{"http:\/\/dx.doi.org\/10.14288\/1.0302463":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Science, Faculty of","type":"literal","lang":"en"},{"value":"Physics and Astronomy, Department of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Malakoff, Walter","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2011-06-02T17:04:00Z","type":"literal","lang":"en"},{"value":"1969","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#relatedDegree":[{"value":"Master of Science - MSc","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeGrantor":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"One of the recently developed methods for studying nuclei depends on the orientation of the spin axes of the nuclei with respect to some axis fixed in space. Since there is an association between the angular momentum properties of a nuclear system and directional effects in the absorption or emission of radiation by such a system, this nuclear ordering is characterized by anisotropic effects in the interaction of the nuclei with radiation, whether particle or electromagnetic.\r\nThis thesis encompasses the preliminary work done in assembling a system consisting of cryogenic equipment and electronics to measure the anisotropy in radiation emitted from radioactive nuclei oriented in a ferromagnetic host lattice (iron) at very low temperatures (\u223e0.01\u00b0K) and to observe the changes in anisotropy with changes in temperature.\r\nChapter 1 contains a condensed account of the information that can be obtained from oriented nuclei, the methods of producing oriented nuclei and the theory required for extracting information from the observed anisotropy.\r\nChapter 2 describes the low temperature apparatus and-includes a description of the low temperature cryostat, the Dewar vessels, the specimen assembly, the superconducting solenoid, and the polarizing solenoid. Chapter 3 deals with thermometry at low temperatures, the technique used for cooling adiabatically and the preparation of the Co\u2076\u00ba specimen used for thermometry.\r\nChapter 4 explains the function of each module of electronics used in the experimental configuration.\r\nNuclear orientation of Co\u2076\u00ba is covered in Chapter 5 and includes an analysis and discussion of results.\r\nChapter 6 outlines the improvements to be made in the design of a new low temperature system and includes a brief summary of the future program of studies in nuclear orientation at very low temperatures.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/35071?expand=metadata","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"Nuclear Orientation at Very Low Temperatures by Walter Malakoff Bachelor of Education (B.Ed) - Secondary, University of British Columbia, 1967 This thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Physics We accept this thesis as conforming to the required standard The University of British Columbia March, 1969 (i) In presenting this thesis in partial fulfillment of the require-ments for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia Vancouver 8, Canada ( i i ) ABSTRACT One of the recently developed methods for studying nuclei depends on the orientation of the spin axes of the nuclei with respect to some axis fixed in space. Since there is an association between the angular momentum properties of a nuclear system and directional effects in the absorption or emission of radiation by such a system, this nuclear ordering v. is characterized by anisotropic effects in the interaction of the nuclei with radiation, whether particle or electromagnetic. This thesis encompasses the preliminary work done in assembling a system consisting of cryogenic equipment and electronics to measure the anisotropy in radiation emitted from radioactive nuclei oriented in a ferromagnetic host lattice (iron) at very low temperatures (ro0.01\u00b0K) and to observe the changes in anisotropy with changes in temperature. Chapter 1 contains a condensed account of the information that can be obtained from oriented nuclei,, the methods of producing oriented nuclei and the theory required for extracting information from the observed anisotropy. Chapter 2 describes the low temperature apparatus and-includes a description of the low temperature cryostat, the Dewar vessels, the specimen assembly, the superconducting solenoid, and the polarizing solenoid. ( i i i ) Chapter 3 deals with.thermometry at low temperatures, the technique used for cooling adiabatically and the pre-paration of the Co 6 0 specimen used for thermometry. Chapter 4 explains the function of each module of electronics used in the experimental configuration. Nuclear orientation of Co 6 0 is covered in Chapter 5 and includes an analysis and discussion of results. Chapter 6 outlines the improvements to be made in the design of a new low temperature system and includes a brief summary of the future program of studies in nuclear orientation at very low temperatures. (Signature of Examiner) ' (Signature of Examiner) (iv) TABLE OF CONTENTS Page . TITLE (i) ABSTRACT ( i i ) TABLE OF CONTENTS (iv) LIST OF TABLES (vi) LIST OF FIGURES (vii) ACKNOWLEDGEMENTS ( v i i i ) CHAPTER 1 NUCLEAR ORIENTATION AT LOW TEMPERATURES 1 1.1 Introduction 1 1.2 Production of Oriented Nuclei at Low Temperatures 3 (i) Brute Force Method 3 ( i i ) Magnetic H.F.S. Polarization 4 ( i i i ) Magnetic H.F.S. Alignment 5 (iv) Electric H.F.S. Alignment 5 (V) Orientation in Ferromagnetics and Antiferromagnetics 6 1.3 Angular Distribution of y-Radiation from Nuclei Oriented in Ferromagnets 7 1.4 Information Obtained from the Study of Oriented Nuclei 12 CHAPTER 2 THE LOW TEMPERATURE APPARATUS . 2.1 The Low Temperature Cryostat 2.2 The De\\^ ar Vessels 2.3 The Specimen Assembly 2.4 The Superconducting Solenoid 2.5 The Polarizing Solenoid CHAPTER 3 CONTACT COOLING AND THERMOMETRY 3.1 Introduction 3.2 The Specimen used for Thermometry 3.3 Preparation of the Specimen 3.4 Magnetic Cooling 15 15 18 19 21 23 25 25 27 -30 32 Cv) CHAPTER 4 THE ELECTRONICS USED FOR DETECTING AND MEASURING THE ANTSOTROPY OF Y\"RADIATION 35 4.1 The Detectors 35 (i) The Equatorial Detector 35 (i i ) The Axial Detector 35 4.2 The Preamplifiers ' 37 (i) The Fe't-Input Preamplifier 37 (i i ) The Transistorized Preamplifier used with the Photomultiplier 37 4.3 The Linear Amplifiers 40 4.4 Routing and Analysis of Signal Pulses 41 (i) Timing Single Channel Analyzer 41 (i i ) The Delay Amplifier 42 ( i i i ) The Baseline Restorer 43 (iv) The Pulse Generator 43 4.5 The Experimental Configuration for Co 6 0 in Fe 43 CHAPTER 5 NUCLEAR ORIENTATION OF Co 6 0 49 5.1 Introduction 49 5.2 The Experimental Procedure 51 5.3 Analysis of the Results 55 5.4 Discussion 57 CHAPTER 6 FUTURE PROGRAM 60 6.1 Improvements . 6 0 6.2 Future Experimental Work 62 REFERENCES USED IN THIS THESIS 65 APPENDIX Al THE CORRECTION FOR THE SOLID ANGLE SUBTENDED BY THE COUNTERS 68 APPENDIX A2 AMENDED VENTRON INSTRUCTIONS FOR OPERATING SUPERCONDUCTING SOLENOID 72 (vi) LIST OF TABLES TABLE 5.1 Data: 24, July, 1968 Co 6 0 in Fe 53 (vii) LIST OF FIGURES FIGURE 1.1 Simple Decay Scheme 10 FIGURE 2.1 Low Temperature Apparatus 16 FIGURE 2.2 Low Temperature Cryostat and Specimen Assembly 17 FIGURE 2.3 Current Sweep and Supply for Polarizing Solenoid 22 FIGURE 2.4 Polarizing Solenoid 24 FIGURE 3.1 Decay Scheme of Co 6 0 28 FIGURE 3.2 Co 6 0 Thermometer 29 FIGURE 3.3 Magnetic Saturation of Fe Sample 31 FIGURE 4.1 Fet Preamplifier for Solid State Detector 33 FIGURE 4.2 Preamplifier and Power Supply for NaI(Tl)-PM Detector 39 FIGURE 4.3 Experimental Configuration ' 44 FIGURE 4.4 Nal(T.l) Energy Spectra ' 46 FIGURE 4.5 Ge(Li) Energy Spectra 47 FIGURE 5.1 Anisotropy of Co 6 0 in Fe as a Function of Temperature 50 FIGURE 5.2 e (Co 6 0) as a Function of Temperature 24, July, 1968 56 FIGURE A l . l Finite Solid Angle Subtended by Detector at Specimen ( v i i i ) ACKNOWLEDGEMENTS I would like to thank the Physics Department of the University of British Columbia for extending to me the use of the Nuclear Magnetic Resonance Laboratory and the f a c i l i t i e s of the nuclear physics (Van De Graaff) group. I am most grateful to Dr. P. W. Martin for his invaluable supervision, encouragement and financial assistance (provided in the form of a Graduate Assistantship). Thanks are also due to Dr. B. G. Turrell for his assistance with the research problems and experimental work. Mr. L. Gorling is being thanked for assembling and maintaining the low temperature apparatus, and assisting in the experimental work. The Low Temperature Laboratory is gratefully acknowledged for providing the liquid helium required for the experimental work. I thank my wife for her encouragement. CHAPTER 1 Nuclear Orientation at Low Temperatures 1.1 Introduction Thermal equilibrium nuclear orientation techniques at low temperatures u t i l i z e the coupling of nuclear magnetic dipole moments with magnetic fields or electrical multipole moments with electric f i e l d gradients. Orientation occurs \\\\fhen the nuclear system is coupled in some way to an axis of quantization (defined as the z-axis in the following discussion). In a field-free space a system of identical nuclei each of spin I (total angular momentum of the nucleus) a l l have the same energy since the 21+1 magnetic substates are degenerate. The application of a magnetic or inhomogeneous electric f i e l d to the magnetic or electric multipole moment of the nuclei causes each substate M to have a different energy E(M). The population of each substate is governed by a Boltzmann function of the form a M = A exp \" E ( M )  M kT When the temperature of the system is such that the quantity B, defined by B = [E (M) - E(M+'l)]\/kT, approaches unity the populations become unequal and the system ex-hibits nuclear orientation. A population difference corresponding to \u00a3<p*l is generally required for observing anisotropic effects 2 temperatures. The magnetic fields or electric fields can be applied externally, or may be obtained for example, by u t i l i z i n g the hyperfine magnetic f i e l d in a ferromagnetic host lattice or an internal electric f i e l d gradient within a crystalline solid. For the general case Abragam and Pryce (1951) have expressed the interaction Hamiltonian as follows: \/\/ = y B [ g n Hz Sz + gj_(Hx Sx + Hy Sy) ] + D[Sz 2 - j S(S+1)] + A Sz Iz + B(Sx Ix + Sy Iy) + Q [ i z 2 . i i ( i + D ] - iM. ->\u2022 where y^ is the Bohr magneton, H the externally applied magnetic f i e l d , S the effective electron spin (spin of the ionic electrons) and A, B are hyperfine structure (h.f.s.) coupling constants (for the interaction between nuclear magnetic moments and unfilled electron shells). D, Q are the crystalline electric f i e l d splitting parameters and g i i , gj_ are the ionic g-factors parallel and perpendicular to the magnetic f i e l d (z-axis) . The Ug term accounts for the splitting of the electronic levels in the external magnetic f i e l d H. The D term represents the splitting of the electronic levels in the crystalline electric f i e l d . The A and B terms represent the h.f.s. splitting resulting from the interaction between the 3 nuclear magnetic moment and the u n f i l l e d e lec tron s h e l l s . The nuclear e l e c t r i c quadrupole s p l i t t i n g i n the c r y s t a l l i n e e l e c t r i c f i e l d gradient i s given i n the Q-term. The H*I term accounts for the d i r e c t i n t e r a c t i o n between the external f i e l d and the nuclear magnetic dipole moment u. There are two types of ordering i n an oriented system. I f the majori ty of nuclear spins point p a r a l l e l (or a n t i -p a r a l l e l ) to the z - a x i s , the expectation value < I Z > -r 0 and one has nuclear p o l a r i z a t i o n defined by I f , however, the spins are p r e f e r e n t i a l l y p a r a l l e l and a n t i -p a r a l l e l i n the z - d i r e c t i o n , the expectation value of <I 2> r 0 and one has nuclear alignment defined by P2 . < y > - \\ Ki\u00abi) | (2I-D Thus, one can have alignment without p o l a r i z a t i o n . The methods for obtaining oriented nuc le i are discussed below. 1.2 Production of or iented n u c l e i at low temperatures ( i ) Brute force method: A large magnetic f i e l d , H , appl ied to an ensemble of nuc l e i causes adjacent nuclear magnetic states to separate uH by a Zeeman energy di f ference \u2014 . The i n t e r a c t i o n depends 4 only on the existence of a fini t e nuclear magnetic moment v, and the observable orientation on the temperature of the system such that B = E(M) - E(M+.l) = v_H ^ 1 a g m e n t i o n e d a b o v e kT IkT (1.1).? The low temperatures required are usually obtained by adiabatically demagnetizing suitable crystals such as Ce 2 Mg3 (N0 3) 1 2 '24 H20. Superconducting solenoids providing strong, steady, localized fields enable this method to be used without the d i f f i c u l t i e s previously encountered. These involved having to apply simultaneously a strong f i e l d while having to demagnetize a suitable paramagnetic salt to obtain the low temperature. The brute force method is useful for studying metals but is not practical for insulators due to prohibitively long nuclear relaxation times. Since E(M) E(-M), the direct interaction leads to nuclear polarization, i.e. non-vanishing terms of Pj. (ii ) Magnetic h.f.s. polarization Gorter (1948) and Rose (1949) independently proposed methods of polarizing nuclei by u t i l i z i n g the hyper-fine magnetic f i e l d produced by the unfilled electron shell in paramagnetic ions. This magnetic f i e l d is of the order of 105 - 107 gauss. At low temperatures the nuclei orient themselves in these fields and when a small external f i e l d is~ applied to the electronic magnetic moments the nuclear \u2022orientation of the system becomes ordered. The A, B and g terms account for this interaction resulting in nuclear 5 polarization. Cooling is obtained by adiabatically de-magnetizing a separate paramagnetic salt or'by using the substance being investigated as its own cooling agent. In the latter case the lowest temperature is determined by the fi e l d on the system and hence presents a problem since a small external f i e l d must remain applied. But since the ionic mag-netic moment is 9^ 103 times as large as the nuclear moment, the external f i e l d can be applied without appreciable increase in T. ( i i i ) Magnetic h.f.s. alignment In some paramagnetic crystals the crystalline f i e l d interacts with the orbital angular momenta of the electrons and thus produces one or more preferred axes for the ionic magnetic moments. The electronic spins are also similarly affected due to spin orbit coupling. Bleaney (1951) suggested that, at sufficiently low temperatures, nuclear orientation could be observed since the nuclear magnetic moments would interact with the ionic magnetic moments and align themselves in these fi e l d s . The Hamiltonian for an ion in such a system would include the D term, with z being the direction of the crystal axes of symmetry. (iv) Electric h.f.s. alignment Pound (1949) proposed the orientation of nuclei u t i l i z i n g the local electric f i e l d s , the directions of which are fixed with respect to the crystallographic axes. This 6 method relies on the interaction of the nuclear electric quadrupole moment and the gradient of the electric f i e l d ( \/ v l O 1 5 esu\/cm3 required to give an energy separation of the required magnitude). This electric f i e l d can be produced by an asymmetrical distribution of the electron cloud immediately around the nucleus (strongly deformed nuclei are required) such as in the rare-earth and actinide elements. (v) Orientation in ferromagnetics and anti-ferromagnetics: At temperatures below the Curie Point (500 - 700\u00b0C for most iron alloys) a small external magnetic f i e l d (^1000 gauss) may polarize the magnetic domains of ferromagnetic materials and produce unidirectional magnetization at saturation. In some rare earth metals, the crystalline anisotropy or the anisotropic exchange interaction causes a preferred direction of domain magnetization. In both of these cases the electronic spins align themselves along or perpen-dicular to the domain magnetization and the nuclear magnetic moments then experience magnetic fields which result in the alignment of the nuclei. This h.f.s. interaction and sufficiently low temperatures of the order of 0.01\u00b0K - 0.1\u00b0K could be used to obtain nuclear orientation. Nuclear orientation in antiferromagnetic crystals depends on the alignment of the electronic magnetic moments along a preferred axis in the crystals (at temperatures below the Neel temperature) , and that the nucleus of the magnetic ion 7 .experiences a relatively large magnetic f i e l d which does not average to zero because of the rapid flipping of the spins from one direction to the antiparallel direction, a phenomenon which results from a degeneracy of the antiferromagnetic state. The orientation mechanism in ferromagnets and anti-ferromagnets is complicated by ferromagnetic and antiferro-magnetic exchange, and by crystalline anisotropics since i t is possible to have more than one axis of alignment. Investigations by Hanna et al (1960) also showed that the magnetic f i e l d at the site of the nucleus is antiparallel to the bulk magnetization of the ionic moments and supported the theory that s-electrons entered into the h.f.s. interaction. Samoilov (1960), Kogan (1961) and Stone and Turrell (1962) investigated the fields induced in diamagnetic atoms dissolved into ferromagnets and found magnetic fields up to a few million gauss. The use of ferromagnetic hosts seems to be a viable method for orienting nuclei and seems only to be restricted by whether or not the particular element to be investigated can be dissolved in iron, or any other suitable ferromagnet such as cobalt or nickel. 1.3 Angular distribution of y-radiation from nuclei  oriented in ferromagliets This section provides a brief summary of the theory of the angular distribution of y-radiation emitted by 8 oriented nuclei in ferromagnets. More comprehensive discussions are found in the articles by Ambler (1960), -Roberts and Dabbs (1961) , Huiskamp and Tolhoek (1961), Blin-Stoyle, Halban and Grace (1961), Blin-Stoyle and Grace (1957), Steenland and Tolhoek (1957) , de Groot (1952) , Morita (1961) , and Ambler (1951 and 1963) . As mentioned in section (1.2), in ferromagnets the electron spins are polarized by strong exchange interactions. The Hamiltonian of Abragam and Pryce (1951) for the ferro-magnetic case takes the form: 1 Vn 1 = -y rA S + .1 I g y 5n n where g n is the nuclear g-factor, u is the nuclear magneton and a l l other terms are as defined in section (1.1). H e f f is the hyperfine f i e l d at the nucleus and consists of the external f i e l d and the f i e l d due to the polarized electrons, where in general: -M_ \u00bb H ^ ^n yn .When the ferromagnet is saturated, Hg^^ at every nucleus is along the same axis since a l l the magnetic domains are parallel. At low temperatures the Boltzmann distribution (see section 1.1) 9 among the magnetic substates provides bulk p o l a r i z a t i o n of the n u c l e i . The angular d i s t r i b u t i o n of y-radiation from a system of oriented nuclei i s given by: W(6) = B U F P (cos 8) V even where 9 i s the angle to the z-axis. The orientation of the parent nuclei i s given by the B^ factors, defined by Gray and Satchler (1955) as functions of the Boltzmann d i s t r i b u t i o n (see section 1.1). The U v are parameters describing the dis-ori e n t a t i o n produced by the B- and y- transitions preceding the y decay whose anisotropy i s being measured. They are functions of the angular momenta, L 0 , carried o f f in the t r a n s i t i o n (see figure 1.1). The F y parameters describe the observed y-t r a n s i t i o n and are functions of the angular momenta of the tran s i t i o n s (as Li i n figure 1.1). These l a t t e r parameters have been tabulated by Ferentz and Rozenzweig (1953) , and the related Racah c o e f f i c i e n t s , by Simon et a l (1954). The P^ are the Legendre polynomials of order v . The maximum value of v i s given by: v < smallest of 2 I 0 , 2 I i , 2L max 1 where I Q i s the t o t a l angular momentum of the parent n u c l e i , 1^  the t o t a l angular momentum of the nucleus preceding the observed t r a n s i t i o n , and L the angular momentum carr i e d away by the unobserved t r a n s i t i o n . The r e s t r i c t i o n of the polynomial to even v means ph y s i c a l l y that the inte n s i t y of the 10 I. (3 fe I: L F I G U R E S I M P L E D E C A Y S C H E M E 11 radiation from the nucleus pointing in one direction is exactly the same when the nucleus points in the opposite direction, i.e. only the \"alignment\" terms contribute. In the particular case where a mixed 8-transition occurs, u\"v 1 replaces in the above equation and is given v , = U v(Io I I j g ) * * 2(Io I I j' p) V 1 + A2 where j . and j ' are the angular momenta of the leptons and P P A is the ratio of the amplitudes of the i ' decay to the j 0 P p decay. Similarly, i f the observed y-transition consist of magnetic dipole (Mx) and electric quadrupole (E 2) transitions the F coefficient becomes: v F ( I ^ z LL) + 2 a F CI 112 L L + l ) t a 2 F v ( I 1 I 2 L + l L + l) F * '= \u2022 \u2022 v 1 + a 2 where a is the admixture ratio of the transitions (see Biedenharn and Rose (1953)). One also observes y-rays which are preceded by more than one observed transition (as in Co 6 0). The U v are then written: U = U ^ \u2022 U ^ ... U ^ , where n is the number of V V V V transitions preceding the observed transition. The W(9) equation is valid only when the population of the intermediate nuclear state is not affected by interaction with the lattice vibrations, recoil of the nucleus from its original lattice position, or changes in magnetic or electric 12 f i e l d gradients following a 3-decay, but depends only on the i n i t i a l equilibrium distribution and the character of the preceding emission process in the cascade. In practice this means that the time between successive emissions must be short (i.e. ^ l O \" 9 sec). The anisotropy of the angular distribution of y-radiation is given by: E = ^^ (^1\/2)^ \u00b0^^  w n e r e a n c* W(TT\/2) are the observed y-ray intensities normalized to the intensity of a \"warm\" or unpolarized system as observed parallel and perpendicular to the z-axis. 1.4 Information obtained from the study of oriented nuclei Depending on the nucleus being oriented one can obtain information either about the orientation mechanism or the nuclear process involved. Atomic information may be obtained i f the nuclear part is known, especially the nuclear spins involved and the nature of the 6- and y- transitions which occur. On the other hand nuclear data such as spins, parities, and magnetic moments can be obtained i f the hyper-fine f i e l d is known. If one measures the angular distribution of the y-radiation (see Tolhoek and Cox (1952)) one can obtain the multipole character of the transition since the W ( 9 ) pre-viously defined (section 1.3) contain the terms (with v = even, since only the alignment terms contribute) which 13 depend on the multipolarity of the transition. A considerable orientation is required to obtain the orientation parameters having higher values of v. Measurement of the linear polarization (see Bishop et al (1952)) would permit one to distinguish between the electric or magnetic character of the radiation since the ratio of the intensity of radiation per-pendicular and parallel to the z-axis is different for electric and magnetic transitions, being larger for electric than magnetic. Measurement of circular polarization would give the orientation parameters with odd v (see Wheatley et al (1955)) . Therefore i f the orientation parameters are obtained from an experiment they can be used to: (i) obtain knowledge about the mechanism of orientation i f this is not already known; ( i i ) obtain the temperature from the parameters i f the hyperfine interaction is known, so that the angular d i s t r i -bution of the y-radiation can be used as a thermometer; ( i i i ) obtain the magnetic moment of the parent nucleus i f the mechanism of orientation as well as the nuclear process is known. One can determine, from the measured values of B , H v eff the value df 8 and from 8 , the value of u , i f \u2014 ; \u2014 is known. IkT The sign of the magnetic moment could be determined by measuring the circular polarization of the radiation. Con-versely, i f ii is known, H ~ f can be determined directly from 6; 14 (iv) obtain the values of nuclear spins and parities from the multipole order and the electric or magnetic character of the y-transitions. If the i n i t i a l and the final angular momenta in a Y-transition are known one can determine the i n i t i a l total angular momentum preceding the 3-transition since the temperature dependence of the angular distribution also depends on the i n i t i a l total\" angular momentum (see Cox and Tolhoek (1953)), and (v) obtain information about the preceding B-transition i f the spins and parities involved in the Y -transition are known. Referring to the theory of B-decay (De Groot and Tolhoek (1950)) i f one knows the ratio of the nuclear matrix elements involved, one can determine the relative magnitude of the Gamow-Teller and Fermi terms in the Hamiltonian for B-interaction. Conversely, i f the relative magnitude of Gamow-Teller and Fermi terms was known, one could calculate the ratio of the nuclear matrix elements. In addition, Y-radiation from oriented nuclei has an intri n s i c value since sources with oriented nuclei might be used as sources of linearly or circularly polarized YV radiation, which could conceivably be applied in other experiments (Cox and Tolhoek (1953)). CHAPTER 2 The Low Temperature Apparatus The apparatus used in the experiment described in this thesis was designed by Dr. B. G. Turrell and was a modified version of the one described by Turrell (1963). Figure 2.1 shows the schematic arrangement of the system including the Dewar vessel assembly. 2.1 The low temperature cryostat A diagram of the low temperature cryostat, with the specimen assembly, is shown in Figure 2.2, which is less than one-half actual size. The cryostat assembly was suspended from the Dewar vessel top cap (see Figure 2.1) by the stainless steel pumping tubes. A brass can soldered to the top cap of the cryostat assembly formed the outer jacket which could be evacuated to thermally isolate the inner jacket. The volume between the two caps immediately below the top cap of the outer jacket and suspended from i t constituted the 1\u00b0K cryo-stat. This space could be evacuated and liquid Helium (4.2\u00b0K) could be admitted from the inner Dewar vessel via the needle valve controlled by a long rod extending above the Dewar vessel top cap. A brass can was soldered to the 1\u00b0K cryostat to form ' the inner jacket which contained the specimen. Wood's metal was used to f a c i l i t a t e mounting the apparatus and taking i t apart. The whole assembly was suspended by the stainless steel pumping tubes and contained in a glass Dewar vessel (the 16 E\u00a33 CfevV4# V^Stru T O ? cflP P U M P I H G L I M E S INNER DEWAR VESSEL O U T S R D E W A R V=SS\u00a3t-N E E D L E V A L V E INfLET I'K CRYOSTAT MA^GANGUS ArvifMONtUfvl S U L P H A T E PILL (D.I'K) P E R S I S T E N T C U R R E N T S W I T C H CHROME POTASSIUM MUM PlLC ( 0 . 0 ) 2 S U P H K C o ; IDU C T I M & SOLENOID \\ H V 1 E R JACKET COPPER HsiAT LIK'K Q U T C R JACKET C \u00a9 \u00b0 - F e SAMPLE LOW T E M P E R A T U R E A P P A R A T U S ***** 17 U iii' I to i I * PUtvlPlNG L I N E 5 . ^ S T P I \\ ^ \\ . E S S S \" \\ ' \u00a3 \u00a3 \" L ) C O P P E R RADlATlO^ BAFFLES Rf\\D\\^T\\Ohi T R A P MEEDLE VALVE OUTER JACKET - M A M G A N O U S S O L P v A A T t -PILL SOLE\"K]G\\D - CHRoMtS POTASS\\OM A L U M F I L L \\ A J r r n C O P P E R W e A t U K l K - T O F ^ O L Fp \u00a3 i V \\ e t f _ iMMai- J A C K E T LOW TEMPERATURE CRYOSTAT AND SPECIMEN ASSEMBLY FIGURE- 2.2 18 liquid helium Dewar vessel) which, in turn, was suspended in another glass Dewar vessel (the liquid nitrogen Dewar vessel). Figure 2.1 indicates the arrangement and identification of these parts. A l l spaces of the inner and outer jacket were connected to a glass vacuum system allowing each to be independently evacuated or f i l l e d with helium exchange gas. The system was precooled with liquid nitrogen in the outer glass Dewar vessel using approximately 1 centimeter of dry nitrogen exchange gas in the interspace of the inner glass Dewar vessel. After the system had precooled, the interspace of this Dewar vessel was pumped out and liquid helium was transferred into the inner vessel to surround and cover the outer jacket about 2 inches above the inlet to the needle valve. When the cryostat had cooled to liquid helium temperature (4.2\u00b0K) with helium exchange gas in a l l spaces, the cryostat was pumped and liquid helium admitted to i t through the,inlet into the pumping tube controlled by the needle valve. The outer jacket was then evacuated, and the helium in the cryostat pumped to 1\u00b0K. 2.2 The Dewar vessels Both of the glass Dewar vessels were made in the Physics Department by Mr. J. Lees, glassblower. The inner vessel was about 13 centimeters in diameter (O.D.) and 92 centimeters in length and had a glass valve which facilitated f i l l i n g the interspace with dry nitrogen exchange gas for the 19 precooliiig process, and evacuating that space before a liquid helium transfer. Since helium gas was capable of moving through the walls of the Dewar vessel, the valve also provided a means for periodically flushing the interspace. This Dewar vessel was suspended on adjustable brass rods from the Dewar top cap and isolated from the atmosphere with a rubber washer between the upper l i p of the vessel and the top cap. The outer Dewar vessel was 17.5 centimeters in diameter (O.D.) and 84 centimeters in length, and had a sealed-off evacuated interspace. It was also suspended from adjustable brass rods fastened to the top cap assembly. Copper radiation baffles were soldered to the stainless steel pumping tubes between the outer jacket and the Dewar top cap to reduce the liquid helium boil-off rate in the inner glass Dewar. The whole apparatus, i.e. the Dewar vessels and the cryostat, the glass vacuum system, and the various other attachments, was fixed on an aluminum frame suspended on rubber shock-absorbers sitting on the concrete floor of the laboratory. This isolated the apparatus from the vibrations of the building which would have caused appreciable heat leaks into the specimen assembly when at very low temperatures. 2.3 The specimen assembly The specimen assembly (see Figure 2.2) in the Co 6 0-Fe 20 experiment employed a cooling p i l l of chrome potassium alum contained in a tufnol cylinder 10 centimeters long and 2 centimeters in diameter (I.D.)' Contact with the specimen plates was made via a copper heat link which consisted of approximately 5000 strands of enamel-coated copper wire (number 38 A.W.G. (B\u00a7S)) and 25 centimeters in length. The sample end of the heat link was cleaned of enamel with Stip-X and the wires were soft-soldered into a 3-faced form about 1.5 centimeters long. Each face was about 1 centimeter square. The specimen plate was soft-soldered onto one of these faces and oriented to face the germanium detector (see Chapter 4). The upper end of the heat link extended the f u l l length of the tufnol former and was impregnated with chrome potassium alum \"jam\". The chrome potassium alum \"jam\" \\\\'as made by grinding 60 grams of the salt to a very fine powder, and then adding to i t a 50\/50 mixture of glycerol and saturated chrome potassium alum solution. This cools to a glass at low temperatures. It was hoped that specimen temperatures down to .012\u00b0K (the Neel point of the chrome potassium alum) could \u2022be obtained by demagnetizing this p i l l . The chrome potassium alum p i l l was connected by a latti c e of six 1 millimeter stainless steel tubes to the manganous ammonium sulphate p i l l which was cooled to about 0.1\u00b0K in the residual f i e l d of the superconducting solenoid. 21 2.4 The superconducting solenoid The superconducting solenoid used for magnetic cool ing was a custom made device designed for our apparatus. I t was manufactured by Ventron (Magnion I n c . , 144 Middlesex Turnpike , B u r l i n g t o n , Mass. 01803). It consisted of a model CF 40-200-45039 so lenoid of niobium-titanium a l l o y 8.5 inches long, of inner diameter 2.03 inches , and outer diameter 3.815 inches , wound on a t h i n brass former. The act ive winding \\vas 7.0 inches long and produced a nominal maximum f i e l d of 48.6K gauss at a current of 61.2 amperes. The magnetic conversion r a t i o was 794 gauss per ampere at 51 amperes. The remainder of the c o i l winding con-s i s t e d of a pers i s tent current switch which enabled the so lenoid to be operated in the pers i s tent mode (no external power r e q u i r e d ) . The solenoid was powered and c o n t r o l l e d by a Ventron CF 100 Power Supply designed s p e c i f i c a l l y for the CF 40-200-45039 solenoid and was capable of producing 100 amperes with v i r t u a l l y no r i p p l e . The supply included a selectable-sweep current contro l and l i m i t e r , two 250 m i l l i -ampere heater current supplies for the pers i s t ent current swi tch , and an automatic protect ive device for the so leno id , c o n s i s t i n g of a quench-sensing c i r c u i t and power supply decoupling mechanism. Modified ins truc t ions for operating the power supply and solenoid are found in Appendix A2. The r e s i d u a l f i e l d remaining af ter a demagnetization was swept out manually using the r e v e r s i b l e current contro l MT X VAC * ZZJl \u2022 > \u00a9 S - S 2 . V . D . C . CURRENT CONiTROL P O S 2N371S. 0-5 AMP | \/ 7 \\ 6 IOK; 7 - ' A\/5 o c \u2014 3 H \u00a3 ~ C U R R E N T LIMIT \u2022 { V .1-5 AMP oor} SLACK\" &3V.A.C. FIGURE 2.3 20,00Oj*f 15V C U R R E N T S W E E P A N D S U P P L Y F O R - P O L A R I Z I N G \" S O L E N O I D N J N J 23 of Figure 2.3 and a 12-volt automobile battery which also doubled in function to power the po l a r i z i n g solenoid. 2.5 The p o l a r i z i n g solenoid The p o l a r i z i n g solenoid was a superconducting device of niobium-zirconium a l l o y wire (25% zirconium) having nylon i n s u l a t i o n wound i n a h e l i x around i t . It was wound on a brass former, as shown i n Figure 2.4, with 900 turns on section 1, 1800 turns on section 2, and 1440 turns on section 3. Platinum tabs were spot-welded to the superconducting wire with an over-lap of about 1 inch to ensure good contact (to avoid Joule heating of the superconductor). Number 20 (A.W.G.) copper wire leads were soft-soldered to t h e platinum tabs, along which power was supplied to the solenoid using the current control of Figure 2.3 and a 12-volt heavy duty automobile battery. It was estimated (see Figure 3.3) that about '3 amperes of current were required in th i s solenoid to magnetically saturate the ion sample. A current of 4 amperes was supplied to ensure that the sample was saturated. 24 CHAPTER 3 Contact Cooling and Thermometry 3.1 Introduction Non-paramagnetic substances cannot be self-cooled by adiabatic demagnetization, hence a suitable paramagnetic salt must be employed as a cooling agent. Generally, direct contact between the specimen and the cooling agent is not practicable (see Chapter 1 section 1.2(ii)), and as a result they are usually coupled by a copper heat link (see Figure 2.2). Since eddy-current heating should be reduced to a minimum, this link is usually in the form of a number of copper strips or in the form of a large number of thin insulated copper wires. According to Mendoza (1948) , for a copper heat link in a pressed p i l l of powdered salt, the heat flow is given by: Q = 100 A ( T j 3 - T 2 3) ergs\/sec. (3.1) where A is the area of contact, and Tj and T 2 the temperatures of the salt and copper respectively. It is obviously advantageous to have an area of contact as large as possible. A large cooling p i l l would have the advantage of providing a large heat sink. Chrome potassium alum is a very useful cooling agent as i t can be demagnetized down to its Neel point (0.012\u00b0K) and has \"a large specific heat between 0.1 and 0.01\u00b0K. 26 Some d i f f i c u l t y i s encountered in measuring specimen temperatures below 0 . 0 5 \u00b0 K in a contact-cooled system. Although the magnetic s u s c e p t i b i l i t y of the alum sink could be used to determine i t s temperature, heat - transfer becomes increas ing ly more d i f f i c u l t at low temperatures, so that a large tempera-ture di f ference between the specimen and cool ing sa l t can e x i s t , e s p e c i a l l y i f there i s a heat leak to the specimen. Since the heat leak i n a s p e c i f i c experiment is not known, t h i s d i f ference in temperature cannot be r e a d i l y estimated. Only i n the instance of zero heat leak would the specimen temperature approach that of the alum ( 0 . 0 1 2 \u00b0 K ) . No such int imate contact would ex i s t in p r a c t i c e , and errors up to 50% could ex i s t in the temperature di f ference between the s u s c e p t i b i l i t y measurement and the specimen temperature. It would be des irable to have a thermometer which measured the specimen temperature d i r e c t l y . In nuclear or i en ta t ion experiments where the y-ray anisotropy is measured, for a given decay, are constant (see Chapter 1 sect ion 1.3) and the v a r i a t i o n in the aniso-tropy depends on the v a r i a t i o n in B ^ . The anisotropy, . . t_r there fore , depends on 6 = \u2014 , so that i t increases as 6 IkT increases . Thus not only i s i t necessary to measure temperature as accurate ly as p o s s i b l e , but a l s o , the lower the temperature a t t a i n e d , the more accurate is the r e s u l t . 27 The specimen used in our experiment was a plate of Co 6 0 iron alloy soft-soldered to the end of the copper heat link as described in Chapter 2. 3.2 The specimen used for thermometry The above considerations suggest the advantages in using a radioactive isotope with a known decay scheme as a thermo-meter. This was in fact the reason Co 6 0 was suggested by Grace et al (1955) and proposed and used for measurements in iron by Stone.and Turrell (1962) . If the isotope were incorp-orated in the specimen and the interaction of the nucleus in this environment well-understood, i.e. y ^eff known, a measurement of the y-anisotropy would determine its temperature, and hence, the temperature of the specimen being studied. Co 6 0 was selected for the following reasons: (1) The decay scheme is \\\\rell established, and is shown in Figure 3.1 obtained from Landolt-Boinstein (1961). The nuclear magnetic moment has been measured spectroscopically and is 3.754 n.m. (Lindgren (1962)). (2) The hyperfine f i e l d on the nuclei of cobalt atoms in an iron lattice has been extensively studied, and a value of H e\u00a3\u00a3 = 2.88 x 105 gauss is valid for cobalt concentrations o\u00a3 ' 1% to 171. (Matthias et al (1966)). (3) The y-radiation anisotropy observed is large, so that high accuracy can be attained in the temperature measurement. 28 .+ C O 6 0 (53Y) ..5I3MEV) (3 (WSIvtEV) tf(l.!73MEV) \u2022tf 0 , 3 3 2 M E V ) 0 i Nl 6 0 ( S T A B L E ) DECAY S C H E M E O E C O 29 30 (4) The isotope has a long h a l f - l i f e (5.3 years). Using the tables of Simon et al and Ferentz and Rosenzweig, for the Co 6 0 decay, we obtain U 2 F 2 = -0.421 and U^  F i , = -0.243 for both y-decays. The values of B 2 and Bi, H for 1 = 5 were obtained from a tabulation against 6 = eff IkT by Blin-Stoyle and Grace. The axial and equatorial intensities are given by: W(o) = 1 + U 2F 2B 2 + U 4 F i tB u W(TT\/2) = 1-1\/2 U 2F 2B 2 + 3\/8 U I ^ B I , These functions are tabulated against 1\/T in Figure 3.2 and provide the temperature scale. 3.3 Preparation of the specimen To determine the strength of the magnetic f i e l d required to saturate the 0.2 millimeter x 1 centimeter x 1 centimeter iron sample with the polarizing solenoid, two c o i l s , each of 50 turns and 1 centimeter in diameter and 2 centimeters long, were connected in opposition and in series with the sensitive range of a Scalamp galvanometer (W. G. Pye \u00a7 Co. Ltd., Cambridge, England) and a suitable damping resistance. The coils were then placed in a high power solenoid and the sample plate was moved from one coil to the other. With this arrange-ment, pick-up in the coils was avoided, and the signal obtained was proportional only to the magnetic susceptibility of the sample. The specimen was found to saturate in fields of about 31 o V ^ --z. Q * f- -u LU _j M LL ~ LU or 3 LU LU <*> 2 0 o % rf -0-L . G O R L W G 0.-2 0,4 O.67 .0.9 l.'o ,1.2. MAGNETIC FIELD (KGAUS.S) 1-5 UQ FIG.3.3 M A G N E T I C SATURATION OF Fe S A M P L E 32 1.6K gauss (see Figure 3.3). This saturation test was performed at room temperature, but no significant change is expected at low temperatures. The sample was cleaned and a C o 6 0 C l 2 solution, with vir t u a l l y no carrier cobalt (Co 5 9), was placed on the surface of the plate so that about 2uC of Co 6 0 were present. Since iron is more electropositive than cobalt, iron atoms go into solution replacing the cobalt of the metallic chloride, leaving the cobalt to spontaneously plate onto the surface of the iron plate. The solution on the plate was then evaporated with a heat lamp, and the plate furnaced at 950\u00b0C in a stream of dry hydrogen for 24 hours. Under these conditions, the Co 6 0 atoms diffused well into the sample. This was checked by etching the specimen plate after furnacing and measuring the activity. No measurable decrease in activity was observed. The specimen was then soft-soldered to the copper heat link. 3.4 Magnetic cooling The Ventron superconducting solenoid described in Chapter 2 was used for magnetic cooling. It was rigidly mounted from the top cap of the apparatus. After the specimen assembly had been cooled to 1\u00b0K, the f i e l d was sloi^ly applied with a few microns of helium exchange gas in the inner jacket. This was supplemented by gas pre-viously absorbed on the lower salt p i l l container, and evolved 33 when i t was heated during magnetization. The temperature of the specimen assembly was deduced from the pressure in the inner jacket, and the cryostat temperature judged from the head in an o i l manometer connected to i t . After the salt p i l l cooled to i t s original temperature the remaining exchange gas was pumped away and the f i e l d then reduced slowly. Any gas present before the demagnetization would, at 0.1\u00b0K be adsorbed on the salt p i l l , for at this temperature the vapour pressure of helium is very small. It was advantageous to adsorb any gas present at a relatively high temperature where the increase in entropy for a given amount of heating is small. (This can be readily seen by considering the second law of thermodynamics, &Q = TdS). After equilibrium was reached around 0.1\u00b0K the f i e l d was reduced to a minimum. The si^eep power supply of Figure 2.3 was connected and the residual f i e l d in the magnet was reduced to a value (^10 gauss) which we anticipated would enable the salt p i l l to approach 0.012\u00b0K. It was essential that the sweep rate be slow otherwise eddy-current heating of the sample occurred. After the demagnetization, the polarizing f i e l d was applied slowly to saturate the specimen plate. The y-ray intensities along and perpendicular to the axis of the magnetic f i e l d (a-axis) were then observed, and counts N ( 0 ) c o ^ and N(*\/2) cold w e r e obtained (see Figure 4.3 for the position of the counters relative to the specimen). Normalization counts N(0) and N ( T T\/2) were obtained at the end of a \"run\" warm v warm 34 when the specimen had warmed above 0.1\u00b0K. A convenient measure of the y-ray anisotropy is given by: \u00a3 . WQr\/2) - WCo) f w h e r e W(ir\/2) W = ^cold . The W(o) and W(TT\/2) are given theoretically by N 'Varm-equation (1.9). NOTE: The temperature of the cooling p i l l of chrome potassium alum could have been derived from its magnetic susceptibility determined with a mutual inductance c o i l located over the outer jacket and positioned at the centre of the chrome potassium alum p i l l container. However, a short circuit developed some-where between the primary and secondary windings\u2022and any attempt to use this technique was temporarily abandoned. CHAPTER 4 The Electronics Used for Detecting and Measuring  the Anisotropy of y-radiation 4.1 The detectors A strong magnetic f i e l d from the solenoid used for adiabatic demagnetization, as well as from the polarizing solenoid, discouraged the use of a sodium iodide-photo-multiplier detector close to the sample.. A f i e l d of the order of 45K gauss defocussed the tube even i f shielded with mu-metal and soft iron. Since a lithium-drifted germanium detector was conveniently available and was not affected by magnetic fields i t was used in the equatorial plane. A suitably shielded sodium iodide-photomultiplier detector was used in the axial direction (a-axis) since i t was not located as close to the magnetic f i e l d as the equatorial detector. (i) The equatorial detector The equatorial detector was a trapezoidal lithium-drifted germanium device manufactured for Dr. G. Griffiths by Nuclear Diodes (P.O. Box 135, Prarie View, I l l i n o i s 60069). The model number of the detector was LGC-4.1S and the model number of the complementary cryostat (Union Carbide) was CFR-10-3P. This detector had an active area of 11.2 square centimeters with a drifted depth of 11 millimeters and was 28.5 millimeters in length. The intrinsic volume faced a thin aluminum window located 12 millimeters from the face. The window was 0.5 millimeters in thickness. The detector 36 had a relative peak efficiency at 1.332 Mev of 3.9% (compared to 2\"X 2\" Nal) and, with the above window, a resolution of 5.0 kev (FWHM) at 1,332 Mev. The peak to Compton ratio was 9:1. It was reverse biased at 1250 volts using a model 210 Ortec Detector Control Unit and a 250 volt battery in series with this control unit. The leakage current of the detector was cer t i f i e d to be 0.4 nano-amperes and its capacitance to be 20 picofarads at 1250 volts. The detector face was located 11 centimeters from the sample. ( i i ) The axial detector The axial detector consisted of a Thalium activated sodium iodide-photomultiplier detector assembled by Harshaw Chemical Company (1945 East 97th Street, Cleveland, Ohio 44106) . A sealed sodium iodide crystal of diameter 5.6 centimeters and length 7.0 centimeters was optically coupled with silicone grease to an RCA model 6342A photo-multiplier tube. The Harshaw model number was 858 (serial number Co383) . A resolution of 5.61 at 1 .332 Mev was measured with the tube operating at a positive 1105 volts. The voltage between the focus grid and signal ground (or cathode) was 112 volts and between the f i r s t dynode and signal ground was 237 volts. The photomultiplier was operated with a model 412B Fluke High Voltage D.C. Power Supply. The detector window was located 26 centimeters from the center of the sample. 37 4.2 The preampl i f iers ( i ) The FET input preampl i f i er : . The preampl i f i er (see Figure 4.1.) used with the l i t h i u m - d r i f t e d germanium detector was s i m i l a r to the model 1408A charge-sens i t ive preampl i f ier manufactured by Canberra Industr ies (50 S i l v e r S tree t , Middletown, Conn. 06457). The p r e a m p l i f i e r incorporated a modified pole \/zero cance l la t ion c i r c u i t capable of rapid recovery from overloads. It i^ as l i n e a r to bet ter than 0.1% for outputs from 0 to \u00b15 v o l t s and. had an e x t e r n a l l y - s e l e c t a b l e gain (X2 or X10). The detector bias i s o l a t i o n was 2000 VDC and the output impedance was 51 ohms. A cable 14 feet in length and compatible with the model 1410 Canberra Industries Linear Ampl i f i er provided the required \u00b124VDC and \u00b112VDC power. With the 20 pf detector the noise contr ibut ion was 2.0 Kev (FWHM) with a r i s e time of 60 nanoseconds (using a 2 microsecond RC shaping constant) . ( i i ) The t r a n s i s t o r i z e d preampl i f ier used with  the photomult ipl ier^ Figure 4.2 contains the c i r c u i t diagram for the preampl i f i e r used with the a x i a l detector as wel l as the associated 9.5 v o l t power supply. This preampl i f i er provided un i ty voltage gain but s u f f i c i e n t power gain to drive a 53 ohm coax ia l cable 14 f ee l i n length terminating on the e l e c t r o n i c s panel . The output impedance was 47 ohms. An externally-mounted two-posit ion (DPDT) switch provided con-venient output s i gna l p o l a r i t y s e l e c t i o n . The unit was b u i l t with compactness as an important factor and th is preampl i f i er \u2022 F E T P R E A M P L I F I E R FOR' S O L D - S T A T E D E T E C T O R S -2*V T E S T I N P U T (C ->,T0 S E C O N D P R E A M ? IN3I4 m IN750 > T o S E C O N D P R E A M P I N 4 0 0 Z H 7 V A C 4 L \/ V V \\ ~ : J < 7 V A G ~1 - N 1 A A A r 1 K 4 0 0 Z 200^? 25V FIGURE 4 . 2 \u2022 9 5 V P R E A M P L I F I E R A N D P O W E R S U P P L Y F O R N A I C T L ) - P M D E T E C T O R S \u20224.0 was mounted d i r e c t l y on the photomult ip l ier with a dual male BNC coax ia l connector (UG-491A\/U). 4.3 The l i n e a r ampl i f i ers The model 1410 Linear Ampl i f i ers manufactured by Canberra Industries (see sect ion 4.2 above) were used with the detector systems described above. These ampl i f i ers allow a v a r i e t y of shaping modes for high reso lu t ion nuclear spectroscopy and counting. The 1410 could be conveniently switched on the front panel into s ingle or double d i f f e r e n t i -at ing delay l i n e , or RC-shaping modes. In the RC pulse shaping mode, RC time constants were switch se lectable from 0.1 to 7 microseconds. In the delay l i n e mode, 1.2 micro-seconds delay l ines were standard. Two unipolar (one prompt and one delayed) and two b ipo lar (one prompt and one delayed) outputs were simultaneously a v a i l a b l e . This allowed the use of the s ingle d i f f e r e n t i a t e d s igna l for energy re so lu t ion while the double d i f f e r e n t i a t e d s i gna l could be used for zero crossover t iming.purposes . The delayed s ignals were then ava i lab le for multichannel pulse height analys is af ter the log ic decis ions were completed (see sect ion 4.5 below). An i n t e r n a l switch could remove the in tegrat ion from the b i p o l a r outputs in order to obtain the sharpest zero cross ing timing while r e t a i n i n g in tegrat ion on the unipolar s ignals for optimum 41 energy analysis with the kicksorter. The rise time of each unit was less than 90 nanoseconds (with the integration switch OFF and in the double delay line mode). Crossover walk was certified to be less than 1 nanosecond over a dynamic range of'0.5 to 8 volts (with amplifier in the double delay line mode and the integration switch at any position from 0.1 to 0.7 microseconds). The noise output was certified to be less than 8 microvolts (rms) measured with single RC shaping time of 1 microsecond at f u l l gain. The integral nonlinearity is less than 0.11 from 0.3 volts to 10 volts output. The amplifier gains were found to be very stable with time and were specified to have gain st a b i l i t y of better than 0.005%\/\u00b0C from 20\u00b0C to 50\u00b0C. The linear amplifier used with the lithium-drifted germanium detector employed an RC time constant of 2 micro-seconds. The linear amplifier used with the sodium iodide-photomultiplier assembly was operated in the double delay line mode (DDL). 4.4 Routing and analysis of signal pulses (i) Timing single channel analyzers: Canberra Industries model 1435 Timing SCA's were used as single channel pulse height (energy) analyzers. The Timing SCA's combined, in one module, the two functions of single channel pulse height analysis and 42 pulse crossover or leading edge (timing) discrimination. In the Window analyzer mode, the pulse height analyzer portion of the module generated a logic pulse whenever a unipolar or bipolar input pulse f e l l within the energy range defined by the Baseline and Window Width controls. In the Discriminator analyzer mode, only the Baseline restriction applied. When-ever the energy restrictions established by the controls were met, the timing portion of the model 1435 generated a timing signal when a bipolar input signal crossed the zero voltage baseline, or at the leading edge of a unipolar input signal. Leading edge timing could also be used on bipolar input signals by selecting the Unipolar operating mode. Two prompt, simultaneous routing pulses, one negative and one positive, were available as outputs. A fast negative output pulse for use with time-to-pulse-height converters was also available and could be delayed from 0-1000 nsec. The negative routing pulse was directed to either the Canberra Industries models 1474 or 1473 scaler or to the Ortec model 430 scaler to be counted. The positive pulse was used, in con-junction with the Nuclear Data Model 101 kicksorter, primarily for setting up and adjusting the windows of the timing single channel analyzers. ( i i ) The delay amplifier: A model 427 Ortec Delay Amplifier was used to compensate for the time difference between the signal pulse 43 and the coincidence logic pulse arriving at the kicksorter. The delay amplifier was only essential for setting up and adjusting,the windows of the timing single channel analyzers. ( i i i ) The baseline restorer: A model 438 Ortec Baseline Restorer was employed as an inverter to provide a signal compatible with the kick-sorter input requirements. (iv) The pulse generators: Datapulse model 101 generators were triggered by the timing single channel analyzers and provided a signal of positive polarity and amplitude required by the coincidence circuit of the kicksorter. Fine delay times were obtained simultaneously with the above operation using the Delay mode of the generators. \u20224.5 The experimental configuration for Co 6 0 in Fe The experimental configuration used for measuring anisotropic effects in the y-radiation from Co 6 0 in an iron (Fe) host lattice is found in the block diagram of Figure 4.3. The y-radiation was detected in the axial direction by the sodium iodide s c i n t i l l a t i o n detector described in section 4.1 above. A typical \"singles\" spectrum was obtained as in Figure 4.4(a). The trigger input of the pulse generator was connected to the positive output of the timing single channel F I G U R E 4 .3 ?NYT D\u00a3V>'AR . A S S E M B L Y ; SAMPLE EQUATOR! At  i DETECTOR LINEAR AMPLIFIER I SCA TO DELAY 'AMPLIFIER SCA AX IAL NAl(TL) DETECTOR AND PHOTOM'ULTIPLIER P R E -A M P Ll NEAR AMPLIFIER A A A TO DATAPULSE-S C A . a DELAY AMPLIFIER. ! -! DATAPULSE J \u00a3 L A A SCA S C A L E R v TO DATAPULSE ' A I S C A L E R BASELINE RESTORER r TO SCOPE TRIGGER r SCALER SCALER H1 .173 M E V 1.173+1.332 MEV TO KICKSORTER ANALYSE - vTO KICKSORTER COINCIDENCE 1.173 M E V E X P E R I M E N T A L . C O N F I G U R A T I O N 45' analyzer which was adjusted to put out a logic pulse only i f the input signal ranged from 1 Mev to the upper limit of the 1.173 Mev photopeak. The pulse generator output was adjusted to be greater than 3 volts, as required by the coincidence c i r c u i t af the kicksorter, and slightly wider than the pulse presented to the kicksorter analyzer section. The kicksorter, in the coincidence mode, remained inhibited to pulse height analysis unti l a coincident pulse \"opened\" the analyzer to the pulse presented at the input (corresponding to the energy limits determined by the single channel analyzer). The other timing single channel analyzer was set to energies ranging from 1 Mev to the upper limit of the 1.332 Mev photopeak of Co 6 0 and a typical gated spectrum appeared as in Figure 4.4(b). In both of the above cases the negative outputs from the single channel analyzers went to scalers which recorded a l l the \"singles\" accepted by the present range of the single channel analyzers. The timing single channel analyzers effectively integrated an energy spectrum between preset upper and lower limits and the scalers counted and displayed the total number of events in those limits, in the f i r s t case the photopeak of the 1.173 Mev y-radiation and in the second case, the number of events from 1 Mev to the upper limit, of the 1.332 Mev photopeak. The equatorial y-radiation was detected by the lithium-drifted germanium detector. The remainder of the circuitry was essentially identical to the arrangement used with the 46 o .10 2 0 S O 4 0 5 0 6 0 O (.cf) SlMGLES F I G U R E NAI E N E R G Y S P E C T R A 47 jo .2 o X )^ 2 Ul > Iii IL O (Y HI CD Z. ) S N-> > - 2 ^ 2 2 0 30 40 (a) SINGLES s o 60 - J \\ , - * - , , t I \u00bb , t fl f i _ * 0 L o 10 F I G U R E 4.5 30 , 4 0 , ^ C H A N N E L N U M B E R (b) GATED GEOLOENERGY' SPECTRA 48 sodium iodide detector except that the linear amplifier used an RC time constant of 2 microseconds instead of the double delay line mode. A typical \"singles\" energy spectrum and a gated spectrum from 1 Mev to the upper limit of the 1.332 Mev photopeak are found in Figures 4.5(a) and 4.5(b), respectively. CHAPTER 5 Nuclear O r i e n t a t i o n of C o 6 0 5.1 I n t r o d u c t i o n Very low temperatures of the order of 10~2\u00b0K are necessary to o r i e n t n u c l e i . Such temperatures are obtained by a d i a b a t i c a l l y demagnetizing a s u i t a b l e paramagnetic s a l t . I t i s very d i f f i c u l t , however, to measure the very low temperatures at which n u c l e i are o r i e n t e d w i t h p r e c i s i o n since the,magnetic s u s c e p t i b i l i t y of the c o o l i n g s a l t does not n e c e s s a r i l y i n d i c a t e the temperature of the specimen (see Chapter 3) since large thermal b a r r i e r s between the s a l t and the heat l i n k e x i s t at very low temperatures and a l s o r a d i o -a c t i v e heating can cause thermal gradients between the heat l i n k and the specimen. A convenient means by which low temperatures can be measured i s to use o r i e n t e d n u c l e i whose mechanism of o r i e n t a t i o n i s w e l l understood and whose n u c l e i are known to e x h i b i t a large temperature dependence. C o 6 0 i n c o r p o r a t e d i n Fe i s one such thermometer having a lar g e c o n s i s t e n t anisotropy i n y - r a d i a t i o n at very low temperatures. The hy p e r f i n e f i e l d ( H e f f ) of C o 6 0 d i s s o l v e d i n Fe, i t s n u c l e a r magnetic moment ( p ) , and i t s decay scheme are w e l l known. C o 6 0 a l s o e x h i b i t s a large anisotropy of the order of 0.49 or 49% at a temperature of 0.012\u00b0K (see Figure 5.1). Thus C o 6 0 appears to be a good thermometer and to t h i s end has been used s u c c e s s f u l l y by Gorter et a l (1953) Bleaney et a l (1954) and Poppema et a l (1955). 50 51 Co 6 0 was employed in our apparatus to test how well the system functioned. The measured anisotropy should indi-cate the lowest temperatures attainable by our system and i t might also reveal problems that were not anticipated in the preliminary design of the low temperature apparatus. 5.2 The experimental procedure The preparation of the Co 6 0 - Fe specimen has been described in Chapter 3. Precooling, cooling to 1\u00b0K, and the procedure for adiabatic cooling has been described in detail in Chapters 2 and 3, respectively. The electronics used to detect the y-radiation has been described in Chapter 4. Considerable d i f f i c u l t y had been encountered in obtaining a suitable demagnetizing f i e l d ('^ 45K gauss) due to the inefficient operation of the persistent current switch in the superconducting solenoid. Whenever the heater of the persistent current switch was operated for more than 20 minutes an amount of heat (from the switch) sufficient to cause the superconductor to go normal at one of its input terminals, caused the quench-sensing circuit of the CFC-100 Power Supply to deactivate the current supply. The effect of removing the current source was. similar to charging the solenoid too rapidly, i.e. an L < -^~ voltage appeared at the solenoid terminals, a quench \\\\ras indi-cated, and liquid helium was boiled off due to Joule heating and eddy current heating. Hence i t was essential that the 52 superconductor be charged to a desired l e v e l i n less than 20 minutes. The current, however, could not be increased more rapidly than suggested in the operating instructions published by the manufacturers of the solenoid (Ventron Inc.). An acceptable upper l i m i t of 36 amperes was then estimated according to the recommended charging rate, and the super-conductor, when the upper l i m i t was achieved, was rapidly put into the p e r s i s t e n t mode ( i . e . heater current reduced to zero and then the power supply current reduced to zero) to avoid a quench. No quenching occurred with this method and on July 24, 1968 a successful demagnetization was obtained. A 4-ampere p o l a r i z i n g f i e l d was applied after the residual f i e l d had been swept out and the counting procedure started with the counters at 0 = 0\u00b0 and 90\u00b0 from the quantization axis (axis of the p o l a r i z i n g f i e l d ) . The data i n Table 5.1 was obtained during the \"run\" of July 24, 1968. It was taken d i r e c t l y from the log book. Groups 1, 2, and 3 were taken immediately after the p o l a r i z i n g solenoid was turned ON, i n that order. Group 4 was taken with the p o l a r i z i n g f i e l d ON but after the specimen had warmed up to a temperature where no anisotropic effects were observable (\u2022WK) and was used to normalize the counts obtained i n groups 1, 2 and 3. TABLE 5.1 JULY, 1968; POLARIZING FIELD CURRENT: 4 AMPERES; DEMAGNETIZING CURRENT: .36 AMPERES COMMENTS EQUATORIAL COUNTER: Ge(Li) AXIAL\u2022COUNTER : Nal(Tl) (All Counts Per 2 Min.) 1.175 PLUS 1.332 Mev 1.173 Mev 1.173 Mev 1.173 PLUS 1.33 2 Mev Counts Before Mag. 28196 \u00b1 167.7 7356 \u00b1 86 8754 + 93.6 .18158 \u00b1 134.8 (1) Average of 6 Two-Minute Runs 28597 \u00b1 28.2 7530 \u00b1 14 .4 8280 \u00b1 15.2 17343 + 22.2 (2) 6 Minute Run 2 8698 \u00b1 56.5 7523'+ 28 .9 7993 \u00b1 29.8 17124 + 43.7 (3) 6 Minute Run 28582 \u00b1 56.4 7439 \u00b1 28 .8 8278 \u00b1 30.3 17376 + 43.9 Warm Count (avg. of One 12-Min. and Three 6-Min. Counts 27619 \u00b1 33.3 7228 \u00b1 17 .1 8873 \u00b1 18 .9 18580 + 27.2 CD W N(Cold) N(Warm). 1 .0354 \u00b1 0.0001 1.0417 0.9331 0.9334 + 0.0002 (2) w N(Cold) N(Warm) 1 .0390 -\u00b1 0.0002 1.0408 0.9008 0.9216 + 0.0003 C3) w N(Cold) N(Warm) 1 .0348 \u00b1 0.0001 1.0291 0.9329 0.9351 + 0.0002 ANISOTROPY 1.332 PLUS 1.173 Mev 1. 173 Mev APPROX. TIME AFTER CD \u00a3 0.098 \u00b1 0.001 0 .104 DEMAGNETIZATION 14 MIN (2) e. 0.113 \u00b1 0.002 0 .135 22 : MIN (3) z' 0.096 \u00b1 0.001 0 .093 28 ] MIN 24, TRIAL 54 The following corrections i n the raw data were cons idered: (i) There was an is o t r o p i c background from the surroundings i n the observed i n t e n s i t i e s of Co 6 0. For the time inter v a l s used, this correction was of the order of 1.2%. ( i i ) The 1.173 Mev y-ray in t e n s i t y included a back-ground of anisotropic 1.332 Mev y-radiation. However since the 1.173 Mev y-radiation was used only to check the con-sistency of the results obtained in the 1.173 Mev plus 1.332 Mev window, this correction was not e s s e n t i a l . The 1.173 Mev plus 1.332 Mev counts were used to determine the temperature since they provided larger s t a t i s t i c s and both y's exhibited the same anisotropy. There were no higher-energy transitions in this experiment to contribute s i g n i f i c a n t l y to the 1.173 Mev plus 1.332 Mev counts. ( i i i ) A correction due to the f i n i t e s o l i d angle sub-tended at the specimen by the y-ray counters (see Appendix Al) was required but could not be made since the exact shape of the l i t h i u m - d r i f t e d germanium detector was unknown. Subsequent improvements w i l l be made that w i l l enable us to make this correction (see Chapter.6). (iv) Since e was being measured no correction arising . from the decay of the Co 6 0 source was required' as. W(o) and W(TT\/2) were attenuated i n the same proportion. 55 The errors quoted in the values of the anisotropy of the 1.173 Mev plus 1.332 Mev y-radiation were obtained from the s t a t i s t i c a l uncertainties in the total counts contributing to the experimental points. 5.3 Analysis of the results The decay scheme of Co 6 0 was shown in Figure 3.1. The nuclear magnetic moment and the spin of the Co 6 0 ground state have been measured as 3.754n.m. and 1 = 5 , respectively, as indicated in Chapter 3. The parities of the various levels in the decay are a l l positive so that the i n i t i a l decay is an allowed electron-capture transition. The normalized axial and equatorial intensities are given by: W(o) = 1 + U 2F 2B 2 + U i^B,, \u2022 W(ir\/2) = 1 - i U 2F 2B 2 + | U^B,, the anisotropy being defined by E = W(TT\/2) - W(o) WO\/2) For both of the y-transitions of Co 6 0 and the preceding unobserved 3-transition, as indicated in Chapter 3, U 2F 2 = -0.421 \\)hVh = -0.243 56 57 The Co 6 0 orientation parameters B 2 and Bu are functions of 11H 3 = eff . The variations of B 2 and B^  are given by Blin-IkT Stoyle and Grace (1959). Thus we are able to calculate the variation of the y-anisotropy, e, with 1\/T since y, H and K are known quantities. Figure 5.1 summarizes, graphically, the values of e plotted as a function of 1\/T. The three experimental points obtained were plotted on Figure 5.2. It is apparent that a low temperature of the order of 0.037\u00b0K was obtained in this preliminary experiment. The temperature indicated by the order of points (1) and (2) suggest that the specimen had been warmed on the application of the polarizing f i e l d or that thermal equilibrium has not been achieved bet\\\\reen the cooling salt and the specimen, or both, before the counting had commenced. Theoretically, Figure 5.1 suggests that at a specimen temperature of the Neel temperature (0.012\u00b0K) of the cooling salt one should expect an anisotropy of the order of about 0.49 or 4-9% . 5.4 Discussion The results obtained suggest that we can achieve temperatures approaching those required for orienting nuclei (^0.01\u00b0K), but some modifications in the low temperature apparatus are essential before any original experimental 58 work can be attempted. The following l i s t of improvements are essential: (i) To reduce the liquid helium boil-off rate due to heat leaks along the cryostat and magnet supports, along the e l e ctrical wiring, and in particular, along the large copper leads to the superconducting solenoid. ( i i ) To reduce the vibrations being transmitted to the specimen during an experiment. (These originated from the pumps and other associated equipment mechanically coupled to the frame or directly to the low temperature apparatus). ( i i i ) To redesign the magnetic susceptibility system so that reliable estimates of the temperature of the cooling p i l l can be made. (iv) To reduce the effects on the temperature of the cooling p i l l caused by the residual f i e l d remaining in the Ventron superconducting solenoid (even after sweeping i t to some minimum level) , and (v) To have the persistent current switch modified to enable us to achieve higher demagnetizing fie l d s , and hence, lower temperatures. The f i r s t four problems are discussed in Chapter 6 where solutions are also suggested. Ventron Inc. has voluntarily agreed to i n s t a l l a recently-developed persistent current switch which is supposed 59 to operate more e f f i c i e n t l y than the one current ly i n use. It i s ant i c ipated that th i s w i l l a l l e v i a t e the problems encount-ered i n attempting to achieve a high demagnetizing f i e l d ( ^ 45K gauss) . It i s a n t i c i p a t e d , with the above improvements, that i t w i l l not be d i f f i c u l t to achieve a temperature approaching 0.012\u00b0K, af ter which some o r i g i n a l experimental studies w i l l be attempted. Chapter 6 indicated the general d i r e c t i o n of the studies in nuclear or i en ta t ion at very low temperatures. CHAPTER 6 Future Program 6.1 Improvements P r i o r to any new experimental work several improvements in the apparatus w i l l be e s s e n t i a l : ( i ) A large heat leak exists in the present system along the cryostat supports, along the e l e c t r i c a l wiring, and primarily along the large copper leads extending from the top cap of the Dewar assembly to the terminal board that was usually immersed in l i q u i d helium during the course of an experiment. The support system being designed for a new a l l -s t a i n l e s s s t e e l Dewar assembly w i l l incorporate a l i q u i d nitrogen \"pot\" between the top cap and the terminal board or gas from a 20\u00b0K H 2 gas c i r c u l a t o r to shunt the heat leaks and conserve l i q u i d helium. ( i i ) Considerable heating of the sample resulted from vibrations transmitted to the specimen assembly during the course of an experiment. The heating effects were not tolerable since very low temperatures could not be achieved, and i f achieved, could not be maintained. The vibrations originated from the rotary backing pump, from the helium pumping l i n e which was connected to other systems as well as to piston-type pump, and from the manual operations performed during an experiment on the various valves and stop-cocks on the pumping lines and on the pressure-monitoring controls. 61 These effects w i l l be minimized by mounting the low temperature system on a r i g i d chassis (which i t s e l f w i l l be bolted to a concrete floor) and by separating and isolating from the system the various controls and pumps. The pumps w i l l be isolated by using more flexible connectors than previously employed and fixing these rig i d l y to the floor, a concrete wall or a heavy p i l l a r between the pumps and the apparatus. ( i i i ) The susceptibility c o i l - mutual inductance system w i l l be redesigned to function reliably at very low temperatures. In particular, care w i l l be taken to avoid ground loops and pickup from associated electrical and electronic equipment in the v i c i n i t y of the c o i l , the leads, and the mutual inductances used in the bridge network. (iv) The effects of the residual f i e l d remaining in the superconductor after a demagnetization w i l l be reduced by wrapping Netic mu-metal (Magnetic Shields Division, Perfection Mica Co., 1322 North Elston Avenue, Chicago, I l l i n o i s , 60622) around the outer jacket of the cryostat just inside the bore of the superconductor and extending in either direction over the paramagnetic p i l l to shield i t completely'. The mu-metal would readily saturate in high magnetic fields but would shield out low fields of several hundred gauss. Increased cooling efficiency would result but the presence of the mu-metal would necessarily require that the susceptibility c o i l be dispensed with. This would not pose a problem since the y-radiation anisotropy of Co 6 0 (or some other suitable 62 radioactive isotope such as Mn-54) in Fe would provide a direct and reliable measure of temperature. (v) In the future lithium-drifted germanium detectors w i l l be incorporated into the low temperature apparatus rather than used externally. This would reduce the attenuation of the y-radiation, improve the solid angle of the detector (assuming that the detectors are large enough and more closely located to the sample than previously) , and also to improve the resolution of the y-transitions being measured since the effect on the line width due to scattering would be less. This system of detectors would\" be particularly useful in instances where the y-transition from the thermo-meter closely correspond, in energy, to the y-transitions being observed, or in the case where two or more different y-transitions are close together in energy. 6.2 Future experimental work Other thermometers that show large anisotropies at low temperatures w i l l be calibrated to make the system versatile. It would, for example, be d i f f i c u l t to measure the anisotropic effects in Fe 5 9 in Fe using Co 6 0 in Fe since the 1.10 Mev y-transition of Fe 5 9 and the 1.173 Mev of Co 6 0 * ' f a l l outside the resolution capabilities of the sodium iodide detector. This problem might not be as d i f f i c u l t i f lithium-drifted germanium detectors were incorporated into the low temperature system. One could also use a suitable computer 63 program to separate or \"st r i p \" the Fe 5 9 spectrum from the composite spectrum of Fe 5 9 and Co60-. This involves a computation which uses the ratio(s) of contributions from different transitions and gives the number of events corres-ponding to each of these transitions in the total number of events observed at a given energy. Both of the above methods are relatively complex for long-lived radioactive isotopes, however they become very complex for short-lived radioactive isotopes since time then complicates the computations. A simplier method would be to incorporate a Mn51* thermometer, as the 0.835 Mev y t r a n s i t i o n of Mn 5 4 is well-separated in energy from the 1.10 Mev y-transition of Fe 5 9 and only corrections for the contributions of higher energy transitions need to be made. Several other radioactive isotopes, like Mn5Jt, which have relatively long lifetimes, have well-under-stood transitions and show appreciable temperature-dependent anisotropic effects at low temperatures, w i l l be calibrated and used for thermometry, the selection of any particular one depending on the sample nuclei being studied. The study of oriented nuclei at low temperatures w i l l be extended to other radioactive isotopies that can be alloyed with iron, Eventually nickel and cobalt alloys w i l l be investigated. Nuclear magnetic resonance experiments w i l l be incorporated into the system to measure some of the \"unknowns\", in particular, the effective f i e l d , H f f . Hopefully, a 64 significant contribution w i l l be made to the understanding of orientation mechanisms and nuclear processes involved in $- and Y\"- transitions. 65 REFERENCES USED IN THIS THESIS A b r a g a m , A., and P r y c e , M. H. L., P r o c . Roy. S o c . S e r . A 205 (1951) 135. A m b l e r , E., P r o g r e s s i n C r o g e n i c s ( e d . by K. M e n d e l s s o h n ; Heywood L o n d o n ! 2_ (1960) 23~3~; A m b l e r , E., N u c l e a r O r i e n t a t i o n , - U n i v e r s i t y o f M a r y l a n d , T e c h . Rep. (1961) 248. A m b l e r , E., M e t h o d s i n E x p e r i m e n t a l P h y s i c s ( e d . by L. M a r t o n ; A c a d e m i c P r e s s , N.Y.) (1963) 162. B l e a n e y , B., P r o c . P h y s . S o c , A 6_4_ (1951) 315. B i s h o p , G. R. , D a n i e l s , J . M., G o l d s c h m i d t , G., H a l b a n , I I . , K u r t i , N. , a nd R o b i n s o n , F. N. H., P h y s . Rev. 88^  (1952) 1432 . B i e d e n h a r n , L. C , and R o s e j M. E., Rev. mod. P h y s . 25_ (1953) 729. B l i n - S t o y l e , R. J . , G r a c e , M. A., and H a l b a n , H., P r o g r . N u c l . P h y s . 3 (1953) 63. B l e a n e y , B., D a n i e l s , J . M., G r a c e , M. A., H a l b a n , H., K u r t i , N., R o b i n s o n , F. N. H., and S i m o n , F. E., P r o c . Roy. S o c . A 221_ (1954) 170. B l i n - S t o y l e , R. J . , and G r a c e , M. A., H o r d b u c h Der P h y s i k 42_ (1957) 555. C o x , J . A. M. , and T o l h o e k , H. A., P h y s i c a 19_ (1953) 673. De G r o o t , S. R. , and T o l h o e k , H. A., P h y s i c s 1_6 (1950) 456. De G r o o t , S. R., P h y s i c s 1J3 (1952) 1201. F e r e n t z , M., and R o z e n z w e i g , N., T a b l e o f F C o e f f i c i e n t s , ANL (1953) 5324. G o r t e r , C. J . , P h y s i c s 1_4 (1948) 504. G o r t e r , C. J . , Poppema, 0. J . , S t e e n l a n d , M. J . , and B e u n , J . A., P h y s i c s 1_7 (1953) 1030. G r a c e , M. A., J o h n s o n , C. E., K u r t i , N., S c u r l o c k , R. G., and T a y l o r , R. T., C o n f e r e n c e de P h y s i q u e des b a s s e s t e m p e r a t u r e s , P a r i s , 2-8 S e p t . 1955 ( P a p e r n o s . 150, 159). 66 Gray, T. P., and Satchler, G. R. , Proc. Phys. Soc, A 68 (1955) 349. Hanna, S. S., Heberle, J., Perlow, G. J., Preston, R. S., and Vincent, D. H., Phys. Rev. Letters 4 (I960) 513. Huiskamp, W. J., and Tolhoek, H. A., Progress in Low  Temperature Physics 3 (ed. C. J. Gorter; North-Holland Publishing Co., Amsterdam, 1961) 333. Kogan, V., Kulkov, V. D., Nikitin, L. P., Reinov, N. M., Sokolov, I. A., and Stelmah, M. F., Soviet Physics JETP 12_ (1961) 34; 13 (1961) 78. Landolt-Bornstein, Springer-Verlag (1961) 2-124. Lindgren, in Perturbed Angular Correlations (edited by Karlsson, E., Matthias, E., and Siegbahn, K . ; North-Holland Publishing Co., Amsterdam, 1964) 385. Mendoza, E., Ceremonies Langevin-Perrin College de France, 5 (1948) . Morita, M. , Lecturers Thor. Phys. Colorado 4_ (1961) 358. Matthias, E., and Holliday, R. J., Phys. Rev. Letters 1_7 (1966) 897. Pound, R. V., Phys. Rev., 76^  (1949) 1410. Poppema, 0. J., Steenland, M. J., Beun, J. A., and Gorter, C Physics 21 (1955) 233. Rose, M. E. , Phys. Rev. 75_ (1949) 213. Roberts, L. D., and Dabbs, J. W. T., Ann. Rev. Nucl. Sc. 11 (1961) 175. Simon, A., Van Der Sluis, J. H., and Biedenharn, L. C , Numerical Tables of Racak Coefficients, ORNL (1954) 1679. Steenland, M. J., and Tolhoek, H. A., Progress in Low  Temperature Physics 2 (ed. by C. J. Gorter; North-Holland Publishing Co., Amsterdam, 1955) 292. Somoilov, B. N., Sklyarevskii, V. V., and Stepanov, E. P., Soviet Physics JETP 11_ (1960) 261; 9 (1959) 44BL, 972 , 1383 Stone, N. J., and Turrell, B. G., Physics Letters 1_ (1962) 3 67 Tolhoek, H. A.,, and Cox, J.. A. M. , Physics 18 (1952) 357 . T u r r e l l , B. G., Ph.D. Thesis, Oxford (1963). Wheat ley, J . C , Huiskamp, W. J. , Diddens, A. N., Steenland, M. J . , and Tolhoek, H. A., Physics 21 (1955) 841 .. 68 APPENDIX Al The Correction for the Solid Angle  Subtended by the Counters' The angular distribution of the y-ray intensities from a system of oriented nuclei is given by: W(e) = 1 +, A 2P 2 (6) + A,,Pi, (e) ( A l . l ) where A 2 = U 2F 2B 2 , \u2022 Aj, = Ui^F^B^ , and P(e) are the Legendre polynomials. Let us consider the case of the \"axial\" intensity counted by a crystal subtending angle WQ at the specimen as in Figure A l . l . The Legendre polynomials are given by: P 2 = |(3 cos 2 6 - 1) (A1.2(a)) Pn = -(35 cos 4 6 - 30 cos 2 6 + 3) (A1.2(b)) 8 and the solid angle is given in terms of the half-angle 6 by w = 2TT(1 - cos 6) from which du = 2u sin 0 d 6 The count registered in the interval e to 6 + de is given by equation ( A l . l ) , and the axial registered by the counter, which subtends a half-angle a, is ,69 SPECIMEN DETECTOR FINITE SOLD ANGLE SUBTENDED BY DETECTOR AT SPECIMEN RGURE M-I 70 W(o) ' = \/ \u00b0 [1 .+. A 2P 2(o) \u2022 + A^P^Ce)]. do) o (A1.3(a)) \u2022 to 0 . \/ d M \u2022 o \/ [1 + A 2 P 2 ( e ) + A^P^Ce)] s i n e de 0 . : (A1.3(b)) a \/ sin e de \" o I + ~ j (3 cos 2e-l) sin e de Li 1 ' ' 0 \/ sin e de o + \u2014 \/ (35 cos^e - 30 cos 2e + 3) sin e de  8 o I \u2014 -\/ sin 9 de (A1.3(c)) o from where W(o)' = 1 + \u2014cos a(l+cos a)A 2 + icos a(l+cos a ) ( 7 cos 2a-3)A 4 2 8 - (A1.3(d)) = 1 + g 2A 2 + g l +A 4 (A1.3(e)) where g 2 = \u2014 cos a (1 + cos a) , and 2 g 4 = \u2014 cos a (1 + cos a) ( 7 cos 2 a - 3) 8 71 This can be compared v\/ith the true a x i a l count, obtained by-putting 6 = 0 i n equation ( A l . l ) , i . e . W(o) = 1 + A 2 + Ah In fact these s o l i d angle correction factors are v a l i d over any observed angle so that i n general W(e)' = 1 + g 2A 2P 2 (e) + g^P,, (6). 72 APPENDIX A2 Amended Instructions For Operating' .Veritron. Superconducting soTenoid and~CFC 100 Power Supply 1. Check that the diode is connected across the input terminals (above Dewar assembly). 2. Check that output from power supply is connected + to white cable, - VE to black cable. 3. Check quench sensing leads are connected - white to terminal 3, black to terminal 4. 4. Check that heater leads are connected to terminals 7 and 8. 5. Turn current control to minimum position. 6. Set desired current limit. 7. Check that sweep rate knob is disengaged. 8. Press stop button on sweep selector. 9. Press P.C. off button. 10. Turn on AC power and wait a minimum of 3 minutes (warm up period). 11. Press DC on button. 12. Manually rotate current control pot until 5 amps is indicated on the meter. 13. Check that heater current control #1 is maximum counterclockwise and turn heater 1 on. 14. Turn up heater current until a voltage jump is seen (persistent switch is now normal). 15. Return current control to minimum. 16. Engage desired sweep rate and press up_ button to increase current linearly. 17. Depress stop button when desired current level is reached (if below selected current lim i t ) . 18. To place magnet into persistent mode wait until voltage has decreased to a minimum and turn the heater current pot to zero. Carefully lower the power supply current to zero manually or \\^ith the downsweep f a c i l i t y . 19. To return to the sweep mode, carefully turn up the supply current to its previous level and turn up the heater current to its original level. 20. To de-energize gradually reduce the current to zero (manually or with sweep f a c i l i t y ) . When voltage reaches a minimum depress the P.C. off button. \u00bb '\u2022 21. If a quench is indicated press quench reset button and return current control pot to zero. Do not press P.C.  off button before returning current control pot to zero. 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