THE SOLID STATE PARTICLE DETECTOR and THE Be (d,a) Li REACTION by EDWARD GEORGE AULD B. A. Sc., University of British Columbia, 1959. A THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of Physics We accept this thesis as> confirming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1961. In presenting 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 of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the 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 reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives. It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Physics The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date August 15th, 1961. ABSTRACT The Important characteristics (the window thickness and energy linearity range) of an RCA type A solid state charged particle detector were measured for protons, trltons, and alpha particles. The window thickness varies from 150 Kev for protons to 1.00 Mev for alpha particles. The maximum energy of the linearity range varies from 5 Mev for protons to 20 Mev for alpha particles. The RCA detector was then used to study the reaction products from bombarding Be9 with .500 to 1.35 Mev deuterons. The following reactions were studied in detail: (i) the angular distribution of the alpha particle transition to the ground 7 9 7 (a,) and first (a ) excited state of Li in the reaction Be (d,a)Ll . The ground state trans-ition fits an analytical curve of the type: a+ bcos# + c cos#* , where 8 is the angle of emission in the centre of mass coordinates of the reaction products. The ratio a:b:c is approximately; (1): (-.7): (.5). Neglecting the minimum near 150 degrees in the distribution, if fits a curve of the type a + bcos5 + c cos20 where a:b:c is approxi-mately (1):(.4): (.15). Q (ii) the angular distribution of the triton transition to the ground state of Be in the reaction Be9(d,t)Be8. An indication of an alpha transition to a 5.64 - .11 Mev excited state in L i 7 was found. No indication of a 6.5 Mev level in L i 7 was found. Included as an appendix in this report, is a description of the recently installed Corona Stabilizer. The Corona Stabilizer supplies the feedback control that stabilizes the Van de Graaff accelerator energy at any set value. ACKNOWLEDGEMENTS The author wishes to thank Dr. K. L . Erdman for his assistance throughout all phases of this research. His suggestion especially on electronic problems, saved many hours of fruitless endeavour. Useful discussions with Dr. G. M . Griffiths and Dr. B. L . White aided considerably in the interpretation of the experimental results. Thanks are due to Mr. D. Lindquist for his many helpful suggestions con-cerning the operation of the Corona Stabilizer. The author gratefully acknowledges the receipt of an NRC Bursary and a scholarship from the British Columbia Telephone Company. TABLE OF CONTENTS Page I. INTRODUCTION: 1 II. THE SOLID STATE DETECTOR: A. Theory of Operation 1. Interaction of a Charged Particle in a Solid 3 2. Hole-Electron Pair Motion 4 3 . Production of High Fields in Semiconductors 7 4 . Noise in the Devices 12 5 . Variation of Signal Pulse with Reverse Bias 13 B. Characteristics of Solid State Devices 14 III. EXPERIMENTAL APPARATUS: 17 IV. RESULTS: A. Introduction 19 o 7 B. The Bev(d,a)Li Reaction 22 9 8 C. The Be (d,t)Be Reaction 25 D. Target thickness and Impurities 25 V. CONCLUSIONS: 28 APPENDIX I: Secondary Break-up of L i 7 " and Be8' 30 APPENDIX II: The Corona Stabilizer 33 SUPPLEMENTARY ILLUSTRATIONS 40 BIBLIOGRAPHY 66 LIST OF ILLUSTRATIONS In Body of Text: Figure Title Opposite Page 1. Excitation of Electrons in a Semiconductor 3 2. Parallel Plate Ionization Chamber 5 3. Electron Velocity vs Electric Field 6 4. Charge-depleted Region of a Solid State Detector 8 5. Solid State Detector Electric Field Configuration 10 6. Charge Collected vs Time in a Solid State Detector 11 7. Schematic: Output Pulse vs Incident Energy Relationship 11 8 . Actual: Output Pulse vs Incident Energy Relationship for Two Different Window Thicknesses 12 10. Pulse Height vs Incident Proton Energy & Proton Linearity Range for an RCA type A Detector 14 12. Typical Scattering Spectrum for Protons on Nickel 15 13. Variation of Charge-depleted Region with Reverse Bias 16 11. Increase of Device Noise with Neutron Flux 15 15. Target Chamber 17 18. Complete Reaction Products above Scattered Deuterons (160 degrees, .500 Mev) 19 19. Transitions Noted in this Experiment 20 20. High Energy Emission Products (160 degrees, 1.35 Mev) 21 Figure Title Opposite Page 21. High Energy Emission Products (120 degrees, 1.35 Mev) 22 22. High Energy Emission Products (105 degrees, 1.35 Mev) 23 9 31. Be plus Target Backing spectrum , and Target Backing Spectrum (1.00 Mev, 60 degrees) 24 32. Subtraction of two Spectra In Figure 31. 25 a 35. Proton scattered Spectrum from Be Target (1.600 Mev, 155 degrees) 26 9 36. Deuteron Scattering Spectrum from Be Target (1.35 Mev, 75 degrees) 27 39. Symbols for Discussion on Secondary Emission of Alpha Particles 30 40. Graphical method of Finding Laboratory Coordinate Velocities of Secondary Particles 31 42. Block diagram of Stabilization System 33 47. Schematic Diagram of Gain Analysis for Cascode Configuration 35 48. Schematic Diagram of Fluctuating Beam 36 Figure Title . . . . '•" Page 41. Schematic Diagram of Corona Stabilizer Circuits 56 43. Corona Needle Mount in Van de Graaff Tank 57 44. Circuit for the Motor Drive of the Needle Mount 58 45. Measured Characteristics of the Gas Triode 59 46. Diagram of 6BK4 Mount 60 49. Approximations to a Focused and an Unfocused Beam 61 50. Loop Gain Results for the Corona Stabilizer 62 51. Corona Stabilizer Characteristics . (Stabilization vs Relative Humidity and amount of Freon) 63 52 . Corona Stabilizer Characteristics . (Stabilization vs Needle Position) 64 53 . Corona Stabilizer Characteristics . (Stabilization vs 6BK4 Plate Voltages) 65 After Main Text: Figure Title . Page 9. Scale Drawing of RCA Counter (Type A) 40 14. Schematic Diagram of Experimental Set-up. 41 16. Target and Counter Geometry 42 17. Bias Supply and Pre-amplifier Diagram 43 23. Alpha Particle Angular Distributions (.500 Mev) 44 24. Alpha Particle Angular Distributions (.750 Mev) 45 25. Alpha Particle Angular Distributions (1.00 Mev) 46 26. Alpha Particle Angular Distributions (1.16 Mev) 47 27. Alpha Particle Angular Distributions (1.35 Mev) 48 28. Alpha Particle Angular Distributions (1.16 Mev) 49 29. Alpha Particle Angular Distributions (1.35 Mev) 50 9 7 7 ' 30. Fraction of Alpha Particles from Be (d.a)Li , Li , which go to the First Excited State, and the Alpha ^ Distribution at .500 Mev 51 33. Secondary Alpha Maximum Energies as a Function of Angle, for a Deuteron Energy of 1.35 Mev 52 9 o 34. Angular Distributions of Be (d,t)Be at deuteron Energies of .500, 1.16 and 1.35 Mev 53 37. Low Energy Spectrum of Reaction Products (1.35 Mev 45 degrees) 54 38. Low Energy Spectrum of Reaction Products from a Fonnvar Backing 1.35 Mev, 45 degrees) 55 I. INTRODUCTION The solid state detector is a relatively new tool for the charged-particle spectroscopist, having been developed in the past ten years. McKay and McAfee (51) were one of the original discoverers of the properties that led to the semiconductor di-odes usefulness in this field of study. Up until the past year most of the work in the field of these semiconductor charged particle detectors has been channeled into the con-struction and improvement of the devices. The symposium on Solid State Radiation De-tectors, Oct. 3-5, 1960, sponsored by the IRE professional group on Nuclear Science is a good example of the general pre-occupation on device characteristics. Now, however several groups are reported to be using these devices in different applications, such as: (i) nuclear reaction angular distribution measurements (Dearnaley, 61: Amsel et al. 61). (ii) electron detection (McKenzie and Ewan, 61). (iii) fission product measurements (Joyner et al. 61). (iv) fast neutron spectroscopy (Love and Murray, 61). One of the purposes of this investigation was to test the solid state devices adaptability to the study of nuclear reactions. The preliminary studies were done by using the device to detect the scattered protons from a thin Nickel target. Further studies of the devices characteristics were done with the reaction products of the bom-9 barding of Be with deuterons . 9 7 The main purpose of this investigation was to study the reaction Be (d,a)Li . Up until now, no one had adequately resolved the alpha.transitions.to.the ground and - 2 -first excited state of Li so that an angular distribution of these reactions could be measured. The angular distributions have been measured here at several energies. Other groups (Gelinas and Hanna, 53), have resolved these two alpha transitions using magnetic spectrometers, but their angular measurements were usually limited to one position. 7 The alpha transitions to the other excited states in L i were studied in less detail, however a search was made for a state near 5.5 Mev. A level near this energy has been predicted by Wildermuth et al (61). 7 The break-up of the excited Li nucleus into a triton and an alpha particle was studied to determine whether the 6.5 Mev state in L i ' existed. Similar studies have been done by Jung and Cuer (56). Wildermuth et al (61) have cast some doubt on the existence of this excited state. 9 8 The angular distribution of the reaction Be (d^)Be , was studied at three different energies. The reaction Be^(d,p)Be1^), Be1^ was not studied in any detail; the peaks corresponding to these transitions were only noted. t A A (a) (b) FIGURE l j (a) Excitation of Electrons i n a Semiconductor after the Passage of an Energetic Charged Particle. (To) Residual Excitation after a time of approximately 10" sec. - 3 -II. THE SOLID STATE DETECTOR: A. Theory of Operation 1. Interaction of a Charged Particle in a Solid: Charged particles lose kinetic energy rapidly through Interaction with the electrons of solids. For non-relativistic particles the maximum energy that can be transferred to an electron is approximately, Emax = 4Em/M, (I) where m is the electron mass and M} and E are the mass and energy of the heavy particle. In a semi-conductor these collisions may lift electrons from the valence to the conduction band but they may also lift electrons from deeper lying occupied bands. This is illustrated in Figure la . Electrons appear at various levels in normally full bands . This condition persists for only about 10"1 2 sec . , after which the excited electrons drop to lower levels in the unoccupied band and the holes fill equivalent positions in the valence bands as illustrated in Figure lb. During this de-excitation process, many more holes and electrons can be created. On the average this complex process results in the creation of one hole-electron pair for each 3.5 ev of energy lost by the incident heavy particle in Si (McKay and McAfee 51, 53). The final step in the de-excitation is the recombination of the electrons and holes in Figure lb. It is imp-ortant in semiconductor radiation detectors that the time for the last step not be too short. A low value for the energy "e" required to form a hole-electron pair is ad-vantageous in a counting device because the larger the number of electron-hole pairs produced per unit energy of the incident particle leads to a reduction in the statistical - 4 -fluctuations of the number of pairs produced. Silicon with an "e" of 3.5 ev per elec-tron-hole pair offers a substantial gain in this respect over an air ionization chamber, in which the value of "e" is of the order of 30 ev per ion pair. The energy gap between the valence and conduction band in Silicon is 1.1 ev. Shookley (60) has recently proposed a theory to explain why it takes 3.5 ev rather than 1.1 ev to produce an electron-hole pair in Silicon. He calculates "e" using constants determined from data on the quantum field for Photons (Vavilov, 59) in the visible and near ultraviolet (Chynoweth, 57). He obtains a value in good agreement with the measured 3.5 ev. The extra energy is wasted through strong coupling of electrons to lattice vib-rations of the solid. Experimentally no significant differences have been found in the value of "e" for a wide variety of particles and energies, although there must be a limit in which this is not the case. As a heavy primary particle slows down, it eventually comes to an energy below which the probability of producing pairs becomes very low and the principal inter-actions are Rutherford or hard-sphere collisions with the nuclei of the solids. Seitz (49) suggests that this energy is roughly t l _ 8m U ) where I is the lowest excitation energy of the electronic system, the band energy gap in the case of a semiconductor. For alpha particles on Silicon, E^ is about 1 Kev. This energy is less than the best resolution yet obtained with solid state detectors. 2. Hole-Electron Pair Motion: The holes and electrons created by a primary charged particle in a solid are FIGURE 2: (a) Semiconductor Parallel Plate Ionization Chamber with Hole-electron pairs produced by an Energetic Charged Particle, (b) Potential and Electric Field Distribution across the Chamber - 5 -analogous to the positive ions and electrons produced in a gas ionization chamber. The carriers drift in an electric field and give rise to an external current. The integral of the current, the collected charge, can be used as a measure of the energy deposited in the counter by the primary particle. Figure 2. illustrates the situation for either a solid state detector or a gas ionization chamber in parallel plate geometry. In the electric field the electrons move toward the left and the ions or holes toward the right. The contribution of each carrier to the total current has been derived by Brown (61). The current caused by one carrier is given by (assuming parallel plate configuration) i - 9 £ - (3) where q is the electronic charge, u the carriers mobility, V the voltage across the device and x in the spacing between the plates. The total current is the sum of contributions of this kind for all the charged carriers. For Silicon at room temperature the electron mobility u n is 1200 cm2/volt-sec. and the hole mobility U p is 500 cm2/volt-sec. The rise-time of the pulse in a solid state device is the transit time for a carrier across the device. where v is the carrier drift velocity under the electric field E . The transit time will be approximately 10 sec. for the mobilities in silicon, field strengths of 10 volts/cm and transit distances of 1 mm. This is a great deal faster than the rise-time in gas ionization chambers of comparable stopping power, principally because of the relatively small transit distance required in the solid state detector. Unfortunately, the mobility >-\-co UJ 2 Q 10 UJ or or z> o Q UJ N or o o 4.8 f2-cm. x 20 + 80 D 300 " + / o 8 1.210 .210 6 .2-10 o -\-O O _ l UJ > o or f— o UJ _ l UJ IO 10 10 ELECTRIC FIELD volts/cm. FIGURE 3: ELECTRIC FIELD DEPEITOENCE OF ELECTRON VELOCITY ttf ^ i L M A * ROOM * « A ' T U R E ' - 6 -is not a constant for high electric fields; there is an upper limit to the rise-time. Figure 3. is the work of Prior (60) and shows this effect. The vertical scale in the figure is proportional to the drift velocity of electrons. The linear increase in velocity with 3 electric field ceases at fields above 10 volts/cm and the maximum electron velocity at 10^ volts/cm has been obtained by increasing the electric field by a factor of 100. Trapping of holes and electrons can alter this simple picture considerably. There are structural imperfections and chemical impurities in solids which have significant capture cross-section for the drifting electron. These trapping centres do not nec-essarily destroy the electron by returning it to the valence band but they interrupt its contribution to the current. The electron may be released and trapped several times before it reaches the edge of the field. The current contribution by this electron will be a group of spikes of random length and at random intervals whose sum is equal to the contribution of one electronic charge. In many cases the release time from the trap is much longer than a microsecond and the rise time of a pulse at the amplifier may be unusually slow. The release time of these traps is a strong function of the temper-ature . (Shulman and Wylunda, 56). A trap at low temperatures (130 degrees K) becomes a recombination centre at room temperature. The carrier transit may be affected by recombination as well as trapping. A recombination may occur at a trapping centre if carriers of opposite signs are trapped. In the hole-electron track of a charged particle, as the electrons : drift one way and the holes the other, the two particle clouds will be moving through one another until they are spatially separated. If during this time a recombination centre is exposed to both - 7 -holes and electrons it can carry out the two-step process which results in the removal of one hole and one electron from the flow. The recombination time, commonly called the lifetime, involves the capture cross-sections for electrons and for holes and the den-sities of recombination centres. For particle detection the electron and the hole must complete the transit of the field without interruption. This sets a practical limit on the dimension x. The average time an electron remains free before being trapped by centres with a density N t and capture cross-section d n is: where v n is the thermal velocity of the electrons. For electron transit without significant trapping we require that Tr<< tn . A completely analogous situation exists for holes. Since tn can be as large as 100 usee, when appropriate care has been taken 7 to reduce the N f in the crystal, and considering the maximum drift velocity of 10 cm/sec., it should be possible to get transit without appreciable trapping across a distance of 10 cm. However, experimentally a realistic counter thickness is found to be of the order of 1 to 10 mm across the charge-depleted region. As mentioned, the density of trapping centres can be reduced to a point where tn is 100 usee, but according.to Brown (61) -7 -8 there are other considerations which limit tn to a value of 10 to 10 sec. In the p-n junction device where the carrier lifetime can be long there are other considerations which limit "x" to the same range. These considerations are discussed in the next section. 3. Production of High Fields in Semiconductors: The uniform field, parallel plate geometry can easily be achieved in a semi-conductor counter, but the need for a high DC electric field demands special attention hi SOLID STATE DIFFUSED JUNCTION DETECTOR Electron Band Levels for Detector - 8 -to the DC current. The magnitude of the current resulting from hole-electron pairs produced by a charged particle is in the order of 10"^ amps. For a good device this current should be very large compared with the noise fluctuations in the DC current of the device. Obviously a high resistivity is required before any solid state device o could be of any use. As an example; a device 5 mm in area and 1 mm thick made of 1000 ohm-cm silicon, will have a resistance of about 500 ohms. At a field of 10 volts/cm it would carry a current of .2 amps and develop 20 watts. Such a resis-tivity is not nearly high enough. A resistivity of 10^ ohm-cm, for the same sized device would give a noise current of about 0.02 microamps; a more useful level of noise. Ways in which the resistivity of the material may be increased are discussed by Brown (61), and will not be discussed here . There is a second way of achieving a high electric field in a semiconductor without having to use high resistivity material. This is through the use of a reverse bi-ased p-n junction. A discussion of the principles of operation of this device will be aided by referring to Figure 4. This is a junction formed by diffusing donor impurities to a shallow depth into the surface of originally high purity p-type material. In the RCA solid state counter, as used in these experiments, the p-type material is silicon and the shallow layer at the surface is phosphorous. In this configuration a charge-depleted region is formed between the p-type and n-type material. This region contains an equal number of positive donors and negative acceptors. Since the density of the acceptors is relatively low the charge-depleted region is much wider on the p-type side than on the n-type side. The potential difference between the two sides may be - 9 -0.5 volts and the region may be 10 cm wide. The electric field in the charge-depleted region may be reduced consider-ably by the cloud of holes and electrons produced by the passage of a charged particle. 1 ft 3 For a 1 Mev proton, in Silicon, the density of this cloud will be about 10 ° pairs/cm . The electric field in the region of this plasma will be much less than in the rest of the depletion region. Therefore only the carriers on the surface of the plasma will be affec-ted by the electric field. This plasma effect should increase the collection time beyond the simple transit time of a single charge in the field. An indication of an increase in collection time which may be attributed to this effect has been observed in fission fragment counting (Miller et al, 60). The charge depleted width x may be increased with reverse bias. In the type of junction shown, the magnitude of xp or x is given by: where X p and x Q are the widths of the charge-depleted region in the p-type and n-type material. V 0 is the potential barrier at zero bias volts V and is the concentration of ionized impurity centres in the region considered, and k is the dielectric constant for the p-type material. In a diffused junction, x /xn= (dn/d )2 may typically have o a value of 10 , where d n and d p are the conductivities of the n and p-type regions. Thus the major portion of the depletion region exists beyond the junction into the bulk of the p-type silicon, and only a small region exists in front of the junction approaching the surface . The charge-depleted region does not extend right to the surface of the n-type region, leaving a particle insensitive window. Since die resistivity of the material (6) is ( 7 ) P = JUNCTION D E T E C T O R •max FIGURE 5: (a) Electric and Potential Field for a p-n junction detector under reverse bias, (b) Current wave shape resulting from a hole produced at maximum field. - 10 -where n and p are the concentrations of electrons and holes, the width of the depletion region or sensitive depth of the device is proportional to (upV)2 . From this it can be seen that the combination of high resistivity and high applied voltage is required to utilize detectors that respond linearly to highly penetrating particles. k The maximum applied voltage that can be used is governed by the reverse current noise level of the device. This level increases with increasing applied bias voltage. The electric field in the charge-depleted region is not a constant. It is zero at the edges of the region and a maximum at the inner edge of the donor concentration, as shown in Figure 5a. The maximum field is given very approximately by; Emax«y8qNiVA (8) 4 A representative value of Emax is 10 volts/cm. When a charged particle Is incident on the face of the device the resulting holes and electrons will be swept out of the charge-depleted region by this field. The current due to the motion of one carrier is (Brown 61), i - f - « where E is the local electric at the position of the carrier. The total current is the sum of the contributions of this kind from all of the carriers produced by the charged particle. The shape of the current pulse in time, assuming constant mobility, is i=[u pE^q/v]e- ( 2 uPE m tA ) (10) for carriers created at the position of the maximum field E r n . This current pulse is shown in the second half of Figure 5b. Hole-electron pairs created outside the charge-depleted region do not contri-FIGURE 6: CHARGE COLLECTED VS TIME INCIDENT E N E R G Y FIGURE T: OUTPUT PFLSE VS INCIDENT ENERGY -11 -bute to the current immediately. This will occur every time a particle passes through the thin dead window in front of the charge-depleted region and every time a particle passes right through the region without losing all of its energy. These free holes and electrons will diffuse about in the field free region and may come to the edge of the charge-depleted region where one or the other type (depending on whether the region is in front of the active area or behind it) of carrier will be swept across. This second contribution to the current pulse caused by an incident charged particle, will occur much later after the main contribution from the active region, and will be much broader in time, (see Figure 6). Carriers in the field free region diffuse a distance given by: in a time t , where D=ukT/q is the diffusion coefficient. The possibility of ever observ-ing a carrier created outside the charge-depleted region depends upon the lifetime in the material, since the lifetime process is working to destroy the carriers that have been produced. In silicon D is 10 to 30 cm2/sec so that in 10"? sec. carriers will diffuse _3 approximately 10 cm. Collection through diffusion is slow if It is to be used over significant distances, and because it requires long lifetimes for good collection efficiency, it is not a very useful way of extending the sensitive region of a junction particle det-ector . The thickness of the charge-depleted region limits the energy range of the solid state device, but the "window thickness" of the surface layer may limit the line-arity of the output pulse vs incident charged particle energy relationship. Because of the variation of the dE/dx for charged particles with energy, the dead window will cause low 5 r FIGURE 8: ENERGY AFTER WINDOW OIMFUT POISE VS IHCIDEICTEMERGY; RCA DEVICE WITH TOO DIFFERENT WTHDQW THICKNESSES X l^t THICKNESS 0 IO/i T H I C K N E S S i \s Y I l lZ_L INCIDENT ENERGY - 12 -energy particles to lose more energy in passing through it than higher energy particles. This effect is shown in Figure 7. Figure 8 shows the possible effect on an RCA device witii different dead window thicknesses . The surface barrier detector (Dearnaley, 61) which works under the same principles as the diffused junction detector has the advantage that its dead window thick-ness is zero. Unfortunately, at the present level of development, its charge-depleted region is considerably thinner than a diffused junction region using the same resis-tivity silicon. 4 . Noise in the Devices . All junction devices have leakage currents under reverse bias that arise from several sources: 1. diffusion 2 . space charge generation (Sah et a l . 57) 3. surface effects. (Kingston, 56: Garrett et a l . 56) The first is a current due to the small equilibrium density of electrons in the p-type material. The electrons can diffuse to the charge-depleted region edge and contri-bute current. This is the normal reverse current found in all solid state diodes, and is of little importance in silicon devices at reasonably low bias voltages (50 volts cr less for the old RCA type A and 75 volts for the new). The second current is due to recombination centres in the charge-depleted region. Here the centres generate holes and electrons in succession at a rate depending upon the cross-sections and density of such centres and their location in the energy band - 13 -gap. The rate depends roughly upon inverse lifetime. This contribution can be very significant and it has a dependence on the junction bias because the number of centres inside the charge-depleted region increases with x. The third current contribution is the most serious in most devices and is sub-ject to change, as the surface chemistry at the edge of the junction changes with time and environment. It i s , of course, not the current magnitude that matters but the fluctuations in the current, and it seems that the surface generated currents often contain much more than shot noise. The origin of the surface current is stil l open to some question, a l -though a number of features seem explicable on models of junction leakage such as pro-posed by Kingston (54). 5 . Variation of Signal Pulse with Reverse Bias . If a voltage sensitive pre-amplifier is used in conjunction with the solid state device,Jthe overall resolution of the system will be decreased, because of the effect the reverse bias has on the ouput voltage signal of the device. The signal pulse from the device, is: vs= §- (i) where Q is the charge collected from the passage of a charged particle of energy £ through the device. For Silicon: 0 = ( E - 3E W > ' - 6 1 0 " 9 (2) where £ is the energy the particle loses in passing through the dead window of the w device. C is the total output capacitance to the pre-amplifier. It includes the device capacitance , and all the stray capacitances C g . Normally is much larger than FIGURE 10a: 1.0 2 .0 INCIDENT PROTON ENERGY t.O 2.0 3.0 4 .0 5.0 INCIDENT PROTON ENERGY - 14 -C g , so for simplicity assume that 0 = 0^. From the parallel configuration of the charge-depleted region of the counter: where A is the counter area, x is the charge-depleted region thickness and k is the di-electric constant of silicon (13.32-10" 1 0 farads/meter) From (1) and (3): V s OC x But: x « / V b + V 0 Therefore: V s « ^ V b + V 0 To avoid this situation, a charge sensitive pre-amplifier can be used. Then the output pulse from the pre-amplifier will be proportional to the total charge Q. Q is a slowly varying function of the bias voltage as the energy loss E w in the device window changes with bias. However this effect is small compared to the change of with respect to the reverse bias . B. Characteristics of Solid State Devices. Before using these devices for the detection of charged particles in an exper-ment, several of their properties must be known. The more Important ones are: (1) the linearity of the output pulse vs the incident energy of the particle. (ii) the range of partfcle energy over which the linearity holds. (iii) the dead layer thickness. This determines the amount of energy an incident particle loses before it reaches the active region of the device. (iv) the capacity of the device (the parallel plate configuration of the 5 10 4 _J to UJ z: z X 10 O or 00 3 O 10 o FIGURE 11: \ INCREASE OF DEVICE NOISE WITH NEUTRON FLUX N ^ ^ 5 S S Q ^ ^ X COUNTER in a -FLUX. o COUNTER in n-FLUX +C0UNTER in nSa-FLUX ^^^^^x. ^^^^^^ 2 4 6 8 10 12 14 16 18 2 0 CHANNEL NO. 4 lO 3 _ l 1 0 UJ z z < X O 2 rr 1 0 UJ QL CO Z 3 10 O O • " V 5 0 v. FIGURE 12: / \ • J - ^ , 5 v -SCATTERED PROTONS / 7^"r» \ ' FROM A THIN NICKEL TARGET / ^ \ Reverse Bias o f Detector / \ i s v a r i e d . \ \ V 1 1 1 1 1 2 0 4 0 6 0 8 0 100 C H A N N E L NO. - 15 -charge-depleted region). (v) the effective lifetime of the counter when it is subject to the radiation damage caused by any particle impinging on its surface. For all experiments an RCA type A charged particle detector was used. A scale drawing of it and its mounting (as supplied by RCA) is shown in Figure 9. Figure 10a shows a plot of pulse height vs incident proton energy for one of these devices. The slight increase in the slope for the lower device bias voltages shows the effect of the change in the device capacitance. The increasing energy intercept with decreasing bias is caused by the increasing window thickness. The slopes and intercepts were calculated by the usual least squares method. The protons were obtained by scattering a beam on a thin Nickel film. A typical scattering spectrum is shown in Figure 12. Figure 10b shows the range of linearity for protons. The high energy protons were obtained from the reactions Be9(d,p)Be10 (Q=4.59 Mev) and Be9(d,p)Be10 (Q= 1.22 Mev). The proton peaks are Identified in Figure 18 of Section IV-A. Estimating the dE/dx of the protons in silicon from Whaling (58), gives the thickness of the charge-depleted region as .16 mm at 60 volts reverse bias. This compares favourably with .115 mm at 40 volts bias, as calculated from the know pulse height and capacitance relationships shown in equations (1) and (3) of section II-A-5. These results were ob-9 tained using a different device than that used to look at the Be reactions. Figure 13 shows the variation of the thickness of the charge-depleted region and of the capacitance with reverse bias, and also shows the thickness and capacitance values for the device used in the Be9 reactions. For the calculations the stray capacitance of the wiring ZOO-FIGURE 13: VARIATION OF CHARGE-DEPLETED REGION WITH REVERSE BIAS 0 / 10 2 0 3 0 4 0 5 0 R E V E R S E B I A S 6 0 • Region Thickness Alpha Measurements X Region Capncifcfcnce Alpha Measurements 0 Region Thickness Proton Measurements Region Capacitance Proton Measurements - 16 -oucside the device was assumed to be 5 pf. These measurements were done using a vol-tage sensitive pre-amplifier. Enumerated below are the counter characteristics for alphas, protons and tritons. Counter Characteristics: Proton Triton Alpha Reverse Bias (volts) 60 10 60 10 60 10 Window loss (Mev) .200 .450 - .500 .750 .850 Maximum of Linearity Range (Mev) 4.60 2.60 - 4.00 - 8.00 These values will vary about 10% for different devices. The pulse-height vs incident energy curves for alphas and tritons is essentially the same as that for protons; the only differ-ence being that caused by the fact that the dE/dx for alphas and tritons is larger, hence making the window thicker and the linearity range larger for the alphas and tritons. Radiation damage is the limiting factor for the useful lifetime of a solid state device. According to Babcock, (61) the reverse current of the device increases about flve-13 9 fold during an exposure to 10 neutrons per cm z . At this level of integrated neutron flux the device capacitance was found to increase by about 25%. A 1000 hour room temperature anneal restores about 50% of the change caused by this total irradiation. A neutron flux of 7X10^ per cm^per sec. was found to increase the counter noise by a factor of two while it was being used, as illustrated in Figure 11. The largest integrated flux of charged par-10 2 tides and neutrons reached by one device in this lab was 10 per cm . This caused no measurable change in the properties of the device. Because of electronic considerations, the maximum counting rate allowable was 5 6 about 10 counts/second. This corresponds to approximately 2x10 particles per sec per 2 13 2 cm . To reach a total Integrated flux of 10 particles per cm means approximately 1400 hours of continuous running. DETECTOR MOUNT VACUUM S E A L EZZZZZ ROT A T A B L E S H A F T FIGURE 15 TARGET CHAMBER SCALE: £ FULL SIZE COVAR S E A L S FARADAY CAGE ASSEMBLY B E A M T R A P LUCITE INSULATO.R F L A T INSERT IN CYLINDRICAL C H A M B E R •f L U C I T E MOUNT SS D E T E C T O R SIDE-ARM COUPLING 2 - 17 -III. EXPERIMENTAL APPARATUS: A schematic diagram of the experimental set-up is shown in Figure 14, and the target chamber in more detail in Figure 15. The target chamber was designed so that the Solid State counter, mounted inside on a rotatable shaft, would subtend a small angle without making the overall chamber size too cumbersome. The RCA type A counter, used in the experiments, has a 5 mm 2 window area. This window has an angular width of 1.1 degrees and sub-tends a solid angle of 1.3 steradians at 6 cm from the target. The energy variation of a charged particle lias a function of angle due to kinematical effects is much less than 1% (the approximate resolution of the counter) in the chosen geometrical arrangement. The general target and detector geometry is shown in Figure 16. The counter was mounted to a lucite holder with an epoxy resin (R-313), and was shielded with a copper strip which allowed particles, to enter the device window only when they came from the target areas. The counter holder is small enough to allow the beam to hit the target while the counter is sitting at a backward angle of 165 degrees. The central post has a vacuum seal that allows the counter to be rotated 360 degrees. The necessary electrical lead goes through one of the covar seals in the central post of the counter-mount assembly, and connects to an amphenol plug at the other end of the mount. The counter bias supply and the pre-amplifier are mounted directly on the target chamber. The bias supply is a battery and potential divider, to vary the bias voltages. The pre-amplifier is a charge-sensitive type similar to that built by Higin-botham (61). The pulses from the pre-amplifier were fed directly to the main amplifier - 18 -of the Nuclear Data 256 Channel Pulse-height analyzer, which was used to record all the reaction spectra. A diagram of the bias supply and the pre-amplifier is shown in Figure 17. Section II-B gives a detailed description of the solid state counters used in these experiments. TARGETS: The Nickel targets, used for the proton scattering experiments to measure the solid state device characteristics, were obtained from Chromium Corporation of America. The Beryllium targets were made by the evaporation of Be metal on a formvar film backing. All evaporations were done in vacuums of 10"^ mm Hg or less. The Beryllium was evaporated onto the Formvar until the white-hot Tantalum boat, contain-ing the melted Beryllium was no longer visible through the film. Stopping the evapor-ation at this point gave a layer of Beryllium approximately 5000 A thick. Attempts were made to remove the formvar backing from the Beryllium by bathing the target in an atmosphere of Trichlorethylene. However, all attempts at removal were unsuccessful, so the Carbon contamination from the formvar had to be taken into consideration. 70Q-FIGURE 18 REACTION PRODUCTS 60Q> 1400-3 O 0 -L U < X o cr 1x1 o_ CO o o 2 O 0 -2 0 H 4 0 6 0 H" 8 0 lOO POSITION OF PEAKS IF DEVICE WINDOW-THICKNESS WAS ZERO D E U T E R O N O N Be E d = .500Mev at 160° 120 140 160 CHANNEL NO. J' E' F' D' D B 180 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 2.0 _1_ 3.0 I 4.0 l_ E a CALIBRATION 1.0 2.o i 3 D i 4.C E p CALIBRATION - 19 -IV RESULTS: A. Introduction: 9 The following reactions from Be were observed and studied: 9 7 (1.) Be (d,a)Li : The angular distributions of the alpha decay to the 7 ground state and first excited state of Li were studied in detail at deuteron energies of .5 to 1.35 Mev, and the angular distribution of the alpha decay to the 4 .5 Mev ex-7 cited state of L i was measured at a deuteron energy of .500 Mev. This 4.63 Mev state was first discovered by Gove and Harvey (51), and also noted soon after by Gelinas et al. (51) and Ashmore and Raffle (52). An alpha group to an excited state at approxi-7 mately 5.5 Mev in L i was looked for at deuteron energies from .5 to 1.00 Mev. 9 8 (2.) Be (d,t)Be : the angular distribution of the triton decay to the ground 8 state of Be was studied at deuteron energies of .5 to 1.35 Mev. (3.) Be9(d,a)Li7 , (t)a: 9 8' Be (d,t)Be , (a)a: the wide continuum of charged particles from 7" 8' these reactions due to the short lifetime of the L i and Be nuclei was noted and compared with the findings of Gelinas and Hanna (53) and Jung and Ciier (56). (4 .) Be9(d,p)Be^: the peaks corresponding to the proton to the ground state and first excited state of Be1^ were noted. Several reactions from target impurities were noted: (i) C 1 2 (d ,p)C 1 3 , C 1 3 ' (iv) 0 1 6 (d ,a)N 1 4 , N 1 4 ' (11) C 1 3 (d,a) B 1 1 ' , B 1 1 " (v) 0 1 6 (d,p) 0 1 7 , 0 1 7 ' (ill) C 1 3 (d,t) C 1 2 (11.237) V/7/A 2 . 9 0 8 B e + t (11.230) 17.5 B e + d + E U 5 . 8 2 2 ) Be + d \ \ \ \ 16.93 16.77 ( 4 . 4 6 ) 2 . 4 6 5 a + a + t (2.13) (11.135) I I Li7+ a ( 8 . 6 7 0 ) B FIGURE 1 9 : TRANSISTIONS NOTED IN THIS EXPERIMENT - 20 -Typical spectra of the reaction products, as detected by the charged part-icle detector are shown in Figures 18, 20, 21 and 22. Figure 18 shows the complete spectrum of reaction products above the scat-tered deuterons at an angle of 160 degrees with respect to the Incident deuteron beam of .500 Mev energy. As an aid to identifying the peaks with their corresponding transi-tions refer to Figure 19, where all the transition, except one, found in this spectrum are marked. Starting from the high energy side of the spectrum: A: is the proton to the ground state of Be*^ in the reaction Be^d.pjBe1^. 7 B: is the alpha particle to the ground state of L i in the reaction 9 Be (d,a)Ll 7 . 7 C: is the alpha particle to the first excited state of Li . D: is the triton to the ground state of Be8 in the reaction Be^(d,t)Be8. 1 o 12 13 E: is the proton to the ground state of C10 in the reaction C (d,p)C (This transition is not shown in Figure 19). F: is the highest possible energy of the alpha particles from the second-ary emission of alphas from the excited states in Be^ and L i ' ' . In Appendix I, an analysis is done on the possible energy range of these particles. J; is the highest energy of the tritons from the secondary emission of the excited states in L i 7 . G: is the proton to the first excited state in Be*^. H: is the alpha particle to the second excited state in LI . Because of the different energy losses for alphas, tritons etc., in the device window, the channel numbers on this and subsequent spectra do not correspond to the - 21 -same energy calibration for the different particles. Each particle has its own calibration as shown by the different scales in Figure 18. The arrows on Figure 18 correspond to the positions where the peaks would occur if the solid state device had no: window. All energy vs channel calibrations were made using the fact that the reaction product energies change with the angle of emission. For an Incident deuteron energy of 7 1 Mev, the energy of the alpha particle to the ground state of L i is 4.02 Mev at an emis-sion angle of 165 degrees with respect to the beam direction and 6.11 Mev at 30 degrees with respect to the beam direction. The energy variation for tritons, deuterons, and protons is not as much, but it is still sufficient to obtain a reasonable calibration curve that enables other energies to be measured with 5% accuracy. Figures 20, 21 and 22 show the effect of the emission angle on the high energy end of the reaction product spectrum. The bombarding deuteron energy is 1.35 Mev. Figure 20 shows the emission products at 160 degrees and Figure 21 at 120 degrees. Several reaction and kinematlcal effects can easily be seen in Figures 20 and 21. They are: (i) the energies of the alpha particles to the ground and first excited 7 state of Li change much more rapidly with die angle than does the energy of the proton 10 s to the ground state of Be and the energy of the triton to the ground state of Be . This effect can be noted by the relative change in position of the peaks in Figures 20 and 21. (Ii) the reaction cross-section changes as a function of the angle as can be seen by the change in the peak heights between figures. The integrated beam of deuterons is the same for all these spectra (40 microcoul.) COUNTS • 8 0 0 h 6 0 0 k o o - 2 0 0 FIGURE 21: HIGH ENERGY EMISSION PRODUCTS E,: 1.35 Mev at 120 degrees a / J . 8 0 1 0 0 1 2 0 1 4 0 160 2 0 0 CHANNEL NO. - 22 -The highest energy proton peak (A) in Figure 21 shows a distinct broaden-ing and assymetric effect from that in Figure 20. At 120 degrees, these protons have enought energy to pass right through the charge-depleted region of the solid state device at a reverse bias of 60 volts. The straggling effect on the peak is caused by the non-uniformity of the charge-depleted region thickness. In order to further study the reaction spectrum at lower angles this broad proton peak had to be shifted from the interesting part of the spectrum. This was done by decreasing the reverse bias of the device? by a factor of 4; hence decreasing the charge-depleted region thickness by approximately a factor .2. This thickness still stops a high energy alpha or triton, but the proton now loses only about half of its energy in the charge-depleted region: hence the peak (A) corresponding to protons from Be9(d,p)Be1^ is shifted far to the left in the spectrum as shown in Figure 22. With a reverse bias of 15 volts, the charge-depleted region is still thick enough to stop approximately 10 Mev alpha particles. 9 7 B. The Be (d,a)Li Reaction: The angular distributions of the alpha particle transition to the ground (a )^ 7 and first (a ) excited state of Li were measured at deuteron energies of .500, .750, 9 1.00, 1.16, and 1.35 Mev, using two targets of Be on Formvar. These distributions are shown in Figures 23, 24, 25, 26 and 27. The distributions at .500, .750 and 1,00 Mev were taken with the same target. As can be seen from Figure 16, reaction products from 90 to 165 degrees were measured from the beam entrance side of the target, and products from 90 to 15 degrees - 23 -were measured from the beam exit side of the target. To change the counter from a position of 95 degrees with respect to the beam direction to 80 degrees, required a rather long angular movement. This movement could easily have caused the whole target chamber to be moved lightly, thus moving the position where the beam would hit the 9 target, j Since the target does not have a uniform thickness of Be , the reaction yield could easily change . This effect was thought to have caused the small peak near 90 degrees in the distribution of at energies of .500, 1.16 and 1.35 Mev. So further measurements were made at 1.16 and 1.35 Mev, making sure the chamber did not move and using a target of more uniform thickness. These distributions are shown in Figures 28 and 29. The small peak at 90 degrees in the a^ distribution still remains after these precautions, but the distributions of a± shows a minimum near 60 degrees indicating that the target may have shifted for the previous measurements. The absolute cross-section for these reactions cannot be accurately determined with these results because of the uncertainty of the target thickness measurements. However the cross-section for the reaction is estimated to be between one and five mb/ steradian. 9 1 i Figure 30a shows the fraction of the alphas from Be (d,a)Li , L i ' , which go to the first excited state at an emission angle of 90 degrees In the lab coordinates. These results are in good agreement with those reported by Gelinas and Hanna (53). The angular distribution of the alpha particles to the second (a )^ excited state In Li was measured for a deuteron energy of .500 Mev. This distribution is shown in Figure 30b. The larger absolute errors in these measurements occur because the alpha 1 8 0 0 1 4 0 0 COUNTS PER CHANNEL 1000 6 0 0 2 o a SCATTERED DEUTERONS d 2 (d,p)C 1 3 (E) FIGURE 31. SEARCH FOR NEW L i 7 LEVEL PLUS TARGET BACKING SPECTRUM - TARGET BACKING SPECTRUM = 1.00Mev a t 6 0 ° 4 0 100 120 140 CHANNEL NO. 3,0 2 4 0 2 6 0 4£_ CALIBRATION - 24 -spectrum was super-imposed on the continuum of secondary emission particles. The width of the second excited state was measured from the width of the alpha peak in the spectrum and was found to be 130 - 30 Kev, as compared with the value of 93 ± 8 Kev obtained by Browne (57). An alpha transition to a level around 5.5 Mev was looked for at several 9 energies (.500 to 1.35 Mev) and several angles. Because the target was not pure Be as shown from the elastically scattered proton spectrum (Figure 35), no peak can be positively identified as the looked-for transition. However, by subtracting a spectrum g of reaction products of the target backing from a spectrum of reaction products of Be 9 plus target backing a fairly reliable spectrum of reaction products from only Be can 9 be produced. Figure 31 is the spectrum from Be plus target backing and the spectrum from the target backing at an angle of 60 degrees and a deuteron energy of 1.00 Mev. Figure 32 shows the subtraction of the two spectra. The peak marked by " U " corresponds to that of 1.76 Mev alpha particle. This corresponds to an excited state of 5.64 - .11 7 Mev in the Li nucleus. Other indications of this transition showed up at forward angles of 50 to 75 degrees and at energies of .700 to 1.00 Mev. 7 No positive indication of a transition to a level near 6.5 Mev in Li was found. A peak corresponding to an alpha transition to this state would be hidden in the scattered deuteron peaks from the target, because of the window thickness of the device. There is, however, another way of testing whether this 6 .5 Mev excited state exists . That is by looking for its break-up into a triton and an alpha particle. The maximum possible 8 energies of an alpha particle from the 2 .90 Mev excited state in Be and the 4 .63 Mev COUNTS PER CHANNEL 1800 h 1 6 0 0 h 1400 1200 lOOOr 8 0 0 600*-400Y 200I-FIGURE 3 2 . SEARCH FOR NEW L i 7 LEVEL DIFFERENCE OF THE TWO SPECTRA IN FIGURE 31. 2.0 i 120 140 CHANNEL NO. 3.o i 4 . 0 l _ CALIBRATION - 25 -and 6.5 Mev excited states in L i have been calculated in Appendix 1. Figure 33 shows . a graph of the calculated maximum energies as a function of the emission angle, for a deuteron bombarding energy of 1.35 Mev. The experimental points on the figure show the measured maximum energy of the alpha continuum for a 1.35 Mev deuteron beam. As 7 can be seen, there is no indication of an alpha particle from the 6.5 Mev state in L i . 7 A similar check on the maximum triton energy from these excited states of Li could 12 13 ,. not be done because the proton peak from the C (d,p)C reaction obscured the end of the triton continuum. Jung and CUer (56) have done this check on the maximum triton energy. 7 Their results indicate a triton from a level at 6.6 Mev lh Li . C. . The De9(d,t)Be8 Reaction: g The angular distribution of the triton transition to the ground state of Be was measured at deuteron energies of .50, 1.16 and 1.35 Mev, as shown in figure 34 . These distributions are in good agreement with those reported by: Smither (57) and Haffner (56). D. Target thickness and Impurities . 9 The thickness of the Be target was measured by looking at the spectrum of elastically scattered protons from the target. Figure 35 shows the scattered spectrum at 155 degrees with respect to die proton beam of 1.600 Mev. The integrated proton beam was 6 . » microcoul. As shown on the figure, the lowest energy peak is that from scattering on Be^ nuclei, the middle peak is from scattering on C nuclei and the high 16 energy peak is from scattering from 0 . The target thickness was measured by two independent methods-(i) calculating the target thickness from the Rutherford Scattering formula, COUNTS 5 0 0 0 4 0 0 0 3 0 0 0 -2 0 0 0 1 0 0 0 FIGURE 35: SCATTERED PROTON SPECTRUM E ; 1.600 Mev at 155 degrees P 2 0 _ i I I L 4 0 6 0 8 0 CHANNEL NO. - 26 -after integrating the counts in the Re peak. 9 (ii) measuring the width of the scattered proton peak from Be and c a l -9 culating the thickness from the know dE/dx for protons in Be . The thickness as meas-ured using the Rutherford formula and the integrated proton flux was about 3 times higher than that measured by the known dE/dx values. This discrepancy may be due to in-accuracy in measuring the beam current passing through the target. The target was at ground potential; hence any electrons knocked out of the target by the impinging protons and in the direction of the proton beam would be collected by the Faraday Cage. These electrons would cause the current reading to be lower than the true beam current. Hence the integrated beam value would be lower than the true value and the.resulting target thickness calculation would be higher than the true value. Any absolute cross-section measurement can only be estimated within a factor of 3. The impurities in the target were more easily determined by looking at the scattered deuteron spectrum. Figure 36 shows the elastically scattered spectrum plus three low energy reaction products at 75 degrees witii respect to the 1.35 Mev deuteron l ? 14 beam. By checking the energy variation of the scattered deuterons from C , N , and O1^, the C1"^ and 0 ^ impurities were identified. The reaction products shown in Figure 36 are: M: an alpha transition to the first excited state in N 1 4 , from the reaction 0 i 6 ( d , a ) N 1 4 * . N: an alpha transition to the second excited state in B* 1 from the reaction C l 3 ( d , a ) B 1 1 * * . COUNTS 5OOj0r 4 0 0 0 3 0 0 0 FIGURE 36; SCATTERED DEUTERON SlfiCTRUM E d ; 1.35 Mev at 75 degrees 2 0 0 0 r IOOO _ l l _ 0 2 0 4 0 6 0 8 0 C H A N N E L N - 27 -O: a proton to the first excited state of C in the reaction C (d,p)C Figure 37 shows the low energy spectrum at an angle of 45 degrees with respect to the 1.35 Mev deuteron beam. The large peak marked "P" is the recoil protons from the deuterons hitting the hydorgen in the formvar backing. Figure 38 shows the spectrum of low energy products at 45 degrees with respect to the 1.35 Mev deuteron beam for a formvar target only. The reaction products due to the Oxygen contaminants are not present in this spectrum, thus suggesting that the oxygen on the targets may have been picked up during the evaporation of the Beryllium. - 28 -V. CONCLUSIONS: The solid state charged particle detector has proved itself to be an invaluable tool for studying low energy nuclear reactions. Because of its small size it can be used for studying the angular distributions of reaction products. Because of the fast rise-time of its signal pulse(10"8 sec), it can be used to study particle-gamma ray correlations and particle-particle correlations. Because of its good resolution, it can resolve the elastically scattered particles from different nuclei, making it an excellent device for target thickness measurements. Because of the devices 100% efficiency in detecting charged particles care must be taken to keep the flux of charged particles incident on the device below 10 ^ per second. Any higher count rate would tend to swamp the elec-tronics . 9 7 This study of the Be (d,a) Li reaction has yielded several interesting results and has indicated further experiments that should be run on this reaction. 7 The angular distribution to the ground and first excited states of Li have been fairly well established between the deuteron energy of .5 and 1.35 Mev. Unfor-tunately the absolute cross-section for the reaction could only be estimated to be between one and five mb/steradian. A further study of the reaction cross-section of these two transitions, as a function of energy would be of interest, to help determine whether there is compound nucleus formation during the reaction. The Indication of an alpha transition to a 5.64 ± .11 Mev excited state in L i 7 is weak, because of the reactions with the target impurities. To check the validity of this indication, the reaction must either be run using a pure Be^ target, or be run using - 29 -a magnetic spectrometer. The fact that the maximum energies of the alpha contiuum do not indicate 7 an excited level near 6.5 Mev in Li does not mean this level does not exist. It does mean, however, that the cross-section for populating this level is considerably lower 7 than the cross-section for populating the 4 .63 Mev excited level in Li . An excellent 7 way of studying these excited states of Li that break up into a triton and an alpha particle would be to run an alpha-triton or alpha-alpha correlation experiment. FIGURE 39a: PARTICLE VTlILOCrTIES IN CENTER OF MASS AND LABORATORY COORDINATES P R I M A R Y R E A C T I O N FIGURE 39^: PRODUCTS OF PRIMARY AND SECONDARY* REACTIONS L ' S E C O N D A R Y R E A C T I O N - 30 -APPENDIX I 7 " R' Secondary break-up of L i ' and Be° . The secondary emission studied in this Appendix is the particle break-up of the: o (i) first (2 .90 Mev) excited state of Be into two alpha particles: (ii) second (4 .63 Mev) and third (6.54 Mev) excited states of L i 7 into an alpha and a triton. These transitions are shown in Figure 19. In calculating the possible range of energies for these particles, it is assumed that the parent nucleus has not lost 9 8' 9 7 " any of the recoil energy it received rom the initial reaction Be (d,t)Be or Be (d,a) L i ' , L i . If the excited nucleus was at rest before the secondary emission occured the energy of the secondary particles would be single-valued. As can be seen from the spectra in figures 18 - 22 the energy is far from being single-valued. Therefore, the assumption that the excited nucleus has lost little of its recoil energy is, at least to a first order approximation, a good one. The lab energy of the excited nucleus from the primary transition is: - | ^ = A [ c o s £ + (C/A-sin2eFf where: E^ = energy of the excited nucleus d 1 ^ V12Sml " V p l L Vp is the 6BK4 plate voltage, rearranging (2) gives V p = r p l ( V 1 2 g m l " i )• (2') (3) i = V o- - V. /r „ vpSm2 p2 g m l is the transconductance of the 6BK4 triode. g m 2 " " gas triode. r is the plate-resistance of the 6BK4 triode , Pi P2 Substituting (2') into (3) and using (1) gives: gas triode. V R L = g m 2 r p l [ v 1 2 g m l _ v 0 / R L ] - V 0 / r p 2 (4) The gain of the circuit is defined as A = V / V 1 2 • Substituting into (4) gives: ! / R L = 9m2 r p ) [ M 2 / A - l / R L ] - l / r p 2 and rearranging gives: A = 9m2 — [— + — ] r p i L R L r p 2 J FIGURE U6i FLUCTUATING BEAM MAGNET ENTRANCE - 36 -Taking values of g m 2 and from Figure 45 for the gas triode as: gm2 4 mumhos r 0 2 X 10 1 0 ohms p2 and the measured values of g and r n i for the 6BK4 triode as: ml p A g 100 mumhos ml r . 11 X 106 ohms. Pi gives the value of A as: 49,000. This is in good agreement with the actual measured gain of 40,000. 2 . Loop gain analysis for the whole stabilizer system . The energy that allows the beam to be bent by 90 degrees through the deflecting magnetic field, is the energy of reference that the corona stabilizer must maintain. The magnetic field bending the beam is the constant of reference to which all stabilization is referred. The corona stabilizer must have enough feedback gain so that any variation in the set voltage is corrected by an even larger feedback signal. The greater the loop gain, the better is the energy stabilization. Figure 48 shows a schematic diagram, used in this discussion, of a beam changing in energy, and hence fluctuating in position because of the magnetic field. The radius of curvature of the beam in the magnetic field is given by: -37*1. x (1) p = K(2mE)2/B, where E is the energy of the particles in the beam, and B is the magnetic field .Dividing the derivative of equation (1) by equation (1) gives: (2) dp/p = |dE/£ If the set volts changes by dE, the beam will move a total distance of "t" at the sniffers At the magnet box opening: 2 2 2 (3) (p + dp) = (dp) + (p + dy) Rearranging (3) gives: (3') dy= y ( p - dp)2 - (dp)2 - p The extra deflection caused by the beam-not leaving the:magnet box opening: (4) D = xdp/(p + dp) = xdp/p ' " Therefore the total deflection at the sniffers is: (5) t = xdp./p + (p2 - 2dp)^ - p Assuming that the beam has a uniform cross-section and a rectangular shape when it passes through the sniffers, one can make a simple calculation to determine the signal reaching the pre-amplifier when a fluctuation occurs in the set volts. If dE is 1 KV v . and E is 1000 KV, then dp is .014 cm., as p is 28 cm. for the Van de Graaff magnet. Therefore "t" is .064 cm. If the beam has a shapeas shown in Figure 49a, the resulting •current difference between the sniffers will be .086/lamp. With a sniffer sensitivity of .47 Meg-ohms, the resulting signal on the bun will be 40,000 volts. The Loop Gain is therefore 40.. The effect of different set energies, different beam cross-sections and different sniffer slit widths, on the loop gain are- summ'arized in Figure 50. Two beam distributions are considered: an unfocused beam, which was ap-proximated by a beam of constant current distribution over its whole area, and a focused - 38 -beam which was approximated by the distribution j = A exp (-x - .04yl), as shown in Figure 49b. For the constant current distribution, the loop gain is independent of the sniffer width, and is an order of magnitude lower than that for the focused beam. The sniffer width has a definite effect on the loop gain for the focused beam. As seen from Figure 50b, for a given amplifier gain a higher loop gain implies a lower current allowed to pass through to the target. A third curve in the figure is the product of the loop gain and the relative current let through the sniffers. This product reaches a maximum at a sniffer width of approximately .65 cm. so a compromise can be made between energy stability and target current. C . Physical Operation Characteristics: Many variables affect the best operation position of the Corona Stabilizer needles. The two most important of these are the tank pressure and the energy of the set. For proper control: the needles must be brought closer to the bun as the pressure of the tank is increased, the energy remaining constant; and the needles must be moved farther from the bun as the energy is increased, the pressure remaining constant. The relative humidity of the tank has has a smaller effect on the stabilizer control. For higher humidity the needles must be farther out for control, if the energy is constant. No measurable change in the stabilization was noted when 10 lbs. of Freon was added to the tank gas. Higher amounts of Freon should have some effect, as it is added to suppress bun-to-ground sparking, so it should also suppress current pick-up on the corona needles. These characteristics are shown in figures 51 and 52. - 39 -Because of the voltage specifications of the lead carrying the current from the needles to the plate of the 6BK4 triode, the highest safe voltage that could be applied to the 6BK4 plate was approximately 10 KV. Under conditions of low beam current a range of stabilization of 450 Kev was obtained, with die 6BK4 plate at 10 Kv. Presumably with higher plate voltages even wider ranges could be obtained. Figure 53 shows the effect of increasing the plate voltages on the stabilization range. Because die beam focusing conditions change quite drastically over such an energy range, larger ranges of stabilization would be inadvisable. 6 mm > SS DEVICE FIGURE Ik: EXPERIMENTAL SET-UP FIDURE l 6 : FIGURE 17 ELECTRONICS E88CC PRE-AMPLIFIER 403B 403B BIAS SUPPLY :47Kft lOKft 2 W X = : 20 90v -z=r - s+ 5 K a , 2W 6.8Kf2 47ft • W W - V W -IMft SOLID STATE DETECTOR i 1 .l/xf l -5pf JL 68Kft 47fi .l/xf 6.8 l -7pf X Y 270X1 A B 5 0 i5Kn X Y JL -r-W J ; I iNlOSO 's DC HEATER SUPPLY - w -HAMMOND I 6 7 - L 6 0 IOOO-Lt 33KX1 . T O P R E - A MPLIF IER 6 5 2 C5 —Kl W IN 100 2 W \0\ T O KS i 5 0 pf ±L T O X POWER SUPPLY .05/xf T O HEATER SUPPLY A B FIGURE 23: ALPHA PARTICLE ANGULAR DISTRIBUTION 70 E„: .500 Mev 1 a 60 -50 GO O I 40 Mo * A MICROCOUI 30 Y t PER * * COUNTS 20 IO * * x Betd,a)Li 7 9 7' o Be(d,a)Li i i i i i i I I i 20 40 60 80 IOO 120 140 160 180 CENTER OF MASS ANGLE J + 5 -m ZD o o o or o or UJ 0-co O o 120 100 8 0 6 0 4 0 r -FIGURE 2k; ALPHA. PARTICLE ATTGULAR DISTPJBUTIOM 0 0 0 2 0 r o Be9(d,a)Li7 BHd,a)Li7' 2 0 4 0 6 0 8 0 100 120 140 160 180 CENTER OF MASS ANGLE -h6-180 FIGURE 25: ALPHA PARTICLE ANGULAR DISTRIBUTION E d : 1.00 Mev I 6 0 h CD o I 4 0 h 120 O o o or o tooL or UJ o o 8 0 6 0 r 4 0 0 0 <> x Be9(d,a)Li7 4 2CH- 9 7' o Be(d,a)Li 2 0 4 0 6 0 8 0 100 120 140 160 180 CENTER OF MASS ANGLE CO ZD o o o or o or Id 0_ (f) h-~ZL ZD o o 8 0 6 0 4 0 2 0 -47-FIGURE 26: ALPHA PARTICLE MGULAR DISTRIBUTION E,: 1.16 Mev a 0 0 0 0 0 o o <> x Be9(d,a)Li7 9 7' o Be(d,a)Li 2 0 4 0 6 0 8 0 100 120 140 160 180 CENTER OF MASS ANGLE -U8-\20\ FIGURE 27: ALPHA PARTICLE ANGULAR DISTRIBUTION E d : 1.35 Mev CD O _J ZD O o o or or UJ o_ CO Z O o IOC+ 8 0 6 0 4 0 2 0 r x Be(d,a)Li ? N = 4 8 - 3 3 C O S 0 + 24COS *0 9 7 ' o Be(d,a)Li N = 5 5 + 2 3 C O S 0 + 8 C O S 2 0 2 0 4 0 6 0 8 0 1 0 0 120 140 160 180 CENTER OF MASS ANGLE CO o 1 6 0 Y Y .L9-FTGURE 28: ALPHA PARTICLE ANGULAR DISTRIBUTION 20Q-E,: 1.16 Mev a O O o or o 120 0 0 or UJ o_ CO t-o o 8 0 k 4 0 L 0 * 0 0 x Be9(d,a)Li7 9 7' o Be(d,a)Li 2 0 4 0 6 0 8 0 lOO 120 140 160 180 CENTER OF MASS ANGLE -50-FIGURE 29: ALPHA PARTICLE ANGULAR DISTRIBUTION E d : 1.35 Mev 2oq-m ZD O o o or o 160 ^ 120 or UJ o_ VI 8 0 | 0 0 0 0 0 o o 4 0 h 9 .7 x Be(d,a)Li o Be(d,a)Li7 J 1 i • • 2 0 4 0 6 0 8 0 IOO 120 140 160 180 CENTER OF MASS ANGLE i : Fraction of^Alpha Particles Be9(d,a)Li',Li' , yhich go to FIGURE 30a from e" the First Excited State. x x .8 1.0 1.2 DEUTERON ENERGY CO Z> O o o or o or UJ o_ 180 140 I O J O T -CO 6 0 4 FIGURE 30b: ANGULAR DISTRIBUTION OF ^ULAR^ ] E^: .500 Mev 3 O O 8 0 100 120 140 160 180 CENTER OF MASS ANGLE -52-4 . 0 0 2.001 © F R 0 M B e 8 ' .7" x F R 0 M Li7' IOO 120 140 160 180 LABORATORY ANGLE FIGURE 33: SECONDARY ALPHA MAXIMUM ENERGIES; * H E O R E T O A L AND AcTuAL E d : 1.35 Mev -53-140 F I G U R E 31+: ANGULAR D I S T R I B U T I O N S OF Be 9 (d,t)Be 8 I20 o o o o or o or 1x1 o_ CO 1-ZD O o 100 8 0 6 0 4 0 2 0H .Y Y + X Ed 1.35 1.16 .50 0 & + + • • -1 1 • • 2 0 4 0 6 0 8 0 100 120 140 160 180 CENTER OF MASS ANGLE COUNTS PER CHANNEL HAMMOND 2 6 9 J X HAMMOND S S 2 5 I l 5 7 " G 5 K f i ^ T J I P Y — W A PRE-AMPLIFIER (S> _ 8 f t f \&fd 6 B K 4 BIAS X • Y 6 B K 4 CATHODE CURRENT 3 3 K & L 2. UPPER SNIFFER TOP TERMINAL ASSEMBLY CORONA NEEDLES BUN Ml* W A L L 6 B K 4 2. FIGURE hi: CORONA STABILIZER L O W E R a , SNIFFER % y:. If) CM : 4.7 1.0 M M JS_N1FFER L E V E L FIGURE 43. CORONA NEEDLE ASSEMBLY LUCITE NEEDLE MOUNT CLAMPS FOR N E E D L E S (BRASS) ALUMINUM SHIELD ALUMINUM SHIELD BRASS SHIELD 6 B K 4 MOTOR I 1 TOP END CONNECTION KEY 6 1 8 NC 3 4 3 6 Sh 5 8 9 2 1 7 5 2 7 12 4 INSIDE NOS. ' TOP END WIRE NOS OUTSIDE: P A N E L PLUG NOS. MAIN PANEL 2 3 4 5 6 7 8 I I I 6 -o-«-t F I G U R E 44. NEEDLE POSITION MOTOR DRIVE no AC TO 6 B K 4 P L A T E M E T E R in P R E -AMPLIFIER PANEL j FORWARD R E V E R S E SWITCH m.a.FSD METER ZERO PUSH BUTT* M E T E R ZERO -A/WyWVA -59-ALUMINUM CASING LUCITE SUPPORT FOR COMPONENTS FIGURE 4 6 6 B K 4 TRIODE M O U N T LUCITE PLATES SCALE: -J- FULL SIZE OUTPUT PLUG FROM 4 5 0 Mi l CORONA NEEDLES RESISTOR LUCITE NSULATION UPPER SNIFFER BEAM LOWER SNIFFER FIGURE 49a UNFOCUSED BEAM 115mm 3.0mm 1.5mm. 15mm. LOOP GAIN FIGURE 51a: MAXIMUM ENERGY OF STABILIZATION WITH AND WITHOUT FREON o - o o NITROGEN PRESSURE 34p Si WITHOUT FREON +. WITH FREON 4 6 8 10 <2 CORONA NEEDLE POSITION 1.30 FIGURE 51^: . STABILIZATION RANGE VS RELATIVE HUMIDITY OF TANK NITROGEN >-CD or UJ z < UJ CO I 20 1.10 i C'J t I 00 12 13 14 15 16 RELATIVE HUMIDITY 17 18 FIGURE 52: STABILIZATION RANGE VS NEEDLE POSITION MAXIMUM ENERGY OF RANGE • • + a + D O X NITROGEN x PRESSURE • 1 2 6 psi + 9 0 " o 73 " x 34 „ 2 4 6 8 CORONA NEEDLE POSITION MINIMUM ENERGY OF RANGE O o x o X X o • + • o + X X 2 4 6 8 10 12 CORONA NEEDLE POSITION .25 O O > .20- O •z. 9 .15 y— < M CO < I— CO o UJ o -z. < or .10 .05-X O N E E D L E POSITION o i inch inches FIGURE 53: STABILIZATION RANGE VS bBKfl- PLATE VOLTS Tani 60 p s i o f Nitrogen 12$ R e l a t i v e Humidity i ON t —X I I I 1 L_ 2 4 6 8 6BK4 PLATE VOLTS IO , -66-BIBLIQGRAPHY G. Amsel, P. Baruch, O. Smulkowski, IRE Trans, on Nuclear Science, NS-8, #1, 21, (1961). A. Ashmore and J. F. 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