G. Jarvis, Phys. Rev. 99 > 6 2 1 (A) ( 1 9 5 5 ) . 6 . V. I. Strizhak, V. V. Bobyr and L. Ya Grona, JETP 13 ( 1 9 6 1 ) . 7 . L. F. C. Monier, G. E. Tripard, and B. L. White, Nucl. Instr. and Meth. ^5, 2 8 2 , ( 1 9 6 6 ) . 8 . R. C. Mobley, Rev. Sci. Instr. 3*f, 2 5 6 ( 1 9 6 3 ) . 9. C. V. Gorlov, N. S. Lebedeva, and V. M. Morozov, Zheft Pisma 5, No. *f, 1 3 1 ( 1 9 6 7 ) . 1 0 . Blair, Frier, Lamp, Sleator, and William, Phys. Rev. 7IK 1 5 9 9 ( 1 9 ^ 8 ) . 1 1 . i 9 6 0 Nuclear Data Tables Part 3 Page 2 6 Fig. 1 2 . 1 2 . M. White, Vacuum 1 5 , M+9 ( 1 9 6 5 ) . 1 3 . G. T. J. Arnison, Nuclear Instr. Meth. ^ 0 , 3 5 9 ( 1 9 6 6 ) . lh. G. E. Tripard and B. L. White, R.S.I., Vol. 3 8 , No. 3 PV35 ( 1 9 6 7 ) . 1 5 . ' (C2D^n from Merck Sharp and Dohme of Canada Ltd., Montreal, Canada. 1 6 . 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Infante and F. Pandarese in Nuclear Electronics Conference Proceedings, Belgrade, I96I (International Atomic Energy Agency, Vienna, 1962), Vol III, p. 29. 31. G. Jones, Rev. Sci. Instr. 3k, 938 (I963). 32. P. A. Tove and K. Falk, Nucl. Instr. and Meth., 12, 287, (1961). 33. G. Fabri and V. Svelto, Nucl. Instr. and Meth., 35 (1965). 3^ . R. A. Bell, N. G. Chapman and P. B. Johnson, Nucl. Instr. and Meth. 13 (1965) 35. L. W. Put, PhD Thesis, University of Amsterdam, 1965. 36. W. E. Stephens Phys. Rev. ^ 5, 513 (1931*-)-3 7 . Wo. Go. Cross. Rev. Sci. Instr 2 2 , 717 ( 1 9 5 D . 3 8 . Marion and Fowler ( i 9 6 0 ) , "Fast Neutron Physics," Inter-science Publishers IncD, New York. 3 9 . L. W. Put, Co Bot., W. J. Coenders, J. W. Koene, and J. Blok, Physica 3 2 , 1397 (1966). ^Oc J. H. Towle and W. B. Gilboy, Nucl„ Phys. kk, 256 (1963) . *+l. Do J. Hughes and R. B. Schwartz, Brookhaven National Laboratory Report BNL 325 , second ed. ( 1958) . *+20 J. B. Marion.and J , L. 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Cashwell and Everett, "The Monte Carlo Method", International Tracts in Computer Science and Technology and their Application (1959). 82. Ortec, Catalogue Number 1000 page 20. 83. Sergio DeBenedetti, "Nuclear Interactions" Section 3»3> publishers - John Wiley and Sons, Inc., New York (196>0. 

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