UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Nuclear orientation of Bi²⁰⁶ in nickel McConnell, Peter Robert Henderson 1975

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1975_A6_7 M32.pdf [ 7.57MB ]
Metadata
JSON: 831-1.0093256.json
JSON-LD: 831-1.0093256-ld.json
RDF/XML (Pretty): 831-1.0093256-rdf.xml
RDF/JSON: 831-1.0093256-rdf.json
Turtle: 831-1.0093256-turtle.txt
N-Triples: 831-1.0093256-rdf-ntriples.txt
Original Record: 831-1.0093256-source.json
Full Text
831-1.0093256-fulltext.txt
Citation
831-1.0093256.ris

Full Text

NUCLEAR ORIENTATION OF Bi IN NICKEL by PETER ROBERT HENDERSON MCCONNELL B.Sc,, University of British Columbia, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT 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 October, 1975 11 In presenting t h i s thesis 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 Library 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 further agree that permission f o r extensive copying of t h i s thesis 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. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis 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, Canada V6T 1W5 ABSTRACT A study of the Pb decay was performed by Nuclear Orientation 206 of Bi nuclei in a Nickel host at very low temperatures. The hyperfine f i e l d of B i ^ ^ / N i was determined to be 400-34 kiloGauss, with only 65 % of the Bismuth nuclei occupying 'good' lattice sites. Mixing ratios 206 were determined for several transitions in the Pb decay. Attenuation coefficients due to reorientation effects in the isomeric state at 206 2200 keV, excitation in Pb were measured. A discussion of the fractional occupation of 'good' lat t i c e sites By the Bismuth nuclei is given. i v TABLE OF CONTENTS TITLE i ABSTRACT i i i TABLE OF CONTENTS i v LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS i x .vHAPTJ-R, 1 INTRODUCTION CHAPTER I THEORY OF NUCLEAR ORIENTATION 1 1.1 Theoretical Review 1 1.2 Methods of Orienting Nuclei 9 1.3 Experimental Techniques 13 1.4 Present Measurements 25 CHAPTER II EXPERIMENTAL APPARATUS AND PROCEDURES 28 2.1 Methods f or Producing Low Temperatures 28 2.2 Experimental Apparatus 33 2.3 C o ^ Gamma-Ray Thermometry 39 2.4 Gamma-Ray Detection System 42 2.5 Analysis Procedure 46 CHAPTER III NUCLEAR ORIENTATION OF B i 2 0 6 IN NICKEL 4 7 .3.1 Introduction 4 7 3.2 B i 2 0 6 Decay 51 3.3 The Samples 53 3.4 The B i 2 0 6 / N i Experiment 59 3.5 3.4.DiscuisiofiduTe 83 3.6 # Conclusions 90 V APPENDIX A Spectrum Analysis Program SPECTAN I I 91 B The Angular D i s t r i b u t i o n Program ANGDIST 100 C The Nuclear Orientation F i t t i n g Program NOFIT 111 D Ca l c u l a t i o n of the U v C o e f f i c i e n t s 130 E Hyperfine D i s t r i b u t i o n F i t t i n g Program HYPFIT 134 BWLIOGRAPHY 140 TABLE 1.1 TABLE 1.2 TABLE TABLE TABLE 2.1 2.2 LIST OF TABLES A summary of various experimental techniques. Hyperfine f i e l d s at Bismuth impurity n u c l e i . Data f or paramagnetic s a l t s . Factors describing the Co^/Fe anisotropy 3.1 Host metal powders used i n the sample preparatipreparation. TABLE 3.2 F i t t e d values of the f r a c t i o n f, Hyperfine f i e l d H, and the standard deviation f o r the two models used i n the an a l y s i s . TABLE TABLE TABLE TABLE 3.3 3.4 3.5 3.6 206 data. TABLE 3.7 TABLE TABLE 3.8 Cl TABLE C2 Results of the analysis of the Bi Det a i l s of the P b 2 0 6 decay. Table of Uy c o e f f i c i e n t s . Energies of the Compton edges and sing l e escape P e ^ | associated with gamma-rays of the Pb and Co decays. Mixing rating and attenuation c o e f f i c i e n t s f o r the Pb decay. Atomic diameters f o r B i , Fe, Co, and Ni. Theoretical and psieudo-experimental data points f o r Co60. Tabulation of the r e s u l t s when f and H were va r i e d . 24 26 32 39 53 66 68 69 72 74 77 86 120 127 v i i FIGURE 1.1 FIGURE 1.2 FIGURE 1.3 FIGURE 1.4 FIGURE 1.5 FIGURE 1.6 FIGURE 1.7 FIGURE 2.1 FIGURE 2.2 FIGURE 2.3 FIGURE 2.4 FIGURE 2.5 FIGURE 2.6 FIGURE 2.7 FIGURE 3.1 FIGURE 3.2 FIGURE 3.3 FIGURE 3.4 LIST OF FIGURES Ty p i c a l decay scheme f o r a nucleus of spin I decaying to f i n a l state spin of I 2 > ° D e f i n i t i o n of the angles <*• and fi used i n the determination of the s o l i d angle co r r e c t i o n f a c t o r . Experimental arrangement f or detecting angular co r r e l a t i o n s of successive gamma ra d i a t i o n s . Ground and excited states of ^^2^3 t n c * t n e h L ' : i ' absorption spectrum of Fe20^. Mossbauer spectrum f o r Yttrium Iron Garnet showing the e f f e c t of nonequivalent l a t t i c e s i t e s on the Iron hyperfine s p l i t t i n g . The e f f e c t of R.F. r a d i a t i o n of frequency V Q on the population d i s t r i b u t i o n of magnetic substates i n a system of po l a r i z e d n u c l e i . 4 t Resonant absorption curve f o r Co^/Fe. Elements of a t y p i c a l d i l u t i o n r e f r i g e r a t o r . D e t a i l s of low temperature cryostat. D e t a i l s of inner jacket assembly. Typical system performance. The decay scheme of C o ^ . 206 The decay spectrum of Pb f o r a 2"x2" Nalf T l ) detector. Block diagram of the e l e c t r o n i c systems. V a r i a t i o n of the A v parameters as a function of the quadrupole i n t e r a c t i o n parameter X. 206 The decay scheme of Pb The quartz v i a l and graphite block dimensions as used i n the sample preparation. Block diagram of the apparatus used to determine the saturation magnetization of the samples. 2 8 16 20 22 23 29 34 36 38 40 43 44 49 52 56 57 v i i i FIGURE-3.5 Figure 3.6 FIGURE 3.7 FIGURE 3.8 FIGURE 3.9 FIGURE 3.10 FIGURE 3.1H FIGURE 3.12 FIGURE 3.13 FIGURE Al FIGURE Cl FIGURE C2 FIGURE C3 FIGURE C4 Data obtained from the cir c u i t of Figure 3.4 58 Bi206/Co6P warm spectra with Ge(Li) detectors. 60 Flow chart for the analysis of the Pb spectra. 206 64 Data for the 1719 keV gamma-ray with best f i t s 70 for the two cases discussed. 206 ' Decay scheme of Pb showing the location of /'; 75 the Compton edges of Table 3.6. Spectra for the 497 keV , 516 keV,, and 537 79 keV, transitions showing the effect of the Compton edge from the 803 keV. transition on the background calculations. . Fi'action of Bismuth nuclei at substitutional 83 latt i c e sites for various annealing temperatures, la Annealing behaviour tor Yb in Fe. 85 206 Hyperfine f i e l d for Bi /Fe as a function 87 of annealing time at 800 °C. Sample calculation of the type performed by 92 SBEGTAN II. Results of the 6gitting routine NOFIT on 122 theoretical Co data. Results of NOFIT on ecuedpseudo-experimental 124 data. Results of NOFIT on Co 6^ ps'eudo-experimental 126 data with a standard deviation of d=0.20 . Exagerated effect of f and H on the f i t to the 128 data. i x ACKNOWLEDGEMENTS The author wishes to express his sincere gratitude to The National Research Council of Canada for i t s f i n a n c i a l assistance, Dr. P. W. DrrtRn W. Martin and Dr. B. G. T u r r e l l f o r t h e i r supervision during the experiments, R. L. A. GRrlL,.<gA.RGorjHngr,RanKei'ser:, andyPfoW.tDaly for.their•• assistance during the experimental runs, J . Lees and E. Williams of the glassblowing shop f o r t h e i r 206 assistance i n the preparation of the Bi samples, Anne E. H i l t z f o r her assistance i n typing the t h e s i s , and to M. K i l l i a n f o r her assistance with the computer programming. 1 CHAPTER I ' THEORY OF NUCLEAR ORIENTATION 1.1 Theoretical" Review Nuclear Orientation refers to the production of an ensemble of nuclei whose spins are grderededalong'some preferred axis in space. The relative populations of the magnetic substates of such a system are not equal, that is a(M) ^  (21 +1) ^, where a(M) is the relative population of the substate M for a nucleus of spin I. If there exists a distinction between up and down along this preferred axis (i.e. a(M) •$ a(-M) for at least one value of M) , then the ensemble of nuclei is referred to as polarized, • If the nuclei are oriented but there exists an up-down symmetry (i.e, a(M) = a(-M) for a l l M), then the ensemble i s said to be aligned. It i s often useful to note whether a specific orientation process produces polarization or alignment of the spin ensemble. These aspects of nuclear orientation w i l l be dealt with in greater detail in the discussion of experimental techniques. In a system of oriented nuclei, the angular distribution of the radiation from the decaying nucleus is dependent on the quantum numbers describing the states involved in the decay process. Consider a nucleus of spin I q , with the population of the magnetic substates M q given by a(M Q), decaying to an intermediate state 1^ by emission of radiation with angular momentum L q . If this state promptly decays to a f i n a l state of spin I by a transition involving radiation of angular momentum L^, the angular dependence of this radiation i s given by W ( 9 ) = J J n a ( M o ) | C ( I l ' L o ' I o ; % ~ m' ^\2\ca2,hvIi; MQ - m - n, n)| 2F L M (9 ) (1.1) where C i s the Clebsch-Gordan co e f f i c i e n t and F L M ( 9 ) " y = n l ^ l ' 1 ' ^ M - y, y)| ^ _ y(9) Here M refers to the z component of the radiation L. +3 +2 +1 0 ^1 .^ 2 ^3 In=3 Ii=2 » y y — t-2 — +1 — 0 — -1 — -2 L1=2 (1.2). I2=0 FIGURE 1.1 Typical decay scheme for a nucleus of spin I decaying to f i n a l state spin I^. The many sums involved i n (1.1) can be reduced to a sim p l i f i e d form using Racah coef f i c i e n t s and Legendre Polynomials, yi e l d i n g W(9) = Z B U F P (cos0) (1.3) V even Here,,v, r e s t r i c t e d to even values for parity-conserving t r a n s i t i o n s , i s carried to the maximum index value of 21 , 21,, or 2L., , whichever i s o' 1 1' the smallest. In practice, the sum is usually terminated at v = 4, The Bv coefficients describe the I n i t i a l state and involve only parameters describing this state. Thus B v = (2v + l ) h z C(I o,v, I Q ; M q , o) a(MQ) M o (1.4). O In this work static nuclear orientation is employed, in which case the populations of the nuclear magnetic substates are given by the Boltzman distribution (this shall be discussed in detail later). Therefore a ( M ) = exp ((BMQX = sinh 6(1 + h) oJ z exp(pM ) sinh (B/2) M ° o (1.5). and (1.6). The term 3 involves the hyperfine interaction and contains the temperature dependence of the observed radiation. At high temperatures where 3 ». 0, the intensity of the observed radiation is normalized such that W(9) =1, an isotropic distribution. The ratio of the yield at low temperatures, cold counts, to the yield at high temperatures, warm counts, is defined as the anisotropy. The Uv c o e f f i c i e n t s describe r e o r i e n t a t i o n effects caused by the unobserved t r a n s i t i o n ( s ) to the intermediate state. It involves only the spins of the states involved and the angular momentum connecting them. For the decay sequence considered here, I + I - L + v' x  UV = .(-1) ° ° .['(2I0 + D ( 2 I i + 1)1^ (^ 1^  I l 9 I -;Lov) (1.7). where W i s a Racah c o e f f i c i e n t . In the case of several unobserved t r a n s i t i o n s , the U ,^ factor i s the (k) (k) product of factors U v , where U^, i s the re o r i e n t a t i o n factor f o r each of the preceding t r a n s i t i o n s . For example, the cascade L L 1 L„ L . T o 1 2 m - 1 I »I. » I_ > I i > I o 1 2 m - 1 m (1.8) would have an e f f e c t i v e Uv c o e f f i c i e n t given by Uv = U V ( 0 ) (L ) U V ( 1 ) (IO Uy (L ) " o 1 m-1 (1.9). If the t r a n s i t i o n i f one of the mixed m u l t i p o l a r i t y i involving r a d i a t i o n with angular momentum L and L'", the U v c o e f f i c i e n t s must be replaced by the incoherent average of the combination. The mixing r a t i o i s defined by the parameter 6% such that < I I L' I v 1  N i l I SL 2' _ amplitude of r a d i a t i o n L7"' ^ = ( I | |"L'|I^)> amplitude of r a d i a t i o n L ^ ^ Then 2 UV(L) + <j U v (L' ) U v = — 2 " 1 + 6 (1.11) In most cases, one can restrict the mixtures to the two highest multipoles, L = AJ and L'' = AJ + 1. If there exists an appreciable interaction between the intermediate state of the nucleus and any extranuclear fields, an attenuation of Uv coefficients mayl be observed. The angular distribution of the radiation observed in the cascade Lo * L l I » I i-» T o 1 x2 (1.12) * is altered when the intermediate state 1^ is appreciably perturbed. Such perturbations can be caused, for example, by the interaction of the magnetic dipole moment u of the nucleus with a magnetic f i e l d H, or by the electric quadrupole moment Q interacting with an electric f i e l d gradient 2 2 3 V/3Z . The classical interpretation describes this i n terms of the Larmor precession of the nuclear spin about the symmetry axis. If the lifetime of the intermediate state is long enough, the orientation of the spin axis changes before the emission of the observed radiation L^. Quantum mechanically this corresponds to transitions among the magnetic substates of the intermediate state 1^ . The observed radiation then occurs from a state with an altered population distribution. Depending upon the type of interaction, this can result in an attenuation of the anisotropy of the observed radiation. Mathematically the effect can be 6 expressed i n terms of attenuation c o e f f i c i e n t s , A v , as follows: U v ' (IO = A-yUvC^) .(1.13) For most states with l i f e t i m e s l e s s than 10 ^ seconds, no attenuation Is observed and we have Av = 1. However, there are cases where the intermediate state l i f e t i m e i s long enough to cause appreciable perturbation of theintermediate state, with the r e s u l t that A-y < 1, A d e t a i l e d discussion of t h i s e f f e c t w i l l be given i n Chapter I I I . The observed gamma-ray t r a n s i t i o n i s described by the Fy c o e f f i c i e n t s , and involves only the angular momentum of the observed r a d i a t i o n and the spins of the states which i t connects. I t s formula, i n terms of the Clebsch-Gordan and Racah c o e f f i c i e n t s , i s 1 , - 1 2 + 1 ± = X-D (2L 1 + D(2I 1 + l ) 2 C d ^ v ; 1 - 1 ) W d ^ I ^ , ; I 2 v ) ,(1.14) where C i s the Clebsch-Gordan c o e f f i c i e n t and W i s the Racah c o e f f i c i e n t . In the case of a t r a n s i t i o n of mixed m u l t i p o l a r i t y , the Fv c o e f f i c i e n t for a t r a n s i t i o n of dominant multipole L and l e s s e r multipole L'1 i s given by the coherent average, F ^ I ^ L L ) + 26 F V ( I 1 I 2 L L ' L ) + 6 2 F^d^^I^L'S F v = —. - - _ 1 + 6 ,(1.15) using the sign convention of Biedenharm and Rose (1953). Here the mixing r a t i o 6 i s the same as defined i n (1.10). The Pv(cosG) are Legendre Polynomials, containing the angular 7 dependence of the observed radiation at an angle 9 relative to the orientation axis. In practice, a relatively large solid angle is subtended by the detectors which monitor the radiation. As a result the detectors do not look at a unique value of 9. In the case of cylindrical detectors i t is possible to calculate the correction to the angular distribution exactly. Rose (1953) has shown that for cylindrical detectors, the form of the distribution remains unchanged, with the exception of an attenuation factor multiplying the Legendre Polynomial terms. A detailed discussion of the derivation of these attenuation factors is given by Rose (1953) and Yates (1964). The solid angle correction factors give the corrections to the anisotropies which must be made because of the f i n i t e solid angle subtended by the detector. In the analysis of the data, no energy dependence of this factor was considered. It was f e l t that since the cold counts were being normalized to warm counts of the same energy, that any corrections for the energy of the peak would be negligible. In particular, the attenuation factors are given by 1 - cosa /. Piy(cosg) sing dg (1.16) where the angles a and g are defined in FIGURE 1.2. 8 Z axis FIGURE 1.2 Definition of the angles a and $ used in the determination of the solid angle correction factor. Here a refers to the half-angle subtended by the detector face. The result is a new term which appears in the anisotropy expression given by (1.3) as p^(cose) = g^(cose) ^ 17y The Bv coefficients are calculated explicitly using the expression given in (1.4). Other methods exist for describing the in i t i a l state population (see DeGroot, Tolhoek, and Huiskamp (1965)). The Uv and Fv coefficients can be evaluated from tables of Yamazaki (1967) or using tables of Clebsch-Gordan and Racah coefficients. Ferentg and Rosenzwelg (1955) have tabulated the F coefficients up to.I = 12. A Fortan computer program is included in Appendix D for the calculation of the U0 and U, coefficients. 1.2 Methods of Orienting Nuclei There are several methods a v a i l a b l e f o r obtaining nuclear o r i e n t a t i o n at low temperatures. A l l of the methods reviewed i n t h i s work make use of the i n t e r a c t i o n of the nuclear magnetic dipole moment or the e l e c t r i c quadrupole moment with magnetic and e l e c t r i c f i e l d s r e s p e c t i v e l y . Abragam and Pryce (1951) express.the i n t e r a c t i o n by a Hamiltonian of the form H - %V . I + g|;.yBHgSz + g.B(Vx + VY> + A S g I z + B ( S X I X + S y I Y ) +D LSg -. 1/3 S(S + 1) + P [ l 2 - 1/3 1(1 + 1) where (1.18) = magnetic moment i n units of nuclear magnetons H = external applied magnetic f i e l d S = vef f ectivehionisi-spi-n? • *~ ::. raaa^v A & B = hyperfine structure coupling constants D & P = c r y s t a l l i n e e l e c t r i c f i e l d s p l i t t i n g parameters gjU & gj^ = spectroscopic s p l i t t i n g f a c t o rs u = Bohr magneton Only the 'Brute Force' method and method of o r i e n t a t i o n i n ferromagnets 10 shall be discussed in this section. Further methods of orienting nuclei are discussed by J e f f r i e s . (1963) -and Frauenf elder ""and *Stef fen. (1965). i) Brute Force Method This method involves the application of a large magnetic f i e l d to a system of free nuclei, causing Zeeman splitting of the level I into i t s 21+1 magnetic substates. The energy levels are given by m " — (1.19) and the relative populations of these levels are given by the Boltzman distribution a = exp (-Bin) Z exp '(-gin) (1.20) In this case, polarization of nuclear spins results since a(m) f a(-m). Appreciable polarization of the spin ensemble is achieved when 6 is the order of unity. In case of typical nuclei, such as Co^ with y = 3.56 and 1 = 5 , using 100 kilogauss as the limit of current magnet technology, temperatures of the order of 10 2 °K are required. D abks et•al. (1955) f i r s t used this technique, followed by Stolovy (1960), 115 to polarize In . Using the polarization parameter f of Rose (1949) . Em exp (-gm ) f = ± x i • i- • i N I ^ / . . • ^ -,>exp(-3mi) (1.21) which reduces to (for yH/kT ^ 1) 1 1 f „ 1 / 3 H i rN ' I kT (1.22) they were able to obtain polarizations for 2.1% and 3.0% respectively. i i ) Ferromagnets In ferromagnetic materials, the unpaired electron spins are aligned spontaneously along the easy axis of magnetization of the crystal domain. Upon application of an external magnetic f i e l d , the domains whose magnetization is more or less parallel to the external f i e l d increase in size, while the remainder decrease. The magnetization of the domains remain parallel to the direction of spontaneous magnetization during this process, which requires fields the order of a few hundred gauss. Application of even larger fields, the order of a few kilogauss, cause saturation of the domain magnetization so as to polarize them parallel to the direction of the external f i e l d . The orientation of impurity nuclei in ferromagnets occurs via the Fermi contact interaction between the 4'ssconduction electrons and the nucleus. These 4s electrons are polarized by the 3d electrons localized on the ferromagnetic atoms, and maintain this polarization. Impurity nuclei in the ferromagnetic host see a large hyperfine magnetic f i e l d produced by interaction with the polarized conduction electrons. This results in Zeeman splitting of the nuclear magnetic substates and subsequent polarization of the impurity nuclei at low temperatures. Marshall (1958) considers the orientation of nuclei in ferromagnets in detail. The effective magnetic f i e l d at the impurity nuclei may be written as 12 H ~> + H + H erf 1 c a (1.23) If we neglect the Lorentz f i e l d , the local f i e l d is given by IL = H - DM 1 e (1.24) where H & is the external f i e l d and DM is the demagnetizing f i e l d . This latter term is dependent upon the specimen shape. The contact term H results from the contact interaction from the 4s c conduction electrons which are spin polarized by the 3d electrons. A detailed discussion of this contribution to the effective f i e l d i s given by Shirley and Westenbarger (1965). The H term arises from the interaction of the nucleus with the a electrons of the same atom. The relevant terms in the spin Hamiltonian describing this interaction are H - AV2 + B<SXIX + S.YIY) (1.25) from (1.18). Forrtfreecasgeoffferroma^ the electron spins are aligned by the exchange interaction, hence and eanlbeirepiaced by zero'',cThe resutts-ist is H = -AST = a Z y (1.26) The result of this interaction is that the nuclei within a domain are polarized at sufficiently low temperatures. In the typical multidomain specimen, an external applied f i e l d i s necessary to align the individual domain magnetization along the preferred axis. Grace et.ai. (1955) were the f i r s t to observe this effect when -, -60 they, -oriented- Co ^huc 1-eiiinsa-Co-l^aMige. Orientation of non-magnetic impurity nuclei i s a result of the conduction electron polarization term H^ . Samoilov et.al. (1960) 114 122 198 obtained orientation of In , Sb , and Au in an iron host. Campbell (1969) has calculated the hyperfine f i e l d -in a wide range of impurities for several hosts. The advantage to this method is that a great many impurities are soluble to some extent in ferromagnetic hosts. A review article by Shirley (1971) gives a partial compilation of hyperfine fields in iron, cobalt, and nickel hosts. 14 1.3 Experimental Techniques In the experiments described here, the r a d i a t i o n emitted from a system of oriented n u c l e i i s measured as a function of temperature." and of angle r e l a t i v e to the o r i e n t a t i o n axis (.-_ i t - - i s taken as the d i r e c t i o n of the applied external f i e l d ) . The temperature dependence of the anisotropy i s contained i n the B v terms of Equation (1.3). By studying the temperature dependence of W(9), the hyperfine i n t e r a c t i o n uH e££ may be obtained. Once the hyperfine i n t e r a c t i o n has been determined, and hence the By terms established, the U yFy terms can be extracted f rom the data. The and F^ c o e f f i c i e n t s are exactly determined by the spin assignments to the states involved and the m u l t i p o l a r i t y of the t r a n s i t i o n s between these states. This allows assignments to be made f o r the decay scheme of the r a d i a t i o n being studied. The importance of such a method for studying nuclear decay was f i r s t proposed by Halban (1937). I t should be mentioned that the F^ c o e f f i c i e n t s i n (1.3) are dependent upon the mixing r a t i o , as shown In (1.15). The quadratic form allows not only the magnitude of 6 to be determined, but often the sign as w e l l . One of the two possible values of & can be selected on the basis of a v a i l a b l e i n t e r n a l conversion data. Other experimental methods which determine these quantities are: i ) Angular C o r r e l a t i o n This method i s quite s i m i l a r to that of nuclear o r i e n t a t i o n . For example, i n the case of a gamma-gamma cascade, detection of the f i r s t emitted gamma-ray establishes a quantization axis r e l a t i v e to which the succeeding t r a n s i t i o n i s measured as a function of the angle. For an 1- t r a n s i t i o n , the angular c o r r e l a t i o n function i s given by 15 W(cose) = E F k ( 1 ) F k ( 2 ) (cos8) k even (1.27) Here the F^"^ and F^^^ terms are the F^ coefficients of Ferentz and Rosenzweig (1955) for gamma-rays 1 and 2 respectively. The P^(cosG) are the Legendre polynomials. It has the advantage that i t can be performed at room temperature. The decay scheme is depicted schematically in FIGURE 1.3. A more complete review of this method is given by Fraunfelder and Steffen (1965). i i ) Perturbed Angular Correlation If one of the intermediate states in a gamma cascades is a long lived one, the interaction between internal, or external, electromagnetic fields and the nuclear moments cause a perturbation of the angular correlation. For example, in the case of an electric quadrupole interaction,,an attenuation of the angular correction is observed, of the form w (e) = F k ( 1 ) F k ( 2 ) G k k Pk(cose) (1.28) where the term is the attenuation factor. The original application of this technique was in the measurement of nuclear g-factors, first successfully applied by Aeppli et.al. (1951). It is also extensively used in hyperfine studies where the hyperfine interaction may be derived from the precession of the nuclear spin. A detailed discussion of this technique is given in Karlsson et.al . (1964), Fraunfelder and Steffen (1965), and Steffen (1955). 16 t 2^ f Detector 1 Detector 2 Counter Coincidence Unit 'FIGURE 1.^ 3 Experimental arrangement f o r detecting angular c o r r e l a t i o n s of successive gamma r a d i a t i o n s . 17 i i i ) Internal Conversion When a nucleus decays from an excited state, i t may do so by emission of electromagnetic radiation, or i t may transfer the energy to an orbital electron resulting in i t s ejection from the atom.• This electron ejection process is referred to as internal conversion. • The ratio of the number of conversion electrons per unit time to the number of photons per unit time is defined as the internal conversion coefficient a. These coefficients are determined by the amount of energy involved in the transition, the angular momentum change, and the parity change. A detailed treatment is given by Rose (1960) and (1965). iv) Mossbauer Effect Recoil-free absorption of nuclear resonance radiation was f i r s t discovered by Mossbauer (1958). This resonance radiation makes possible the study of the hyperfine structure in the excited states of many . nuclei. The detection of the resonance radiation arises from the change in the resonance effect as a function of the relative velocity between the source and absorber. The degeneracy of the excited levels involved in the resonant transition can be removed, say by the hyperfine interaction, and the magnetic substates in the absorber s p l i t . As long as the hyperfine splitting of the resonance line is greater than the level half-width, there w i l l be minimal absorption of the resonance radiation (for the case considered in FIGURE 1 .4) . In FIGURE 1.4 (a) i , there exists six different energies for the transition between the 3/2 exdite'd- state and the 1/2 ground states in the absorber. The morio-energetlc transition in the absorber does not match 18 14.4 keV (a) in IV Fe F e 2 O s ( b ) AE Y * 107 eV FIGURE 1.4 (a) (b) Ground and excited states of iron and Ye^O^ i) the 14.4 keV gamma decay of Fe-" *" and i i ) the hyperfine sp l i t t i n g of the two levels. The split t i n g of these levels in FeO is shown for i i ) magnetic hyperfine s p l i t t i n g and i i i ) quadrupole sp l i t t i n g . The chemical shift A is also shown. The absorption spectrum for Fe 0., Kistner and Sunyar (1960) . any of these. As a result, there is minimal resonance absorption of the source radiation. By moving the source relative to the absorber, the Dopple r shift of the source line can be brought into resonance with any one of the transitions in the absorber. It is possible to 'scan' a relatively -4 larger energy spectrum about the resonance line, about 10 ev range, and observe a l l of the transitions between the magnetic substates of the two spin levels in the absorber nuclei. The results of Kistner and Sunyar (1960) on the Fe^, 14.4 keV^ nuclear gamma resonance are shown in FIGURE 1.5 (b) for F e ^ absorber. Another interesting application of the Mossbauer effect is to alloy systems in which the impurity nuclei occupy non-equivalent sites. Bauminger et.al. (1961) used recoil free 14.4 keV~- gamma radiation to study internal fields acting on iron nuclei in Iron Garnet. The absorption spectrum for Yttrium Iron Garnet is shown in FIGURE 1.5.; In FIGURE 1.6, the stronger internal f i e l d i s assigned to the components of the doublets. Superposition of the doublets in lines 3 and 4 causes broadening of the absorption line. Similar results have been found by de Waard et.al. (1971) for various 133 atoms implanted in metals. In some cases (such as Cs Fe) they have found evidence high, intermediate, and low f i e l d sites. The theory of the Mossbauer effect is given by Frauenfelder (1963) and Mossbauer (1965). An excellent description of the experimental technique used in deriving the nuclear information from Mossbauer spectra i s given by Kistner (1966). 20 Relative Velocity - m n r l J s e c . FIGURE I . 5 Mossbauer Spectrum for Yttrium Iron Garnet showing the e f f e c t of non-equivalent l a t t i c e s i t e s on the Iron hyperfine s p l i t t i n g . Bauminger e t . a l , (1961) 21 v) NMR Nuclear magnetic resonance involves the absorption of resonant electromagnetic r a d i a t i o n between magnetic substates which are s p l i t by the hyperfine i n t e r a c t i o n . ' Impurity n u c l e i i n ferromagnetic hosts have been studied, but the impurity concentration must be larger than 0.1 atomic percent f o r a measurable e f f e c t . There are several cases i n which the impurity concentration i s so low that the NMR technique i s no longer f e a s i b l e . The theory of the magnetic resonance technique i s given,.for example, Abragam (1961) and Schumacher (1970). v i ) NMR/ON This technique employs NMR techniques on an oriented system of n u c l e i and the detection of decay r a d i a t i o n from them. The n u c l e i are p o l a r i z e d i n a ferromagnetic sample by standard nuclear o r i e n t a t i o n techniques and i r r a d i a t e d with an externally applied R.F. f i e l d . Resonant absorption of the electromagnetic r a d i a t i o n causes t r a n s i t i o n s between the magnetic substates of the l e v e l I. This tends to equalize the populations of the m substates and destroy the anisotropy of the decay r a d i a t i o n (resonant destruction of nuclear o r i e n t a t i o n ) . Removal of the external R.F. f i e l d allows r e l a x a t i o n of the nuclear spins back to population d i s t r i b u t i o n c h a r a c t e r i s t i c of the l a t t i c e temperature. The energy diff e r e n c e between the 2 1 + 1 substates i s given by AE = E 'm + 1 (1.29). 22 The resonant frequency V q i s then AE uH o h hi (1.30) where h i s Planck's constant. NO R.F. APPLIED. R.F. APPLIED. FIGURE 1.6 The effect of R.F. radiation of frequency v on the population distribution of magnetic substates in a system of polarized nuclei. Advantages to this method are: a) very high accuracy i s obtained in these resonance experiments ~0.05%. This limit results mainly from the inhomogenous broadening of resonance line, as mentioned by Stone (1971); and b) very low impurity concentrations, ~0.01 atomic percent may be studied. This makes NMR/ON very attractive for impurities which are not very soluble in ferromagnetic hosts. 23 The resonant destruction of nuclear o r i e n t a t i o n was f i r s t observed 60 by Matthias and H o l l i d a y (1966) for Co i n an Fe host. Resonance absorption curves are shown i n FIGURE l.<7, ' Count Rate (x 104) 77.0 76.5 76.0 164 167 Frequency (MHz) FIGURE 1.'7/. Resonant absorption curve f o r Co^/Fe [Matthias and Holliday (1966)] Detailed discussions of NMR/ON. are given by S h i r l e y (1968), and Stonet 1971). I t i s i n t e r e s t i n g to compare angular c o r r e l a t i o n , Mossbauer e f f e c t , and Nuclear Orientation as methods of studying the nucleus. A l l three of these methods are quite d i f f e r e n t i n various aspects. A general d e s c r i p t i o n of these techniques i s given i n Table 1,1, where the method of determining various nuclear properties i s given. Each of the three p a r t i c u l a r techniques has i t s own merits, depending upon the system being investigated. In some cases i t i s possible to compare r e s u l t s of a p a r t i c u l a r decay which were obtained by three e n t i r e l y d i f f e r e n t methods. 24 TABLE 1.1 A summary of various experimental techniques. LOW TEMPERATURE -•' MOSSBAUER EFFECT ANGULAR CORRELATIONS NUCLEAR ORIENTATION Preparation Polarized source preceding r a d i a t i o n Polarized parent. n u c l e i Detection resonant absorp-t i o n of r a d i a t i o n by absorber coincidence rate of succeeding r a d i a t i o n count rate of r a d i a t i o n as a function of 9 and/or T. Nuclear Properties Spin of Level number of absorption l i n e s i n spectrum f i t t e d values of F v c o e f f i c i e n t s to W(9) values of UvFv for observed r a d i a t i o n Angular momentum of r a d i a t i o n i n t e n s i t y of i n d i v i d u a l components i n the spectrum through Fv c o e f f i c i e n t through UvFv c o e f f i c i e n t 6 -angular d i s t u n . - a of component radiations and t h e i r i n t e n s i t y through Fv through Fv and/or Uv Hyperfine f i e l d s p l i t t i n g of absorption l i n e s values of attenuation c o e f f i c i e n t as a function of delay between coincidence ; of T - r a d i a t i o n c o r r e l a t i o n , form of W(0)vs. T. Appear i n the Bv(T) terms. 25 1.4 Present Measurements 206 The present nuclear orientation studies of Bi in an iron host lattice_were undertaken for several reasons, involving combined aspects of both nuclear and solid state interest. A great deal of theoretical and experimental work has been done 208 on nuclei in the region of the doubly closed shells of Pb . Nuclei 208 differing from the Pb nucleus by a few nucleons constitute one of the few regions that can be described f a i r l y accurately by conventional shell-model theory. The predicted energy levels of these nuclei are not very sensitive to the nuclear state wave functions. However, the mixing ratios of transitions between states are quite sensitive. Measurements of these mixing ratios can provide theorists with an accurate method for determining the wave functions of the states in these isotopes. From a nuclear structure standpoint, a great deal is known about 206 206 Pb , the daughter product in the decay of Bi . Very l i t t l e data, however, i s available on E2/M1 mixing ratios for several transitions and, for reasons mentioned above, i t was f e l t that measurements of these would be of interest. In addition, the existence of an isomeric state 206 at an excitation energy of 2200 keV, in Pb offered the possibility of studying reorientation effects. 206 The well-known level structure of Pb is of great advantage when attention is focussed on aspects of interest to solid state physics. Several studies of the hyperfine fields acting at Bismuth impurity sites in ferromagnetic hosts have yielded large discrepancies. This is illustrated in Table 1.2, where values of the hyperfine fields obtained by TABLE 1.2 Hyper f ine fields (kGauss) at Bismuth impurity nuclei. 1 * • I Group \ nuclide Host Nickel Cobalt Iron Bafabanov&Delyagin (1968) Bi 2 5 5 935 Zawis lak&Cook (1969) B i 2 1 1 . 160 — Bowman & Zawis!ak(1969) 1 } B i 2 0 7 115 430 6 6 0 Bacon e ta l . (1972) 2 ) B i 2 0 4 325 1180 Kaplan et. aL (1972) 2 ) B i 2 0 6 390 800 -1000 Daly (1973) 2 ) B i 2 0 7 4 0 0 - 6 0 0 1) Perturbed Angular Correlation. 2) Nuclear Orientation. 27 various experimental groups are shown. In this respect, i t was.felt that, in view of the low solubility of Bismuth in ferromagnetic host lattices, the 206 use of Bi as a probe would be particularly advantageous; the short h a l f - l i f e of the isotope (6.24 days) allows high activities to be realized at small concentration levels, while low temperature problems from internal heating of the source are minimized because of the electron capture decay. The possibility that sample inhomogeneities might be responsible for such large discrepancies provided a further aegis for these studies, in that nuclear orientation measurements might give 206 information on the distribution of Bi nuclei within the sample, 28 CHAPTER TI EXPERIMENTAL APPARATUS AND PROCEDURES 2.1 Methods for Producing Low Temperatures Several methods exist for obtaining the very low temperature required to polarize a system of nuclei. The two most common methods are dilution refrigeration and adiabatic demagnetization. A description of both methods i s given to show the merits of each system, i) Dilution Refrigeration 3 This method produces refrigeration by forcing He to dissolve from a 3 3 4 concentrated He phase into a saturated solution of He in superfluid He . 3 The adiabatic dilution of He causes cooling in the mixing chamber. A schematic representation of a dilution refrigerator is given in FIGURE 2.1. 3 In the apparatus of FIGURE 2.1, He gas enters the vaccuum jacket 4 and condenses in a condenser c o i l immersed in pumped He at a temperature of about 0.9 °K. The He^ then goes through the throttling capillary and a series of heat exchangers into the top of the mixing chamber. The 3 3 4 lighter He diffuses across the phase boundary created by the He + He 3 mixture, causing cooling in the mixing chamber. The diluted He continues to the s t i l l , in which the temperature is kept at about 0.6 °K. This 3 heating allows the He circulation rate to be controlled, due to the 3 vapour-pressure dependence on the temperature. Typical He extraction —5 —6 rates are the order of 10 - 10 moles/second. The extraction rate also influences the temperature of the mixing chamber. Temperatures as low as 4.5 m°K have been attained by Wheatley et.al.(1968). Commercially available units are capable of cooling rates of the order of 750 ergs/sec. at 0.1 °K, For nuclear orientation experiments, this allows higher activity samples to be used. This would improve the counting 29 Heater Pumping H e J Lines inlet m He Vacuum Jacket Condenser H e 4 Pot 0.9 °K Thrott l ing Valve Still 0.6 °K Heat Exchanger Mixing Chamber <0.1 °K H e 3 + H e 4 He" FIGURE 2.1 Elements of a t y p i c a l d i l u t i o n r e f r i g e r a t o r . 30 statistics and also allow weak transitions to be studied. One of the major problems in adiabatic demagnetization is the heating of the sample by charged particle emission. The fact that the large cooling rates can be realized for the dilution refrigerator, plus the fact that i t can be operated on an almost continuous basis, make i t a very desirable apparatus for low temperature- physics. For these reasons, the dilution refrigerator is rapidly replacing older techniques for producing very low temperatures. The technique of dilution refrigeration is discussed, for example, by Wheatley (1970). i i ) Adiabatic Demagnetization The process of adiabatic demagnetization is probably the most widely used technique for obtaining temperatures below." 1 °K. It was f i r s t suggested by Debye (1926) that the adiabatic demagnetization of a paramagnetic substance should produce low temperatures. This was proven experimentally by Giauque and MacDougal (1933) who obtained a temperature of 0.25 °K using Gadolinium Sulfate. For a paramagnetic substance at temperatures the order of 1°K, the entropy of the substance i s due mainly to the ionic spins. It is frequently the case in solids that they produce the only significant contributions to the net.magnetic moment, due to quenching of the orbital angular momentum by the crystal fields. These fields produce a very slight splitting of the 2S + 1 degenerate energy levels, the splitting being much less than k^T, The population of these levels i s therefore very nearly equal. If a large magnetic f i e l d H is applied to the system of paramagnetic ions in an isothermal manner, the levels are widely s p l i t (^ E £ k J) . This results in the lowest energy levels being more heavily populated, or a net decrease i n the entropy of the system. The thermodynamics of t h i s system can be represented by the equation TdS = C RdT + T dH (2.1) where S i s the system entropy, C i s the heat capacity at constant f i e l d H, H and M i s the magnetization. For an isothermal magnetization, (3M/3T) < Q, and dT =0. Therefore d S = ( f f ) H d H ' <2'2> and there i s a net decrease i n entropy of the system. If the paramagnetic ions are removed from a l l external sources and the system of ions i s a d i a b a t i c a l l y demagnetized, dS = ^ = 0 (2.3) since dQ = 0. In t h i s case, Equation (2.1) can be simplied to C H d T = - T f l ) H d H <2'4>' Since dH < 0, then dT < 0 and the temperature of the system w i l l decrease from the i n i t i a l temperature. The f i n a l temperature obtained for a paramagnetic substance i s given by Zemansky (1968) to be (2.5) for the case where the f i n a l f i e l d a f t e r demagnetization i s very weak (H f — > 0) . The constant term C c/A can be derived from the data of Zemansky (1968), and i s given i n Table 2.1 for various s a l t s . 32 Table 2.1 Data for paramagnet salts SALT 3 , cm - deg c gr.- ion A/R deg2 gram-ionic mass Cr 2(S0 4) 3-K 2S0 4. 24H20 1.84 0.01.8 499 F e 2(S0 4) 3 - (NH4) 2S04« 24^0 4.39 0.013 482 2Ce(N03)3-3Mg(N03)2-24H20 0.317 6.1 x 10"6 765 Here C c is the Curie constant, A is a constant term developed from Schottky's Equation, and R = N k . The term gram-ion refers to the mass A o of a crystal containing exactly N (Avogadros number) magnetic ions. The magnetic heat capacity per gram-ion of a paramagnetic salt at temperatures above the Schottky maximum are given by CH _ A/R R T2 (2.6). From the data of Table 2.1]': ±t:ican be seehatha't ^ theT*lowest^temperatures w i l l be obtained i f gerium magnesium .nitrate is used, the constant C£/A l of egn (2.5) being almost 100 times larger than that of iron ammonium Sulphate. However, the magnetic specific heat of the "iron ammonium sulphate is about 2000 times greater than that of Cerium magnesium nitrate. A detailed description of the theory involved is given by Zemansky (1968) and White (1968). 33 2.2 Experimental Apparatus The low temperature apparatus used in these experiments is described in detail by Kieser (1974). A brief description of this apparatus is given here. The apparatus used is these experiments in shown in FIGURE 2.2. Temperatures as low as 10 m°K are obtained by the adiabatic demagnetization of a chrome potassium alum salt p i l l in the inner jacket of the cryostat assembly. The cryostat has stages of cooling to provide temperatures the order of 1.2 °K necessary for the demagnetization of the salt p i l l s . i) Cryostat The i n i t i a l stage of cooling in the cryostat is provided by liquid nitrogen at 77°K in a glass dewar surrounding the Helium dewar . This minimizes helium boil-off during the experiments, thus reducing the number of helium transfers that must be made. A level indicator was placed in the nitrogen dewar and controlled a liquid nitrogen transfer system t o , f i l l the dewar automatically. The helium dewar was an evacuated, silvered, pyrex vessel which was supported from the top plate of the apparatus stand by a four wire support system. In order to reduce the heat flow down the pumping lines and electrical leads, .they were passed through a liquid nitrogen pot mounted on the top plate of the apparatus. This reduces the amount of boil-off in the helium dewar. Several radiation traps were soldered to the pumping lines to ensure as much heat as possible is absorbed by the evaporating helium gas. The helium level was monitored visually through unsilvered strips along the length of both the nitrogen and helium dewars. A system of brass jackets is used to house the salt p i l l assembly. The outer jacket contains the helium pot and the inner jacket. - Helium gas 34 5 10 -i i i i • i i Scale in cm. , , ' Top Plate Nitrogen Pot Pumping Lines Radiaton shield Outer Jacket Flange Helium Pot nner Jacke t Flange 22 kG. Solenoid Hel ium Dewar 4 0 kG. Solenoid Ni t rogen Dewar Polar iz ing Solenoid FIGURE 2.2 Details of low temperature cryostat. 35 is admitted to the outer jacket to precool the system. After the thermal equilibrium temperature of 4.2 °K is reached, the outerjacket is evacuated to a pressure of 0.001 micron. The helium pot is then thermally isolated from the inner dewar. A large capacity pump reduces the pressure in ;the helium pot to approximately 600 microns and a resultant temperature of 1.2 °K. Helium exchange gas in the inner jacket at a pressure of 10 microns thermally couples the salt p i l l assembly to the helium pot. The temperature of the guardpill is monitored by a 420 A carbon resistor., When thermal equilibrium i s reached in the p i l l assembly, —6 the inner jacket i s evacuated to a pressure of approximately 10 microns. The details of the salt p i l l assembly are shown in FIGURE 2.3. A chrome potassium alum p i l l constitutes the mainpill. This p i l l i s suspended by nylon supports from the helium pot. The mainpill has a ferric ammonium alum guardpill to isolate i t further from the helium pot. The temperature of the guardpill is approximately 50 m°K after a typical demagnetization. An auxilliary guardpill of Manganese ammonium sulphate was attached to the lower end of the heat shield, which is thermally isolated from the mainpill. This helps to reduce heat conduction to the mainpill produced by eddy current heating of the heat shield during demagnetization. Thermal contact between the mainpill and the sample is provided by a copper heat link. A system of three superconducting solenoids surround the jacket assembly. Two of these are used for demagnetization of the salt p i l l assembly. A Ventron Magnion 40kG. superconducting solenoid completely surrounds the mainpill assembly, while a smaller 22kG. superconducting solenoid surrounded the guardpill. The polarizing solenoid had a Helmholtz configuration and was located at the end of the copper heat link. 36 Helium Pot 4k 0 5 10 Scale in cm. Nylon Support Guardpill Nylon Support Mainpill Heatshield - Nylon Spacers - Aux. Guardpill - Nylon Spacer Copper Heatlink Heatshield Nylon Tip FIGURE 2,3 Details of the inner jacket assembly. t • 37 The conversion factor for this solenoid was 320 Gauss per Ampere and a maximum current of 40 A. could be reached without quenching. During magnetization, the pressure in the inner jacket is maintained at approximately 10 microns to f a c i l i t a t e the removal of the heat of magnetization produced in the p i l l s . The current in the solenoids was increased at 5 A./min. up to 25 A., and 1.5"A./min. to the maximum current desired. Once the magnets were in the persistent mode, the current was lowered to zero at the rate of 5 A./min. The polarizing solenoid was energized in the same fashion. When the salt p i l l reached thermal equilibrium with the helium pot, the inner jacket exchange gas was evacuated. The current to the magnets was increased to the original magnetization value in about 5 minutes to reduce Joule heating in the leads. When this value was reached, the 22 KG. and 50 k~G. magnets were put in the normal mode and.the current reduced at 5 A./min. to reduce eddy current of the copper heatshields. The demagnetization of the salt p i l l assembly produced temperatures of about 10 m°K. Test runs on the apparatus indicated that temperatures below 12 m°K could be obtained for up to 50 hrs. (Kieser 1974). Typical system performance during a normal experiment are given in FIGURE 2.4. It is quite apparent from FIGURE 2.4 (a) that there was a large helium boil-off when there were large currents present in the leads to the solenoids. FIGURE 2.4 (b) shows the cooling of the guard-p i l l to 1.2 °K, which corresponds to a guardpill resistor value of 750 ohms. The system was allowed to stabilize for slightly longer than one hour before demagnetizing the p i l l s . 38 800r TimeChrs.) FIGURE 2.4 Typi c a l system performance. 39 60 2.3 Co Gamma-Ray Thermometry The anisotropy of gamma radiation from\>polarized radioactive nuclei for thermometry was f i r s t used by Stone and Turrell (1962). In 60 the case of Co nuclei in an iron l a t t i c e , a l l parameters necessary for the description of the gamma-ray anisotropy are known, other than the temperature. Each B v i s a single valued function of the nuclear spin temperature T. Measurements of the gamma-ray anisotropy gives these B v values, and hence the value of T. 60 The decay scheme of Co.; is given in FIGURE 2.5. Angular momentum 60 considerat ions of the Co decay reveal that both the 1173 keV and 1332 keV, gamma-rays exhibit identical anisotropies. This allows an averaging of the combined gamma-ray counts to obtain better s t a t i s t i c a l accuracy. The 60 parameters describing the anisotropy of the C o decay are given in Table 2.2. 60 ' Table 2.2 Factors Describing the Co /Fe Anisotropy. Ground State Spin. 5 + Magnetic Moment 3.754 p N Hyperfine Field 287.7 kG Radiation E2 U 2F 2 -0.42056 U4 F4 -0.24281 60 The gamma-ray anisotropy for Co /Fe was calculated by the computer routine ANGDIST. Corrections to the hyperfine f i e l d at the Co nuclei were made for the polarizing f i e l d . A correction was also made for the f i n i t e solid angle subtended by the detectors. The temperatures of the spectra were obtained by correlating the corrected anisotropy with the temperature. ANGDIST- i s described in Appendix B with a sample output. 40 5.25 Yrs 2.5 The decay scheme of Co 41 The use of nuclear orientation thermometers is considered in,some detail by Berglund et . a l . (1972). 42 • 2.4 Gamma-Ray Detection System The gamma radiation of the Cp^ decay and the B i 2 ^ decay was. detected by a lithium drifted germanium detector positioned along the orientation axis (9 = 0°). It was necessary to use this type of detector father-thanhhighr efficiency sodium iodide detectors because of the higher resolution available. 206 The Ge(Li) detector used for the Bi /Ni experiment had a relative phptopeak efficiency of 13.8%. The peak-to-Compton ratio was.20 to 1, and the resolution of the 1332 keV Co^ peak was 3.2 keV.» For the 206 Bi /Co experiment, a detector with a relative photopeak efficiency* of 3.9% was used. The peak-to-Cbmpton ratio was 9 to 1, and the resolution of the 1332 keV Co^ peak was 5.0 keV. Here, the term resolution means the f u l l width at half maximum. Sodium Iodide detectors were not used because of the much poorer resolution of these detectors compared to the Ge(Li) type. Typical resolution for Nal(Tl) are 60 :keV, at the 1332 keV Co 6 0 peak. The P b 2 0 6 spectrum for a 2" x 2" Na(I) TI detector i s shown in FIGURE 2.6, which demonstrates the ina b i l i t y of the detector to resolve several of the transitions. The block diagram of the electronic processing and analyzing system is shown in FIGURE 2.7. When a gamma-ray interacts with the Ge(Li) crystal, a current pulse is produced which i s then converted to a voltage pulse by the preamplifier. This pulse has a short rise time of approximately 10 ^ seconds and a f a l l time of about 10 seconds. The preamplifier output i s The relative photopeak efficiency of a Ge(Li) detector is measured relative to that of a 3" x 3" Nal detector for the 1332 keV. peak of Co source at 25 cm from the detector. 43 P b 2 0 6 2"* 2" Nal(TI) ttt 497 516 537 803 8 9 5 Energy * 10 keV 0.5 1.0 ~i—i—i—i—i-100 -i—T—i—i r~ 2 0 0 3 0 0 Channel Number The decay spectrum of Pb for a 2 " x 2 " Nal(Tl) detector. In this spectrum, the two groups of closely spaced peaks cannot be resolved into the individual transitions which are indicated on the diagram. 44 Power Supply Preamp Amp & BLR Ge(Li) MCA Timer S C A Scaler Teletype Output FIGURE 2.7 Block diagram of electronic systems. 45 further amplified and shaped by the main amplifier. The unipolar output signal from the main amplifier was processed by a baseline restorer before analysis by the multi-channell analyzer, This processing reduces the degradation of the lower energy side of photopeaks, and the poorer resolution which arises from this. The output.from the linear amplifier and baseline restorer was presented to a 'mult^hGhannel^analxzer^CMCA^otoereeord .the^spectrum... A second output from the main amplifier was analyzed by a series of single channel analyzers (SCA's) and scalers. The SCA windows were set on particular peaks in the decay spectrum being observed. These were useful during the experiment to determine the approximate temperature of the sample and size of effect. An accurate determination of these parameters cannot be made by the scaler outputs because they include not only the photopeak counts, but the background counts as well. The f u l l spectrum was recorded in a Northern Scientific NS900, 1024 channel analyzer. In this unit, a pulse height analysis was performed on the linear output of the amplifiers and the data stored in the memory. The MCA could be programmed to count for a preset time, generally 1000 to 4000 seconds, and then the memory contents could be put onto punched paper tape and printed r o l l s . After the memory contents had been obtained, the memory could be erased and a new count.begun. The printed paper output allowed a reliable determination of p i l l temperature to be made from the spectrum. This indicated i f the demagnetization was a successful one. 46 2.5 Analysis Procedure The punched paper tape output of the MCA was converted to magnetic tape for analysis on an IBM 370/l8'4 computer. Separation of the photopeak counts was performed by the computer program SPECTAN I I , described in Appendix A. This program made corrections for gain shifts in the amplifiers and decay of the source. The warm counts were determined by the program and the cold counts were normalized to these. Further analysis of the SPECTAN II output was.performed by the computer program NOFIT, described in Appendix Cl. Using the anisotropy of the peak of interest and the temperature as determined by the Co^/Fe thermometer, several nuclear orientation parameters could be determined. 47 Chapter III 206 Nuclear Orientation of Bi in Ni. 3.1 Introduction As mentioned earlier in Chapter I, nuclear orientation experiments can yield information on both decay scheme parameters of nuclei, of relevance to shell model predictions, and on the electro-magnetic environment in which the decay occurs. These and other specific interests 206 provided a stimulus for the present nuclear orientation studies of Bi in hosts of nickel. a.:.,A '.coalt„ 206 The level scheme of Pb has been studied extensively from the decay 206 of the parent nucleus Bi . This decay scheme has been investigated by several groups (Alburger and Pryce 1954, Allan 1971, Kanbe et.al. 1972, and Manthurithil et.al. 1972). The spins, parities, and energies of a l l levels are well established from these experiments (except for the spin of.the 3225.53 keV level). In addition, internal conversion measurements have placed upper limits on E2 admixtures to the predominantly Ml transitions. True and Ford (1958) have shown that there w i l l be small E2 admixtures due to weak surface coupling to the neutron hole states. The nuclear orientation measurements yield two solutions, together with the signs, for this admixture. In most cases, the internal conversion measurements can be used to select one of the two solutions. The internal conversion measurements of Manthurithil et.al. (1972) have been used in conjunction with the present data. 206 The spin.and magnetic moment of the Bi ground state has been determined by Lindgren and Johansson (1959), using the atomic beam 48 magnetic resonance method.1 This leaves the hyperfine f i e l d as the only unknown in the description of the hyperfine interaction. 206 In the previous nuclear orientation of Bi in nickel by Kaplan et.al. (1973), attenuation of the 516 keV. transition from the 2200 keV, 206 isomeric state in Pb was observed. A similar attenuation was observed in the subsequent decays through the 803 keV.and 881 keV transitions. This effect could not be attributed to uncertainties in the decay scheme or higher order multipole admixtures to these transitions. Kaplan et.al. (1973) and Johnston et.al. (1974) have attributed this attenuation to a reorientation of the nuclear spin during the lifetime of the 120 ysec. isomeric state. The very small magnetic moment of 0.150 nuclear magnetons (Vary and Ginocchio, 1971) for the isomeric state gives rise to Zeeman splitting a factor of 10 smaller than typical values of the magnetic sp l i t t i n g . They investigated the effect of an off-axis quadrupole interaction not coaxial with the dipole interaction. Attenuation factors Av were calculated in terms of electric quadrupole and magnetic dipole contributions to the Hamiltonian. The Av coefficients of their calculations are shown in FIGURE 3.1, where the interaction parameter X is given as 3eQ 9 2V X = 41(21 - 1) r H £ f f 9 2 (3.1) It i s interesting to note that quadrupole effects from the crystal arise only i f the symmetry of the f i e l d is lower than cubic. The crystal structure of Nickel i s cubic and should not contribute to the quadrupole 206 splitting of the 2200 keV isomeric state in Pb . Johnston et.al. (1974) used this fact to suggest a non-substitutional, unique l a t t i c e site i n these hosts for Bismuth impurities. This w i l l be discussed in detail later. 49 FIGURE 3.1 Variation of the A v parameters as function of the quadrupole intera parameter X. 50 206 In order to resolve some of the questions about the Bi impurities in ferromagnetic hosts, a systematic study of the hyperfine interactions in Nickel -was carried out. Mixing ratios for several 206 transitions in the daughter Pb decay were measured, and attenuation coefficients due to reorientation in the 2200 keV- isomeric state were determined. Apart from the desirability of resolving the discrepancies in the values for the hyperfine fields, a question of central importance devolves on the criterion for a good sample. High solubility of the radioactive label in the host material may.not necessarily produce a sample with a high fraction of the impurity nuclei at l a t t i c e sites. It would be of great interest i f the analysis of such nuclear orientation measurements could yield information on this question. A more detailed consideration of this point is considered following the presentation of the results at the end of this chapter. 206 A study of the Pb decay in Iron and Cobalt was undertaken, but the data from the experiments was not of sufficient quality to be analyzed. 51.-3.2 B i 2 ^ Decay 206 The decay scheme of Pb i s shown in FIGURE 3.2, following Manthurithil et.al. (1972). The primary decay of 6 + B i 2 ^ ground state proceeds by electron capture to the 3279 kev\, and 3403 keV levels 206 — of Pb , both of which are 5 levels. A l l other secondary E.C. decays were ignored in the analysis. The 1719 keV, transition from the 3403 keV, 5~ level to the 1684 keV 4 + level proceeds by emission of a pure El gamma-ray. This transition was used to determine the" hyperfine f i e l d and fraction of nuclei at l a t t i c e sites, since a l l other parameters necessary to the calculations were known. The 516 keV. transition from the 2200 keW 7~ isomeric level to the 1684 ke\5i 4 + level has been determined to be a pure E3 transition. The attenuation resulting from reorientation in the 2200 keVV isomeric state was calculated by comparing the experimental anisotropics of the 516 keV " (E3), 803 keV. (E2), and 881 keV. (E2) radiations with those expected with no reorientation. Small E2 admixtures for several other gamma transitions were calculated by determining the F^ coefficients of the particular transitions of interest. B i 2 0 6 1—' I—" h-' h-' o O N O n 00 o O n 00 O J o n 00 (—' I— 1 CD t o CO t o 00 Oi o t o CO o o n o n t o ON 1—' X 4 ST* 7? CD CD CD CO CD CD CD CD CD CD CD CD CD < < < < < < « < < < < < Pb 206 49.6% 44.2%, 3-5% 5402 3279 3244 3016 2782 2647 2384 2200 1997 1684 1340 80: •FIGURE 3,2 The decay scheme of Pb 2°6 f showing only those t r a n s i t i o n s which were analyzed. 53 3.3 The Samples 206 The Bi activity was obtained from Amersham/Searle Corp. in the 206 form of carries free Bi C l 3 in HC1 solution. Since B i C l 3 boils at 400 °C, i t was not possible to prepare the sample by the regular method of evaporating the chloride onto metal f o i l s and furnacing at 700 - 900 °C. The Bi ions are more electronegative than Ni, Co, or Fe. This being the case, the Bi ions were allowed to plate spontaneously onto the surface of about 0.25 grams of Ni, Co, and Fe powders. The reactions were 2Bi(Cl) 4 + 3Ni 2Bi(Cl) 4 + 3Co 2Bi(Cl)~ + 3Fe 2Bi + 3 N i + 2 + 8Cl" 2Bi + 3Co + 2 + 8C1 2Bi + 3Fe + 2 + 8C1 (3.2) The ferromagnetic host were very high purity powders. Details are shown in Table 3.1. Table 3.1 host form purity source Fe 1-5 micron powder 99.9 % Atlantic Equip. Eng.+ Ni nickel sponge 99.99% Johnson and Matthey+ Co coarse powder 99.9 % UBC Metalludgy Dept.+ + SEE References in Appendix The use of the powder specimen maximized the surface area available for spontaneous plating. About 150 microcuries of activity was added to each of the host powders 54 in a sterile Pyrex© v i a l and they were allowed to stand for 5 minutes. These samples were then rinsed with a 0.1 M. HC1 solution and again with d i s t i l l e d water. The activity remaining in the powders was 71% for Fe, 46% for Co, and 35% for Ni. The powders were individually sealed in quartz v i a l s , 0.9 cm. in diameter and approximately 5 cm. in length. They were sealed in a hydrogen atmosphere vat 13 cm. pressure (Hg) which acted as a reducing agent. Quartz was used in these cases because i t softens at a temperature of about 1500 °C, which i s near the melting point of the host metals. The Bi was melted with the host metals by heating them in an R.F. induction furnace. Temperatures in excess of the melting point of each host metal were obtained. In order to heat the v i a l to these temperatures, the v i a l was placed in a graphite block of dimensions 2.5"x 2.5 x 5.0 cm.. The R.F. eddy current heating enabled temperatures up to 1550 °C to be obtained. Temperatures were determined using an optical pyrometer. At 1500 °C, the pressure in the v i a l rose to about 78 cm. pressure (Hg), causing a slight over-pressure in the v i a l . This over-pressure caused expansion of the v i a l , which was at i t s softening point. The walls of the v i a l came in contact with the graphite surface upon expansion, ensuring an even temperature distribution in the v i a l . A graphite block was maintained at a temperature in excess of the host melting point for several minutes and then i t was rapidly quenched in a water bath to a temperature less than 100 °C. The resulting pellets were a l l hemispherical in shape. The measured activities were 25 yC for Fe, 15 yC for Co, and 13 yC for Ni. A diagram of the quartz v i a l and 55 graphite block i s shown i n FIGURE 3.3. The surface of each p e l l e t was l i g h t l y sanded and etched i n 0.1 M. HG1 solution. No change i n the pe l l e t a c t i v i t y could be detected. Bismuth concentration i n these hosts were determined to be _g ~ 10 atomic percent. In order to ensure that an applied polarizing f i e l d would saturate the magnetic domains, the magnetization curve for each p e l l e t was obtained. This was necessary because of the r e l a t i v e l y large demagnetizing factor (~3) a r i s i n g from the sample geometry. The magnetization curve for each sample was obtained by measuring the s e l f -indiictance of a small c o i l wound around the specimen as a function of applied magnetic f i e l d . Alignment of the specimen r e l a t i v e to the direction of the applied f i e l d was as close as possible to the geometry to be used i n the actual experiment. The resultant curves are shown i n FIGURE 3.5. The results of this plot showed that the polarizing f i e l d had to be i n excess of 7 kilogauss for Fe and Co, and i n excess of 4 kilogauss for N i . 56 All d imensions in cm. FIGURE 3.3 The quartz v i a l and graphite block dimensions as used in the sample preparation. 57 Elect romagnet Gaussmeter HP 4342A Q M e t e r FIGURE 3.4 Block diagram of the apparatus used to determine the saturation magnetization of the samples. 58 100> E x t e r n a ! Field (kGauss) FIGURE 3.5 Data obtained from the cir c u i t shown in FIGURE 3.4. Here A L refers to the change in inductance of the sample c o i l , 59 3.4 The B i 2 0 6 / N i Experiment 3.4.1. Procedure: 206 The Bi /Ni sample was soldered to the end of the copper heat link from the paramagnetic salt p i l l . The activity of the pellet at this 60 time was 16 yCuries. A Co /Fe f o i l of activity ~5 yCuries was soldered next to the sample pellet. Due to problems with the equipment, only one Ge(Li) detector could be used for these experiments. This was placed in the axial direction. A typical spectrum taken a t ~ l °k is shown in FIGURE (3.6). The polarizing f i e l d used in this run was 4.7 kilogauss, which ensured saturation of the nickel host pellet. The geometry of the Co^/Fe f o i l was arranged so that the plane of the f o i l was parallel to the polarizing f i e l d . This resulted in a minimal demagnetizing factor. Tests by Daly (1973) found that saturation of the Fe f o i l occurs at 1.5 kilogauss in this geometry. The anisotropy of the observed gamma rays were analyzed as a function of sample temperature over the range 12 to 53 m°k. Temperatures above the 12 m°k obtained by the i n i t i a l demagnetization were produced by introducing small persistent currents (up to 1.3A) in the main magnets. Seventeen different temperature points were obtained in this manner. Every.time the temperature of the p i l l was changed by this method, a period of 10 minutes was allowed for the sample to come into thermal equilibrium with the p i l l before counting was resumed. Spectra were accumulated for 1000 sec. of analyzer l i v e time. Temperatures during the experiment were determined by calculating anisotropics from the teletype output of the MCA contents at the end of every spectrum. The system for gamma-ray detection-is discussed.-ih-537 516 497 1 "I X slnreip / s q.uno3 61 section 2.4 . The resolution of the detection system was determined prior to the actual runs using a 5 pGurie Co^ source. The system resolution was 4.00 t 0.0)8 keV at 1.332 MeV. The solid angle subtended by the detector in the axial position during the experiment was calculated to be 0.224 - 0.015 radians. 62 206 3.4.2. Analysis of Bi /Ni Data The flow chart in FIGURE 3.7 summarizes the analysis procedure for the Bi/Ni measurements. The anisotropies of the observed gamma-rays were extracted from the spectra using the computer routine Spectan I I , 60 which is described further in Appendix A. Data for the Co decay were 60 compared to the temperature-anisotropy table for Co /Fe and the temperature of the sample during the run was determined. 206 In order to determine whether non-substitutional Bi nuclei played a significant role, two models were tried in f i t t i n g the data for the hyperfine f i e l d determination. In the f i r s t case, a simple 6-function profile was adopted, in which 206 i t was assumed that a fraction f of the Bi nuclei were located at lat t i c e sites where they experienced a unique hyperfine f i e l d Hj the remaining nuclei were then assumed to experience an average zero f i e l d . 206 The effect in the anisotropies of the observed Bi decays was expressed as [ W ( 6 ) " H o b s . = f [ W ( 9 ) Obs. - u - ^ ' - j T h . (3.3). This model was incorporated into the nuclear orientation f i t t i n g programme NOFIT, described in Appendix C, in which the experimental data were fitted by the method of least squares to Equation(3.3). This programme also determined the best f i t to the value of the hyperfine f i e l d . In this 206 manner, the fraction f of the Bi nuclei feeling a unique hyperfine f i e l d H could be determined, providing there were no further unknown parameters entering into Equation (3.3)» In the second case, a model similar to that used in the f i r s t case 206 was used. This model assumed that a fraction f of the Bi nuclei f e l t 63 a distribution of hyperfine fields, while the remainder f e l t an average zero f i e l d . In this case, the W(9) of Equation (3.3) would become W(0) = . E Ui,FvP1>(C0S9) E B (Hi)dP„ V Hi 1 (3.4) instead of that given in Equation (1.3). The distribution function was taken to be a Gaussian of the form 1 l ^ ^ l ifer e L ^ J dP_, = -^==- e L 2a- J dHi Hi a «2TT ,(3.5), where Ho is the centroid of the Gaussian distribution and o i s the standard deviation of the distribution. The details of the analysis procedure are given in the description of the program HYPFIT in Appendix E. 206 The Pb decay contains several transitions of pure multipolarity, mainly El in character. Several of these transitions occur between the higher energy states and remain free- of any possible perturbation from the 2200 keV. isomeric state. The strongest of these is the 1719 keV transition for which a l l parameters in the decay scheme are known. It i s 32.2 % as intense as the 803 keV« ground state transition, but the lower efficiency of the Ge(Li) detector at this higher energy alter this to an observed intensity of 20% relative to that of the 803 keV, ground state transition. + + The only feed to the 3402.8 keV». level is by. the 6 —-* 5 electron 206 capture transition from the Bi ground state. It has a log ft value of 6.25, consistent with a f i r s t forbidden, non-unique transition. This allows the assignment of A J E C = 1 to this transition. The 3402.8 keV. 5 64 MCA SPECTRA 1 DATA REDUCTION B..G. subtraction ca i cal cul a't'e-W (9, T) 1 DETERMINE H ~p § f. err 1719 keV TRANSITION. PURE TRANSITIONS I FIT U^F^ TO DATA BY LEAST SQUARES METHOD. I compare 'exp. t Theoretical U^ .F^  from decajr scheme CManthurithil et. al.) ISOMERIC TRANSITIONS 1 DETERMINE U ^ A ^ FOR 516, 803, AND 881 keV. TRANSITIONS. " th. U DETERMINE A v FOR THE -<-2200 keV., ISOMERIC STATE. DETERMINE U^FOR THE MIXED TRANSITIONS INVOLVING THE ISOMERIC STATE. " th_. iTtMI'XEDITRANSITIONS 1 FIT UyFy TO DATA BY LEAST SQUARES METHOD. I < W e x p . v th DETERMINE F v c exp. DETERMINE 8 USING exp. EQUATION 3.8 . FIGURE 3.7 Flow chart for the analysis of the Pb spectra. 65 level decays through the 1719 keV E l transition to the 1684.1 keV 4 + level. The theoretical values for the U VF V parameters of this decay, route are, U 2 = 0.95803 F 2 = 0.86006 U, =0.00000 F, = 0.00000 . 4 4 206 The magnetic moment for the Bi ground has been determined by Lindgren and Johansson (1959) to be 4.56 ±; 0.05 y^ by the atomic beam resonance method. Using these parameters, the anisotropy data for the 1719 keV.=, gamma-ray were fi t t e d by the method of least squares to Equation (3.3), using only the parameters f and H as variables (see NOFIT, Appendix C). The data was also analyzed by the method of least squares using Equation (3.4) (see HYPFIT, Appendix F). In this case, the parameters to be determined by the f i t were the fraction of nuclei feeling the distribution of hyperfine fields, the centroid of the distribution, and the standard deviation of the distribution. 66 3.4.3. Results: The data obtained from the experiment was analyzed by NOFIT and HYPFIT. No problems were encountered when the data was analyzed using the model given by Equation (3.3) in NOFIT, However, the data was not good enough to allow an.analysis for the model of Equation (3.4) in HYPFIT. In order to analyze the data with HYPFIT, i t was necessary to use t r i a l values of the distribution centroid Ho and standard deviation o while allowing f to vary. This was done, and the results of both models are presented in Table 3.2. Table 3.2 Fitted Values of the fraction f, Hyperfine f i e l d H, and Standard Deviation for the two models used in the analysis. Case f Ho kilogauss a kilogauss X 2 Degrees of Freedom Confidence Level 1 a) 0.654±0.043 400±34 NA 15 14 0.378 b) 1.000 237+17 NA 79 - 15 1 x 10"6 2. 0.662 'totiOfl>5 405 30 14.8 15 0.391 It was f e l t that the results of the f i t using the distribution of hyperfine fields did not give conclusive evidence for such a model for the following reasons: i ) the difference between the best f i t anisotropics for NOFIT and HYPFIT ranged from -0.08 % to +0.14 % while the experimental error in the data ranged from ±1.3 % to ±1.5 %. i i ) the data obtained was not accurate enough to allow the parameters H and a to .be fitted by the least squares method. 67 For these reasons, only the model of Equation (3.3) was used in the subsequent analysis. However, the results of the analysis of HYPFIT are shown in Table 3.2 for comparison with NOFIT. (Case 1(a)). The results indicate that the data is not very sensitive to the'width of-the distribution function of Equation (3,3). If a distinction were to be made between the two models, data with an experimental error of about 0.1 % would be required for nuclear orientation experiments. The results of the f i t t i n g routine for the 1719 keV, transition are indicated in Table 3.2 and FIGURE 3.8. These show that, within the 206 limitations of the simple model, only 65.4+ 4.3 % of the Bi nuclei in this sample were located at l a t t i c e sites. The hyperfine f i e l d obtained of 400 - 34 kilogauss is in excellent agreement with the results of Kaplan et.al. (1973), who reported a value of 390'±15 kilogauss. For comparison, the data were also fitted under the assumption that a l l nuclei were at l a t t i c e sites (i.e. f = 1.0). In this case a much poorer f i t was obtained, as evidenced by the fivefold increase in the 2 X , yielding a value of 237 17 kG. for the hyperfine f i e l d . Moreover, when applied to Kaplan's data, the model was consistent, yielding values off=96.8±2.3% and H = 391 ± 10 kG. Reasons for the higher l a t t i c e site occupancy achieved in their sample are presented in the discussion at the end of this chapter. A hyperfine f i e l d of 400 kilogauss and a fraction of 65.4 % were used 206 in the subsequent analysis of the remaining Pb gamma-rays. Using these parameter values in the program NOFIT, data for the remainder of the observed gamma decays were analyzed. The parameters allowed to vary in the analysis were the U2E2'an^ ^ 4^4 values. Results of the analysis on the gamma-rays are given in Table 3.4. Table 3.3 Results of the analysis of the Bi data keV L/L1 U2 F2 U4 F4 2 X Deg. Freedom P(x2) • * 343 M1/E2 0.270 ± 0.051 0.202 ± 0.169 9.1 14 0.825 497 M1/E2 - 0 . 3 0 0 ± 0.010 0.000 10.8 15 0.767 * 516 E3 -0.432 ± 0.026 -0.125 ± 0.079 13.9 14 0.457 * 537 M1/E2 -0.472 ± 0.096 -0.035 ± 0.024 14.3 14 0.428 620 M1/E2 0.462 ± 0.029 -OvOOO 8.4 15 0.907 * 803 E2 -0.372 ± 0.016 -0.092 + 0.050 21 14 0.102 * 881 E2 -0.368 ± 0.015 -0.127 ± 0.046 9.8 14 0.777 895 M1/E2 0.233 ± 0.035 0.000 43 15 0.00016 1019 M1/E2 0.280 ±0.036 -0.033 ± 0.136 17.5 14 0.231 1099 El 0.131 ± 0.013 0.000 9.6 15 0.844 1595 El 0.286 ± 0.020 0.000 7.5 15 0.942 * Transitions involving isomeric state at 2200 keV. Table 3.4 Details of the Pb Decay (from Manthurithil et.al. (1972)) I n i t i a l level keV. IT J Final level keV. TT J keV. Multipole I 7 % relative to GS. trans. 1 Branching Ratio From I n i t i a l State 3402 5" 1684 1998 2384 2782 6 5~ 1719 1405 1019 620 El El Ml Ml 32.2 1.45 7.68 5.32 0.6902 0.0311 0.1646 0.1140 3279 5" 1684 2384 2782 3016 4 + 6" 5~ 5~ 1595 895 497 262 El Ml Ml Ml 5.07 15.8 15.5 3.05 0.1286 0.4015 0.3926 0.0774 3244 4~ 1341 3 + 1903 El 0.353 1.000 3016 5" 2384 2782 6~ 5 632 234 Ml Ml 4.52" .0.244 0.9488 0.0512 2782 5~ 1684 2384 4 + 6 1099 398 El Ml 13.65 10.86 0.5569 0.4431 2647 3~ 803 2 + 1844 El 0.575 1.000 2384 6" 2200 7" 184 Ml 16.00 1.000 2200 7" 1684 1998 516 202 E3 E3 41.2 0.004 0.9989 0.0011 1998 4 + 1340 1684 657 314 Ml Ml 1.930 0.363 0.9883 0.0117 1684 4 + 803 1341 881 343 E2 Ml 66.90 23.70 0.7384 0.2616 1341 3 + 803 2 + 537 70 1.4 1.3 W ( O ) 1.1 i : o 100 1 /T °K"' H=400±34 kG. f =0,654 * 0.043 15.0 f = 1.00 H= 237±17 kG. yS-79 1.719 MeV FIGURE 3.8 Data for the 1719 keV. gamma-ray with best f i t s for the two cases discussed. 71 The Uv coefficients were calculated using the data on the Bi' 206 decay of Manthurithil et.al. (1972). In these calculations, only transitions with an intensity of greater than 1% of the 803 keV, ground state transition were considered. The branching ratios, level spins and parities, and multipolarities of the transitions obtained from their paper are shown in Table 3.4. For convenience, individual Uv coefficients used in the calculations are given in Appendix D, along with a sample. calculation of the type.required for this analysis. In calculating the Uv coefficients for the transition of interest, i t was found that the multipole mixing in the preceding transitions could 2 be neglected. Since the mixing ratio appears as 6 , the following approximation was made. Tabulated values of the Uv coefficients for the transitions of interest are given in Table 3.5. For transitions which involve contributions from the 2200 keV. isomeric state, the attenuation factors Av appear. (Equation (1.13)) . In the analysis of the gamma-ray anisotropies, i t was.necessary to consider effects from Compton scattering in the detector and escape of any gamma-rays caused by pair production. The energy of the Compton edges are given by u v d i , i f , L±) + s 2 u y d i , I f , 1^ + 1) " W f V 1 + S 2 .(3.6) MoC 2 1 + (3.7) * Table 3.5 Table of Uy Coefficients E 7 keV. U2 U4 343 0.50595 + 0.47798 A2 0.53518 ± 0.27955 A4 497 0.95803 0.86006 516 0.83344 A2 0.61004 A4 537 0.46032 + 0.28491 A2 0.30469 + 0.12048 \ 620 0.95803 0.86006 803 0.37978 + 0.35808 A2 0.10813 + 0.10195 A4 881 0.50695 + 0.47798 A2 0.53518 + 0.27955 A4 895 0.95803 0.86006 1.019. 0.95803 0.86006 1.099 0.85554 0.55856 1.595 0.95803 0.86006 1.720 0.95803 0.86006 Based on the data of Manthurithil et.al. (1972) shown in Table 3.4 73 and the energy of the single escape peak is E S E = E 7-MoC 2' (3,8). 2 Here E-y i s the energy of the gamma-ray and MoC is the rest energy of the electron. A l i s t of these energies is given in Table 3.6. These peaks are indicated on Pb 2 0 6/Co 6 0 decay spectrum in FIGURE 3.9. The energies for the single escape peaks are only indicated for Ey> 1 MeV-, since the probability for such an occurence below this energy zero. The mixing ratios were determined by solving the quadratic expression for which i s of the form 2Fv(I ±i fLL+l) + 4'i(. Fvd^LL+1) 2 - 4(Fv(I ±I fL+lL+l) - Fv' ) (Fv(I^LD-Fv'•'•)) 2(Fv(I I fL + 1 L.+ 1) - Fv) (3.9) Using the internal conversion measurements, i t was possible to select one of the two roots for the transition of interest. The Uv coefficients of Table 3.6 were used to determine the experimental Fv coefficients, which appear in Equation (3.3). Results are given in Table (3.9 a) for several mixing ratio determinations. Since the 516 keV., 803 keV., and 881 keV-, gamma-rays are pure multipole transitions, in these cases the Fv coefficients are known exactly These are labelled Fvth in FIGURE 3.7. Thus the fitted values of UyFv th obtained from the data of Table 3.4 were used to derive the U v coefficients. In the case of transitions involving the 2200 keV\ isomeric state, however, the quantity of interest is Uv = AvUv, as described in Equation (1.13). Table 3.6 Energies of Compton edges and single escape peak associated with gamma-rays of the Pb2*^ and Co^^ delays. E T in keV. -If in % r e l . to 803 keV. E c in keV. E S E in keV. 1879 2.03 1585 1368 1719 32.2 1495 1208 1595 5.07 1375 1084 1405 1.45 1185 896 1332 N/A 1118 821 1173 N/A 965 662 1099 13.7 892 588 1019 7.68 818 508 895 15.8 696 -881 66.9 685 -803 100.0 610 -620 5.32 439 -537 30.8 364 -516 41.2 345 -497 15.5 330 -343 E c , _ ^ l + 2E 0 ESE = E'o " • 0.511 MeV. I •% = intensity transition relative t g.s. trans. 76 Comparison of these values with the coefficients of Table 3.6 then yielded the Av coefficients for the 2200 keV isomeric state. These results are given in Table 3.9 b. The Av coefficients from this analysis were used to determine the Uv coefficients for analysis of the 343 keV. and 537 keV ,transitions. Experimentally determined Fv coefficients were then used to determine the mixing ratios using Equation (3.8). These results are given in Table 3.7 c. i) 1595 keV, Transition This is a pure El transition from the 3279 keV, levels. Analysis 206 of the Pb decay spectrum in FIGURE 3.6 shows'the Compton edge of the 1879 keV. transition situated at 1585 keV. The latter is a weak transition and i t s Compton edge produces a very small effect on the background calculation. The experiment c o e ^ ^ i c i e n t was 0.278 ± 0.020, which is in excellent agreement with the theoretical value of 0.282. i i ) 497 keV„ Transition This is a mixed E2/M1 transition from the 3279 keV- level. The E2/M1 mixing ratio was determined to -0.194 ± 0.021, which is in disagreement with the value derived by Kaplan et.al. (1973) of -0.09 . Spectra obtained in their experiment show a very large Compton edge at 610 keV., arising from the 803 keV. gamma-ray. This could have an adverse effect on the background calculations, and subsequent effects on the experimental values of Fv. The use of detectors with a high peak to Compton ratio were used in these experiments to eliminate such effects. A sample comparison of this is shown in FIGURE 3.7, and the effect on the background radiation i s shown schematically for the method used in this analysis. 77 Table 3.7 (a) Pure Multipole Transitions MeV. 6 a %E2/M1 b c 0.497 -0.194 ± 0.021 3.61 '+ 0.76 0.81 ± 0.20 <2.3 0.621 -0.082 ± 0.010 0.64 + 0.16 - <6.3 0.895 0.047 ± 0.025 0.25 + 0.01 0.09 ± 0.01 <13 1.019 0.055 ± 0.020 0.30 + 0.01 0.03 ± 0.01 <22 (b) PureeTransitions Involving Isomeric State E-* MeV. A2 0.516 0.758 ± 0.045 -1.17 ± 0.74 0.803 0.677 ± 0.077 -0.213 ± 0.459 0.881 0.658 ± 0.070 -0.43 ± 0.54 • Average Attenuation: k^ = 0.718 ± 0.034 A, =-0.46 ± 0.32 (b) Mixed Transitions Involving Isomeric State %E2/M1 Ey 6 a b >c 0.343 0.537 0.002 ± 0.020 -0.211 ± 0.080 0.001 ± 0.043 0.01 ± 0.01 <0.8 4.41 ± 3.36 0.00 ± 0.02 <2.9 a) This work b) Kaplan et.al. c) Manthurithil et.al. 78 206 The detector used in this analysis produced Pb spectra as shown in FIGURE 3.9 and 3.10 (a) with a peak to Compton ratio of 20:1. A smaller detector with a peak to Compton ratio of 9:1 was used to obtain the spectrum in FIGURE 3.10 (b). Comparison of the two spectra in FIGURE 3.7 show that the lower peak-to-Compton ratio can result in an over-estimate of the background radiation for the 497 keV,, 516 keV., and 537 keV gamma-rays. The effect on the 516 keV- and 537 keV. gamma-rays w i l l be relatively unaffected by this since they are quite intense transitions. The 497 keV, transition, however, i s much weaker and,as a result of this effect, exhibits an apparently lower anisotropy at lower temperatures. The 803 keV. transition/ has a lower anisotropy at lower temperatures as well, and w i l l show the same effect in i t s Compton edge at 610 keV. This could result in an underestimate of the ^2^2 COE^^^-C^-ENTS> which would result in a higher E2 admixture being determined for this transition. In the analysis of the 497 keV ' data, the U^F^ coefficient was set equal to 0.000, since internal conversion data set a maximum value of 0.00784. i i i ) 621 keV,,Transition This i s a mixed E2/M1 transition from the 3402 keV. level. Internal conversion measurements set an upper limit of the U^F^ coefficient of 0.00195. For this reason, the U^ P^  coefficient was set equal to zero in the analysis. The E2/M1 mixing ratio was determined to be -0.082 ± 0.010, or a 0.64 ± 0.16 % E2 admixture to the Ml transition. This result is in agreement with the internal conversion measurement. iv) 895 keV, Transition This is a mixed transition from the 3279 keV, level, populated by the 79 Linear Approximation to Background. FIGURE 3.10 Spectra for the 497 keV , 516 keV , and 537 keV transitions showing the effect of the Compton edge from the 803 keV transition on the background calculations. The spectra are for detectors with peak to Compton ratios of 9:1 and 20:1. 80 123 keV transition from the 3402 keV level and the 8 decay from the 206 206 Bi ground state to the 3279 keV level of Pb . Internal conversion measurements set an upper limit to the U^ F^  coefficient of 0.00354, and for this reason i t was set equal to 0.000 for the analysis. The mixing ratio was determined to be +0.047 ± 0.025. Analysis of FIGURE 3.8 and Table 3.7 shows that the Compton edge of the 1.099 keV, transition at 892 keV. interferes with the 895 keV. peak. The 881 keV„ peak is also very close to the 895 keV peak, These two factors introduce considerable uncertainty into the determination of the mixing ratio,for this transition. The reason for this arises from the large value of the F2(I iI^L + 2 L) term in the expression for the F 2 coefficients. This is shown in Equation (3.10). _ _ 0.16984 +26 x 0.77831 + 62 x 0.26689 Z 1 + 6Z (3.10) The effect of the 1.099 keV. Compton edge would be an underestimate of the coefficient and a smaller mixing ratio determination. It was fe l t that this effect introduced considerable error in the analysis of the transition. v) 1019 keV. Transition This is a mixed E2/M1 transition from the 3402 keV. level. Internal conversion measurements set an upper limit on the U^F^ coefficients of 0.00334, and for this reason i t was set equal to 0.000. The E2/M1 mixing ratio was determined to be +0.055 ± 0.020. There were no effects from Compton edges of other transitions in this analysis. This value i s in disagreement with the value -0.18 determined by Kaplan et.al. (1973). 81 vi) 516 keV , Transition This is a pure E3 transition from the 2200 keV isomeric state, The attenuation coefficient Av for this transition was determined for v = 2, 4. The values were A 2 = 0.758 ± 0.045 a d A^ = -1.17 ± 0:74. The upper l i m i t of the spectrum used to determine the background was 563 keVr-hence the Compton edge of the 803 keV- transition at 610 keV- would have l i t t l e , i f any, effect on this result, v i i ) 803 keV.' Transition This i s a pure E2 transition from the 803 keV™ level to the ground 206 state of Pb . The attenuation coefficients were determined to be A„ = 0.677 ± 0.077 and A. = -0.213 ± 0.459. There were no effects to 2 4 interfere with the analysis of this transition. The analysis in this case is not complicated by interfering peaks. v i i i ) 881 keV. Transition This is a pure E2 transition from the 1684 keVr. level. The attenuation coefficients were determined to be = 0.658 ± 0.070 and A 4 = -0.43 ± 0.54. The effect of the 1099 keV. Compton edge at 892 keV and the proximity of.the 895 keV. peak were f e l t to be negligible in the analysis. ix) 343 keV. Transition This is a mixed E2/M1 transition from the 1684 keV-,level, which is populated by several transitions from higher levels. Included in these is the 516 keV. transition from the 2200 keV- isomeric state. This requires the average attenuation, as determined by the 516 keV., 803 keV , and 881 keV. transitions, to determine the mixing. Using the average coefficient of 0.718 ± 0.034, a mixing ratio of +0.002 ± 0.020 was 82 calculated. The coefficients used in the determination of the F coefficient, are 0.31339 - 2 6 x 0.94017 + 6 2 . EXP x 0.04477 EXP (3.11) The mixing ratio is extremely sensitive to the value determined for F^ due to the large F^ix^l^L L + 1') coefficient. This allows only an upper limit of 0.044 % for the E2/M1 admixture to this transition. The Compton edge of the 516 keV. transition occurs at 345 keV , but i t was not f e l t that this had an effect on the analysis. x) 537 keV , Transition This is a mixed E2/M1 transition from the 1340 keW level which i s populated by the 657 keW and 343 keV-' transitions. Both of these transitions involve attenuation in the 2200 keV isomeric state. Using the average value of 0.718 ± 0.034, the mixing ratio was determined to be 6 = -0.211 ± 0.080, or a 4.41 ± 3.36 % E2/M2 admixture. This result is in agreement with internal conversion measurements on the 537 keV; transition. The U.F. coefficient was not used in the determination 4 4 of 6 due to the large uncertainty, i t could only be stated the 6 < ±0.06. 83 3.5 Discussion The interpretation of the data for the 1719 keV gamma-ray in terms of the f u l l field-no f i e l d model gives better agreement with the data than a model which assumes a l l nuclei feel a unique hyperfine interaction. 206 The Bi /Ni experiment gives a hyperfine f i e l d value which is in excellent agreement with the data of Kaplan et.al. (1973). For this case, 206 the data indicates that 65.4 ± 4.3 % of the Bi nuclei feel a hyperfine f i e l d of 400 ± 34 kiloGauss, with the remaining nuclei feeling zero f i e l d . Failure to account for this zero f i e l d fraction results in a hyperfine f i e l d value of 237 ± 17 kiloGauss but with a much poorer f i t to the data, as indicated in Table 3.2 and FIGURE 3.7. The distribution of impurity nuclei in host materials has been studied by channelling techniques, For example, Feldman et.al. (1968) 206 used this technique to study the l a t t i c e location of Bi implanted into iron single crystals. Their results indicated that not a l l Bismuth nuclei assumed substitutional l a t t i c e sites, but that some of these nuclei assumed in t e r s t i a l sites. An annealing temperature dependence of the Bismuth nuclei at substitutional sites was also found. Their data is shown in FIGURE 3.11. 100 80 % at substitutional lattice sites. 60 40 2.0. 0. 200 400 600 800 Annealing Temperature °G.; FIGURE 3.11 Fraction of Bismuth nuclei at substitional l a t t i c e sites for various annealing temperature (Feldman et.al. (1968)). 84 The reason for different l a t t i c e locations of implanted nuclei has been attributed to radiation damage of the l a t t i c e , and the temperature dependence of the substltional fraction to differences in annealing processes (de Waard (1975)). Although the samples used in these experiments were not prepared by implantation, the method of sample preparation w i l l certainly cause la t t i c e damage. This w i l l allow some comparisons between results. Kaplan et.al. (1972) found they could only obtain good occupancy of substitional la t t i c e sites by rapid quenching of the alloy from 1500 °C to room temperature. In their iron samples, which were allowed to cool slowly, they could not obtain very good f i t s to the data if'they assumed a l l nuclei f e l t a unique hyperfine interaction. They found i t necessary to introduce a variable population factor." This effect could arise from Bismuth nuclei at non-substitutional l a t t i c e sites which experience a hyperfine f i e l d different from that at substitutional sites. 133 An effect of this type has been displayed in Xe /Fe system (de Waard et.al. (1968)) where high,intermediate and low f i e l d sites are observed of 273 kilogauss, 132 kilogauss, and <30 kilogauss respectively. A strong correlation between the variation of the average hyperfine interaction and the backscattering ratio in channelling experiments as a function of the annealing temperature has been found for Yb and Fe. This effect, which has been attributed to the annealing of defects, i s shown in FIGURE 3.12 (Bernas 1975). 85 r % ( Backscatter Ratio ) ; .V: .. 1.74 MegaGauss FIGURE 3.12 Annealing behaviour for Yb in Fe (Ber nas, 1975) 206 A similar explanation may explain the Bi /Fe experiments of Kaplan et.al. (1973) when they allowed their samples to cool slowly. By rapid quenching of binary alloys, one cannot always expect to have impurity atoms occupy substitutional l a t t i c e sites. The reason for the insolubility of many elements in the 3-d ferromagnetic hosts can be traced in part to the Hume-Rothery rules for alloys.. These rules place limits on the difference in atomic ra d i i which allow the formation of good alloys. The general rule (Hume-Rothery, (1936)) i s that when the atomic diameters differ by ±15%, the size factor is unfavourable and-the^-substit-utionalcs^lid-solutioniiis restricted-.; The atomic, diameters„of Bi, Fe, Co, and Ni are given in TABLE 3.8 . 200 400 600 Annealing Temperature °C. 86 Table 3.8 Atomic diameters for Bi,,Fe, Co, and Ni. Element Goldschmidt Atomic Diameter in ^  Size Factor Difference Relative to Bi Bi 3.64 -Fe 2.47 47% Co 2.50 45% Ni 2.487 46% + from Hume-Rothery (1936). Dr. R. Butters of the Metallurgy Department of the University of British Columbia suggests that the rapid quenching of the binary system 206 might form a substitutional solid solution of Bi in NI.rAhyJ--, subsequent annealing, or even slower cooling, would cause the Bismuth atoms to anneal out of the substitutional sites to take up i n t e r s t i t i a l ones, in agreement with predictions of the Hume-Rothery rules. This could probably explain the results of Feldman et.al. (1968) as shown in FIGURE 3.11 and the Bi/Fe experiments of Kaplan et.al. (1973) when the samples were allowed to cool slowly. Such effects w i l l cause the results to be strongly dependent on the thermal history of the sample in question. The samples used in these experiments were purposely not annealed, . This was done to minimize the formation of i n t e r s t i t i a l impurity l a t t i c e sites. One of the problems with this method i s the formation of a very fine grain structure in the sample, with a large number of grain 87 boundaries owing to the relatively low activation energy of i n t e r s t i t i a l solutes (Brick et.al. (1965)). Bismuth nuclei at these sites w i l l effectively feel a zero f i e l d . In other experiments where the samples were annealed, the grain boundary occupation was reduced by reerystalization and grain growth effects. For example, the results of 206 Bowman et.al. (1969) on Bi in Fe whose results are shown in FIGURE 3.13. Hyperfine Field RiloGauss 800 600 J 400 200 10 20 30 40 Annealing Time in hours. FIGURE 3.13 206 Hyperfine f i e l d for Bi /Fe as a function of the annealing time at 800 °C. (Bowman et.al. (1969)). Their results clearly demonstrate the reerystalization effect. The annealing, however, also promotes the formation of defect clusters which can interact with the impurity nuclei (Bernas 1975) in a complicated manner. The sample preparation in their work differs drastically from that used in the present experiments, and i t must be mentioned that their 88 results also show the largest discrepancy with previous results (Table 1.2). In their analysis, they f a i l to account for a fraction of the nuclei feeling a unique f i e l d and the remainder zero f i e l d , or some f i e l d different from that at the substitutional sites. 206 The data of Kaplan et.al. (1973) for Bi /Ni was consistent with 97-100% of the Bismuth nuclei feeling a unique hyperfine f i e l d of 390 kilogauss (the 97% figure was obtained by f i t t i n g Kaplan's data with NOFIT, Appendix C). This result is in excellent agreement with that obtained in this work of 400 ± 34 kilogauss. The lower fractional, occupation evidenced in the present case may possibly be explained by the soldering of the sample to.the cold finger of the chrome alum p i l l . Some di f f i c u l t y was encountered i n the soldering which required the sample to be kept at the melting point of solder (~270 °C) for a longer time than would usually be required. This may have produced some annealing effects in the sample. The fact that such good agreement can be obtained only by the introduction of a variable population factor offers a good explanation of the discrepancies between previous results in the Bismuth in Nickel system. Failure to account for this population factor results in a hyperfine f i e l d value of 237 kilo&auss with a much poorer f i t to the data. 206 The mixing ratios for the E2/M1 transitions obtained from the Bi /Ni experiment are in good agreement with the internal conversion measurements of Manthurithil et.al. (1972), with the exception of the 497 keV.: transition and the 1099 keV„.transition. Both of these can be explained by the effect of the Compton edge arising from higher energy transitions. As was explained in the analysis of the data, the Compton edge from the 803 keV. .transition interferes with the calculation of the background for 89 60 the 497 keV transition. The Compton edge from the 1.333 MeV Co decay occurs at 1118 keV. , in very close proximity to the 1099 keV 60 transition. To complicate this even further, the Co gamma-rays exhibit a decrease in yield anisotropy in the axial direction, with decreasing temperature, while the 1099 keVr gamma-ray exhibits an opposite effect. This w i l l result in a much lower U^F^ coefficient being determined experimentally, as is shown in Table 3.9. The possibl^ reason' for the discrepancy between this data and that of Kaplan et.al. (1973) is discussed in the analysis, but i s basically due to the extreme sensitivity of the Fv coefficient to the mixing ratio 6 in most cases. The results do, however, agree with the theoretical predictions of small E2 admixtures to the Ml transitions. The attenuation coefficients arising from the intermediate state 206 reorientation in the 2200 keV. isomeric state of the Pb daughter nucleus for a Nickel host are in good agreement with the results of Kaplan et.al. (1973). The negative value for the coefficient is consistent with the parameter X in Equation 3.1, representing the quadrupole interaction, having a negative value. • The value of this parameter was determined to be -0,09 ± 0.02 for the Nickel host. 90 3 . 6 Conclusions The results of the present experiments indicate that great care should be exercised in the evaluation of the data from the point of view of sample quality. Metallurgical problems in the alloying of these systems, and possibly other unknown problems,,are sufficient to cause doubt about the precise l a t t i c e locations of the impurity nuclei. This system should be studied to see i f there is any vacancy clustering or point defects around the impurity l a t t i c e locations. Resistivity measurements should also be made to study.the annealing behaviour as a function of temperature. If any effects arising from l a t t i c e devects were to occur, they would make themselves apparent in such measurements (Mantl 1975, de Waard 1975). The analysis has shown, however, that to some extent, information on sample quality can be extracted from the Nuclear Orientation data, even with a very simple model. These experiments do give a reasonable explanation for the lower hyperfine fields of Bi nuclei in ferromagnets reported previously. The failure to account for non-substitutional impurity nuclei, and consequently a non-unique value for the hyperfine interaction, can lead to an erroneously small value for the latter. While a simple 6 function model affords a reasonable f i t to the data in the present measurements, i t is clear that varying degrees of complexity w i l l be incurred depending on the history of the sample. These remarks also apply to samples prepared by ion implantation. The results indicate that nuclear orientation measurements are sensitive to such defects and suggest that, wherever indicated, specimens should be checked by other techniques. 91 Appendix A Spectrum Analysis Program SPECTAN II Spectan II i s a program to remove the photopeak from the . background contributions and correct the spectrum for any gain shifts which might have occurred in the amplifiers. It determined the counts in the warm and cold spectra, hence calculating the anisotropy from:these data. Spectan II is a modified version of a program developed by P.W. Daly for analysis of nuclear orientation spectra. The background radiation of radioactive sources exhibits an approximately exponential Intensity as a function of energy, in a Ge(Li) detector. In the vi c i n i t y of a photopeak, this background is essentially linear. A typicalGe(Li) spectrum is shown in FIGURE Al . The linear background was described by the Equation (A.l). Y = mN + B (A.l). The counts in AREA 1 and AREA 2 were used to calculate the equation of the background: running under the photopeak. This equation was used to determine the background radiation in the window. To obtain the number of counts in the photopeak,.the total background in the window was subtracted from the total counts in the window. Further details of this program are given by Daly (1973). The effects of the Compton edges are discussed in the analysis of the data. 92 Y=mN+B 5 lo 25 30 34"• Area 1 Gap 1 \ y \ r e a 2 Gap 2 Window N 25 Window Counts = £ Y(N) 10 25 Background Counts = £ (mN+B) 10 25 25 Counts in Peak = £ Y(N) + £ (mN+B) 10 10 FIGURE Al Sample calculation of type performed in SPECTAN II . 93 O O O O i O o o o o o o o o o o o o o o o o ;\> *t jji £> r- It o o o o o o o o o o o o o o o o o o 0 0 0 0 0 0 0 = o o o | 0 0 0 0 0 0 O O 0|0 o o O O O O O O 0 0 0 0 o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 [ 0 0 0 0 0 0 |o o o o o 0 0 0 i o o o z> o 0 0 0 : 0 0 0 c 0 0 0 ; > O O O ' ' o o o < r O O O I • 0 0 0 O 3 O 0 0 0 o o 0 0 0 0 0 0 CJ ui UJ n a. U J O U l * u . CL. v a: o o oc U- <t t o Or <I I-a: -> UJ => > . o in • CD : 3r U J • U J > r co to 1 1 1: a: t ' T> • : (Y. re 11 11 11 jo. - -O < (.9 a. o ; < - ^1 11 11 \rv r\j : ir. <r -a 11 o •.u rr > <j . | U J o 2 O i l :\*-* <r - u j ; cn jjj h- _ r x i» x iij i— j: |L3 Z 7. U . j . T T i tr UJ ar. o Q ~ r I o J : ^ o a- : 2 U J ! j a. ojt 0 f3 : o z z.\. r> -yj x [: 1 'r *o . J O «• — • <3 • - :> L r «* UJ £ I V- to . . ID k l ; f X -• c t n i • o ' 12.*-*: • U J u. ' C/1 UJ I *—' t I i Z l u 1 1 ^ tn . j-1. ^ 1 S I T r r L J • -< m i : •|m o -w fcfWi, X 1 Z ( U Ul E : jm < j j - i ul «* O O l_> U ( o o| o t M I C H I G A N T E R M I N A L S Y S T E M F Q K T K A N G C 1 1 3 3 6 ) M A I N 1 0 - 2 8 - 7 5 1 8 : 3 5 I U 0 PACE POO2 0 V 0 7 Ol'OS 000 9 y 0010 0 i> 1 1 NPAGE=1 H E A D C 5 , l o ' l ) M F I L E CALL S M P ( M F I L E , 0 , 2 ) KE<-[M2) - J F I L E , T I T L E  h S J I E ( o , 1 0 2 J N F I L E . { 1 I T L E ( N } , N = 1 , 1 9 ) 5 1 . 0 0 0 5 2 , 0 0 0 5 3 , 0 0 0 5 " ,OOP C c STA3T O F R U N J J • v y u 5o,000 57 , 0 0 0 0 0 12 ! 0013 c 1 DO 2 1 = ] ,5 T A U ( I ) = ll)0O0O, 50,000 59 , 0 0 0 60 , 0 0 0 0 0 1 a 0 0 15 00 13 D E C A C ( I ) : , F A L S E , : - ~ " ~ — fcRaG(I)=Q, E3IKGC1 )=0, 81,000 82 , 0 0 0 83 , 000 OK' \ 7 0 0 18 0 0 1 S l b ( ] ) = 0 . S I G C t I ) s 0 , N T i i r c n i o 8U.00O 8S.00O 68 , 000 02 0 0 0 21 U022 2 M C O : * U ) = 0 I M T = 0 • T I T = . T ^ U E , fa7,000 68 , 000 69 , 0 0 0 0 0 2 3 0024 i I B A H s l M E A U ( 5 , 101 ,END=52) N - A R M , (NST*T C N ) , N S T 0 P I N ) , J A 1 C N ) , J G 1 C N ) , J G 2 C N ) , 2 J * 2 ( M , N=1 ,<:>), K A Y , M O V E 70 , 000 71 , 000 72 , 000 0 0 2 "3 0 0 2 o 0 0 27 h 0 M i , K A L S c , " ~ I F C N N A K K . u g . n NORMS.THUE, ( i P f t = 5 73 , 000 7a,ooo 7 5.000 0 0 2 3 0029 0 0 3 0 an j i = i,5 ~ — 11=6-1 IF ( M S 7 0 P C I I ) , N E . O ) GO TO ti 7 6 ,000 77 , 000 78 , 0 0 0 00 31 0032 .3 • g N P K S . V P ' W ' ; — — '^111 i o , 1 16) C T I T L E CM) , N = i , i ) ,M0NCMTH),DTEC2) ,DTEC3),NPAGE, C I I T L E C 2 N ) , .M = a , 9 ) 79 , 000 80 , 0 0 0 81 , 000 0 u 3 3 0 0 3 * 0OJ5 N p f_ = ,N p A ii E • 1 ~~ — ~ ~~~ I F ( * A Y , E S . O ) G O T 0 2 0 l 00 202 1 = 1 , K A Y 82 , 0 0 0 83 , 0 0 0 81 , 000 0 0 5b 00 37 o 0 3 .-i 202 W E A D ( 5 , 1 1 7 ) N , X I A U ( H ) s x / 0 , uVJ 1 U7 l.'EC A v C ) : , I K U E . 85 , 0 0 0 66 , 000 87 , 0 0 0 1' 3 9 0 0 a a 0 0a 1 20 1 17 " K I T F. Co,103) ~ ~ ~ ~ ~ DO 17 I = 1 , N P K * ^  1 T E ( 6 , l 0 a ) I . j A l ( I),JG-1CI),JG? ( I),JA2 ( I),TAII ( - I ) 86,000 89 , 000 90 , 0 0 0 0 0 ^  2 0OU3 0'.) a a ^ * I f r. ( o > 1 0 1) M u VI • — — L I ! * E = 7 + N P K • I F C . N O r . v O ^ M ) GO TO 200 ii,ooo 92 . 0 0 0 93 , 0 0 0 0 0 a 3 OOuo « R I T E ( e , ! 0 8 ) ~~- ~ — U I ' - . E : L I M E * 2 9«,00 0 95 , 0 0 0 96 , 000 c S T A H I O F S P E C T R U M : ~ ~ 97 , 0 0 0 o 0 a 7 200 H E A D (5 . 1 0 O , E N O = 52) I 0 F , I 0 L , I N T , N 5 P , C J B L C N ) , J W W ( ' N ) , N S 1 , 5 ) 98 , 0 0 0 99 , 0 0 0 0 0 a S 0 0U9 0050 i F U y F . t l . o ) GO T O 1 I F C I i T L . F j . O ) ! P L = 1DF I F C - M S P . E 3 . 0 ) N S P = 2 100 , 0 0 0 101 , 0 0 0 102 , 000 0 0 51 0052 0053 i: F ( i it i , E J . o) i N r = i ~ ~ —  D O 53 I 0 5 = I O F , I O L , N S P 00 39 i = l,M'K' 103 , 000 104 , 000 105 . 000 to 4^  J U / M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G I 4 1 S 3 6 ) M A I N 1 0 - 2 8 - 7 5 1 B I 3 5 I 4 0 P A G E P 0 0 3 N V 0 0 5 4 0 0 5 5 0 0 5 6 o 0 5 7 3« te « S T S r ( I ) s N S T R T c n + J B L t I ) + J A J C I ) t J G l ( l ) l > S T n p ( n : = N 3 T Q P C I ) + J 3 L ( l ) + J * H C I ) - J A 2 < I ) - J G 2 ( I ) I E N O S O ; < E A ^ ( ? , E s O = t 9 ) I D f O E.Y 1 0 6 , 0 0 0 1 0 7 , 0 0 0 1 0 6 , 0 0 0 1 0 9 , 0 0 0 J 00 5 3 0 0 5 ? OOoO 19 Z F ( I O - I O D ) 1 8 , 2 0 , 1 8 CAUL S K I P C - 2 , 0 , 2 ) CALL S * I = C l , l , 2 ) 1 1 0 , 0 0 0 1 1 1 , 0 0 0 1 1 2 , 0 0 0 0 0 6 1 0 0 = 2 ' 0 0 o 3 I F ( I E « i i ) , > ) E , 0 ) GO TO 5 1 I E N 0 = 1 t;:i ro i s 1 1 3 , 0 0 0 1 1 4 , 0 0 0 1 1 5 , 0 0 0 0 0 6 4 00 o 5 0 0 c 2 0 U 4 D O "4 1 = 1 , N P < •'JOVE C1) = o I F t * O v E . E U . O ) GO TO 3 5 1 1 6 , 0 0 0 1 1 7 , 0 0 0 1 1 8 , 0 0 0 c c c C E M R O I O C O R R E C T I O N S 1 1 9 , 0 0 0 1 2 0 , 0 0 0 1 2 1 , 0 0 0 0 0 o 7 0 0 3 0 0 0 » 9 Ui) 38 l = l « N P K U O 3B 1 1 = 1 , M O V E N 1 s v s l S T [ I ) 1 2 2 , 0 0 0 1 2 3 , 0 0 0 1 2 4 , 0 0 0 0 0 7 0 0 0 7 1 0') 7 2 : < 2 = M S I 0 P ( I ) * 3 = 0 N U = 0 1 2 5 , 0 0 0 1 2 6 , 0 0 0 1 2 7 . 0 0 0 0 0 7 3 ,0 0 7 4 0 0 7 5 37 0 0 37 N : < H , N 2 N 3 = N 3 + * * r C N) N i l = °iU«Y(M) 1 2 8 , 0 0 0 1 2 9 , 0 0 0 1 3 0 , 0 0 0 0 o 7 o O07 7 •0079 ' . 'CE'Jl = r.3/M4 L E K l = ( l C » N 3 ) / M 4 - 1 0 » i C E N T I F ( L E F T . K E , 5 ) NCENTs.MCENT + 1 1 3 1 , 0 0 0 1 3 2 , 0 0 0 1 3 3 , 0 0 0 110 7 9 ooao 0 0 a 1 N C E M i s x C E ^ ' T - n S T R T ( 1 ) IF (JiJAS.EH.l ) > ; X B R C I ) = N C E N T I F ( M i t i - i ( I ) , E 0 . KiCfc' N T ) GO TO 3 6 1 3 4 , 0 0 0 1 3 5 , 0 0 0 1 3 6 , 0 0 0 '0 0 8 2 0 0 8 3 0 0 8 4 3 S i^Ovr. ( I ) = s(> vE ( i ) • 1 MS I R ! C l ) =-'-lS - 1 S T ( I ) + N C E N T - N X B R ( I ) MS TOP ( 1 ) B « S T ' 0 P ( I ) t N X EN I -NXtJR C l ) 1 3 7 , 0 0 0 1 3 B , U 0 0 1 3 9 , 0 0 0 0 0 o 5 0 0 8 8 0 0 » 7 3 6 35 C O l l I Nut I B A R = O A-<M = .MW A R M - 1 1 4 0 , 0 0 0 1 4 1 , 0 0 0 1 4 2 , 0 0 0 C c I N T E N S I T Y A N D B A C K G R O U N D C A L C O L A T I O N S 1 4 3 , 0 0 0 1 4 4 , 0 0 0 1 4 5 , 0 0 0 U 0 S 8 0 0 8 9 0 0 = 0 0 0 6 1 1 = 1 , N P I < N I S M S T R J C U N 2 = M S T Q u ( I ) 14 0 , 0 0 0 14 7 , 0 0 0 1 4 8 , 0 0 0 0 09 1 0 0 9 2 0 0 4 3 o 2 " 3 = 0 0 0 6 2 N = N l , N 2 N 3 = U 3 * Y C M ) 1 4 9 , 0 0 0 1 5 0 , 0 0 0 1 5 1 , 0 0 0 0094 0 0 9 5 0 0 9 6 N S J M ( 1 ) = N 3 DO h o 1 = 1 . N P K M = M S T R 1 ( I ) 1 5 2 , 0 0 0 1 5 3 , 0 0 0 1 5 4 , 0 0 0 0 0'-? 7 , 0 0 4 3 0 099 ;<2=-'S T O " CI ) NNl=.Ml - J A I CI )-JGl C I ) N M 2 = N ! - J S 1 ( I ) - 1 1 5 5 , 0 0 0 1 5 6 , 0 0 0 1 5 7 , 0 0 0 0 1 0 0 0 1 0 1 0 1 0 2 . N \ - 3 s r , 2 t J G 2 C I ) • 1 N N * = M 2 t J A 2 C I ) + J G 2 C I ) L I M = \ 2 - « 1 + 1 1 5 8 , 0 0 0 1 5 9 , 0 0 0 1 6 0 , 0 0 0 96 o o o o o o o o o o o o Z3 O O o o o o o o |o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o a o o o o j o o o o o o l o o o 3 0 ] 0 O O o o o o o o o o o o o j o o o o o o o o o o o o o o o o o o O O O o o o o o o o o o o o o o o o o o o o o 11 11 < —. r u i *n a in n o o o o It II — .-vi ~ or. » > *». c U) < ' o-) r u • .—' >» : T — tn a s in o *~ -O ru -n o o m <M ru o o o •"vi ru rvj a> tr-io o o ru ."vi ru 4 x o o a * o U i •—* ti — o a II it O — (Ul O M ^sl 97 o o c o o o o o o o o o o o o o o o o o o o o o o o o o O o o; o o o j o o o o o o i o o o i o o o Io o o j o o o i o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o |o o o o o o o o |o o o o o o o o o o o o o o o o o o Io o o o o o o o o Io o o o o o o o o o o o o o o o o o o o o Io o o o o o o o o o o o rvj r\j r\j "u O - * f\J j'u ru A J ru ru ru |ru ru ru ru ru ru •o r- .-o o - t l r y -o ^ Iru ru ru Al m m f^i m r-o jru r u r u i r u r u rvii.-v ru (O u 7 -• rr. rr ru <r fNl * UJ * " H ru J : • ^ i - - | " rr. " . re »-* • u; *-> i » x: - tn r H z ix » » Q •—• :v: a t_i a- D o o o o D O o ra x> o> o CJ ru ru ru -« u -n ru ru ru Iru r \ i ru X) 0> ru ru ru —• ru |j"i -j-i in ru ru ru 3 m m in in ru ru ru o r- ;o j i n m i n ru ru ru o o — \m a ^> ru ru ru ru m -3--O -O -O •VJ ru ru s i •> o ru ru M > 7 ) Z » 2 " —• 1 _ J M O ru Z ia - « » it _ i v_ r u — -s* -* -s> l | l | 11 — ix. rr o o '2 jo- O —' o o ru ru M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 4 1 3 3 6 ) MAIN 1 0 - 2 8 - 7 5 1 8 1 3 5 1 4 0 PAGE POOb 0 2 0 2 0 2 0 3 0 2 0 4 0 2 0 5 V A H T s E R T 3 U C I ) / ( X * X ) 2 8 H R I T E 1 6 . U i ) ) I ,NSU.M t i ) ,NCOR C I ) , V A S T L I N E = L I N E + N P * * 1 0 0 TP b 3 2 7 1 , 0 0 0 2 7 2 , 0 0 0 2 7 3 , 0 0 0 2 7 1 . 0 0 0 ( 0 2 u 6 51 N « A R , M = N * A R M - 1 2 7 5 , 0 0 0 c 0 2 0 7 L 3 = 5 2 7 6 , 0 0 0 0 2 0 3 I F ( L I N E , G E . 5 3 ) G O , T O 9 0 2 7 7 , 0 0 0 0 2 0 9 9 5 '••SITE t s , 1 0 5 ) I O D 2 7 8 , 0 0 0 02 ! 0 l . I N E s L l N E + 3 2 7 9 , 0 0 0 0 2 !1 BO ro 5 3 2 8 0 , 0 0 0 02 12 9 0 - R U E ( 0 , 1 1 6 ) ( T I T L E ( N ) , N = 1 , 3 ) , M 0 N ( M T H ) , D T E ( 2 ) , D T E ( 3 ) , N P A G E , ( T I T L E ( 2 6 1 . 0 0 0 2 N ) , N = u , 9 ) 2 8 2 , 0 0 0 0 2 1 3 I F (N'.ARM,GE.O) W R I T E ( 6 , 1 0 8 ) 2 8 3 j 0 0 0 0 2 1 J I F ( N w A R M , L r . O ) R R I T E ( 6 , 1 1 3 ) 2 8 4 , 0 0 0 0 2 1 5 L I N E = u 2 8 5 , 0 0 0 0 2 1 0 H 9 A G E = N P A G E + 1 2 6 6 , 0 0 0 0 2 1 7 0 0 Tu ( 9 1 , 9 2 , 9 3 , 9 9 , 9 5 ) . L b 2 8 7 , 0 0 0 0 2 1 8 5 3 C O N T I N U E 2 8 8 , 0 0 0 0 2 1 9 o o r o 2 o o 2 6 9 j 0 0 0 0 2 2 0 5 2 « E « I M 0 2 2 9 0 , 0 0 0 0 2 2 ! S T O P 1 2 9 1 , 0 0 0 0 2 2 2 1 0 1 F O R M A 1 ( 1 3 , 5 ( 2 ( 3 , 4 1 2 ) , 1 1 , 1 2 ) 2 9 2 , 0 0 0 0 2 2 3 1 0 2 F O R M A T ( 7 H 0 F I L E B I 4 / 1 9 A U ) ; : 2 9 3 , 0 . 0 0 0 2 2 U 1 0 3 F Q R M A T ( 3 4 H o L I N E A R BG C A L C U L A T I O N S US I N G 1 / 7 X , aitiHNp K A R E A 1 G A P 2 9 4 , 0 0 0 21 G A P 2 A ^ E A 2 L I F E T I M E ( H R S ) ) 2 9 5 , 0 0 0 0 2 2 5 1 0 9 F O R M A T ( 1 M 7 X , I 1 , 5 X , U ( I 2 , U X ) , 2 X , F 7 . 2 ) ^ 2 9 6 , 0 0 0 0 2 2 8 1 0 5 F ORMAT ( 4 ? r i * * * * * * * * * * * * * * * * * * ) * * * * * * * * * * * * * * * * * * * > * * * * * * * * / 2 1 H Y O U 2 9 7 , 0 0 0 2 M A V E A S K E D FOR «Iu,ldH B u r I I u O E S N O T E X I S T / 4 7 H ' * * * * * * * * * * * * * * * * * 2 9 6 , 0 0 0 2 9 9 , 0 0 0 0 2 2 7 1 0 6 F O R M A T ( l U I i ) 3 0 0 , 0 0 0 0 2 2 8 1 0 7 r ' j R M j I H b M O M A X I M U M N U M B E R U F C E N T R O I D C O R R E C T I O N S ISI«) 3 0 1 . 0 0 0 0 2 2 9 1 0 8 F y K M f t T ( 7 } > u i f . A R M S ! 10 T I M E H C T P E A K C O U N T S C 0 U N 1 A V A R I A N C E 3 0 2 , 0 0 0 2 nlNOUH N C C ) 3 0 3 , 0 0 0 0 2 3 0 1 0 9 F O R M A T U R , 5 * , I <4 , 1 X , A O , i n ) ; 3 0 4 , 0 0 0 0 2 3 1 1 1 0 F O R M A H I M , 2 0 », 1 2 , 5 X , 21 7, I X , E 1 2 , 6 , 4 X , 1 H ( 1 3 , I H , 13; 1 M ) 2 X , 13) 3 0 5 , 0 0 0 0 2 3 2 1 1 1 F O R M A T ( I R , 7 X , 7 M T 0 T A L S , 1 4 ) 3 0 6 , 0 0 0 0 2 3 3 1 1 2 F O ' - M i T i H , 8 X , 1 O H M E A N S 1) 3 0 7 , 0 0 0 0 2 3 J 1 1 3 T- 0 M A T ( 1 0 2 H 0 C U L 0 S t 10 T I M E R C I P E A K C O U N I B NpRMB E R R O R C O 3 0 8 , 0 0 0 2 U N 1 A N U r - ' M A CXHOH V A R I A N C E W I N D O W N C O " . 3 0 9 , 0 0 0 0 2 3 5 1 1 1 F O R M A T ( 1 H , 2 0 X , I 2 , 2 ( S X , I 7 , 2 F 6 , 3 ) , l X , E 1 2 , 6 , 4 X , l H ( i 3 , l H , I 3 , l H ) 2 X , I 3 ) 3 1 0 , 0 0 0 0 2 3 8 l i e 1- Q R M A T ( I n 1 , 3 A 4 , 2 3 M 1 S P E C T A N A N A L Y S I S O N A 4 , I 2 , 4 H , 1 9 , 12 , 2 9 X , 4 H P A G 3 1 1 , 0 0 0 2 t I 3 / ] 6 X , 6 A 4 ) 3 1 2 , 0 0 0 ' 0 2 3 7 1 17 F O R M A r ( I 3 , F 4 , 0 ) 3 1 3 , 0 0 0 0 2 3 3 1 ( 6 F O R M A l ( 3 I 7 , F « , 6 , I 7 , E 1 2 , 6 ) 3 1 4 , 0 0 0 0 2 3 9 1 1 9 F O R M A ! ( 2 i a , 4 F o , 4 ) 3 1 5 , 0 0 0 0 2 a 0 t N l ) 3 1 6 , 0 0 0 • I J P l I O N S I N E F F E C T * 1 0 , t S C D I C , S O U R C E , N O L I S T , N O D E C K . L O A D , N O H A P "OPT I O N S I N E F F E C T * * J A M E = M A I N , L 1 N E C N T = 57 • S T A T I S T I C S « S O U R C E S T A T E M E N T S = 2 4 0 , P R O G R A M S I Z E = 1 2 1 0 4 « S T A T 1 S T I c S « NO D I A G N O S T I C S G E N E R A T E D N O E R R O R S I N M A I N • 00 J W M I C U S A N T E R M I N A L S T S T t " F u t f l R A N G l « 1 3 3 b ) T I M E J 0 - 2 6 - 7 5 18)35142 P A G E P 0 0 I 0001 0 0 02 00 03 OOou F ' J U C I I 0.-4 T I M E t E ) O I M E N S I U M O I G C U ) L O G I C A L * ! A C U ) , C ( U ) C S U I V A L E M C E (4(1),a) 317,000 3 18,0 0 0 319,000 0 0 0 ; OOOo 0 0 0 7 -t S J I VALE\CE B = E 00 1 I 5 1,« ( C ( 1 ) , N ) 321,000 \ 322,000 3 2 3 , 0 0 0 ' 0 0 0 3 0 0 0-) 0 0 1 0 U = 0 C C ) : * (n 1r lu,EQ.£ y 0) 0 = 0 , 324,000 325,000 326,000 OO 1 1 o o i 2 0 0 1 3 I F C M , t a , 2 « 1 ) I F ( M , E » , 2 « 2 ) IF c ' . t J . ? « 3 ) 0=1 . 0 = 2. 0 = 3. 327,000 328,000 329,000 0 0 1 u 0015 0 0 1 6 I F ( N . E U , 2 « « ) I F ( H . i U . 2 u 5 ) 1 F ( M . E , i , J u (,) 0 = 4. 0 = 5, 0 = 6, 3 3 0,000 331,000 3 3 2,000 00 17 0 0 18 00 I => I F C . E - J . 2 a 7 ) I F C J . t a . 2 U B ) 1 F ( N . £ 0 . 2 ^ 9 ) 0=7. D = l i . 0 = 9, 333,000 33",000 335,0 00 0 0 2 u 0021 Ot'22 1 u j i ' C i ) = u n M E = 0 I G C l ) * l Q , t D < G ( 2 ) + U I G ( 3 ) / b , 0 * D I G ( q ) / 6 0 t .-!E 1 ll»S 336,000 337,000 33B.00O 0023 • 0 ? T I O N S * 0 ^ T I 0 \ S IN IN tNi) EFFECT* ID,E3CDIC,SOURCE, EFFECT* N A « E = T 1 M F , N o n s r , L1NECNT NOOEC*, LOACNOMAP 57 339,000 *0 1 A i i s T I C S * • S T A T I S T I C S * SOu-.CE STATEMENTS = NO DIAGNOSTICS GENERATED 23, PK0GSA.1 S I Z E = 794 NO iHK0•<S in TIME N O S T a [ E r t E * T S F L A G G E D IN _ t _ x : C U T I O * T E K M I N A T E U T H E A B 3 V E C O M P I L A T I O N S . CD CD S 3 J H - L O A D 6s»l)U»«v* 9 s « U U M M Y * 2 = * S T 0 R E * E X E C U T I O N H E G I N 3 _y \J ; Q : 100 Appendix B The Angular Distribution Program ANGDIST The program was developed by P. W. Daly to give the anisotropy of gamma radiation over a range of temperatures for any of the nuclei used in nuclear orientation experiments. Corrections are made to the anisotropy" for the solid angle subtended by the detectors, allowing the thermometer temperature to be determined by looking up the anisotropy in the output table. S C O M P I L ' E '1 i t <X r c •x X • A N G C J I S ' T . ' t N T l i * • S W l v , H » R E H P I ! » E ' P J E U O ' I N • R C ' A U : 3 S , * A O N E , T t I ' C 'MtME*/T ' I N '•W.'H.Wl'TliE ' F O R M A ' T - : ; F U , : 1 ; F 7 . , , ; , F 7 - ; » , U 5 ' W •« • » * * * * - * '••5 '•6 ' '7 "0 '<) J ,1 •| X x c 'EwTf.R U N u B S t X V E O •TWAf.SfT'lO.VI N F = F'l N AL S P l L'l-» l(£ L ] T A : 3QLf 'AR;Et>J L' '2 ; F 0 R K A T; ' i M . , 2 F a , ' i . , F ' 5 , 2 , ' F ' u . . i i • ' I F - T H E R E ' I S MURE T H A N UNE . U N 0 0 3 E R V E O , ' T H £ Y ' M U ' S'T 1 WE ' E t f T E H E O ' I N ' O R O P R '* •* * * • ' I V l l ' l •n i c X • E * y O F - F i I l f S I O H S P R O G R A M * * l l * 3 X • E N T E R o ? sERvto O » K M * S N P * J , , T I N A L ' S P I N , L I . ; O E L T A - ; L ' H * * * * ' r u '15 ! i X c X ' r O r - u i : ' I ' l . , 21-"J,'(., F 5 . 2 , F ' a , ' j 1.2 D E F A U L T S I D ' L l ' + l -A '* '* ' i o '1'7 - is j c c X E N T c ^ S O L I C J A N G L E DATA': H A L F A N G L E S ' I N R A D I A N S ' A ' T D E T E C T O R - , W C 0 ' ) - , * ( 9 0 ' ) F O R M A T : 2T - 7 . 4 ' * ' * " * '19 •20 21 c X r tNTER U ' M - ' E R A T U R E L I M I T S : I C = 0 F O R B E 1 A = 1 F O R 'TEMP ' I N Mrt S T = I N I T I A L ' V A L U E ' ( O F B E T A O R T ) '* '* '* •22 2 3 2 a i c c c S P = F I N A L V A L U E N U « = N U M B E R O F V A L U E S F O R M A T : I 1 , 2 F 7 , 3 , I 3 '* * * 2 5 2 6 2 7 c c c XHS.N F I-N I S n t O » I T R E T U R N S 10 R E A D MORE T E M P L I M I T S E N D - U F - F i L t R E T U R N S T O R E A D MURE U N O B S E R V E D P A R A M E T E R S * * 2 6 2 9 3 0 t M I L ' M A I T * 0 t N , j o - 0 F - F I L E N E C E S S A R Y T O S T O P P R O G R A M * C l t T . . « . « M » M < « M M M * M M « « « » » t J > > « * « « « « » * » » » i l i l « l » * » » * « « l * » « « i l « » » « « » i « » » « « « « » « C 31 3 2 3 3 i 2 3 • O U t N S I i l N C 2 ( 1 0 ) , C a ( 1 0 ) , F I R ( 6 ) , A ( 1 5 ) C O M M U N / F A K U L C / F (bl!) L O G I C A L v f 1 3 a 3 5 3 6 4 c c R t A D ( 5 , 1 0 0 ) S , R , 0 , ( A ( N ) , N = 1 , 1 5 ) C L E S S M - G O R D A N C O E F F I C I E N T S 37 3 8 3 9 5 c S S = 2 . » S 3 R = A H S ( S S ) - A I N r I S S ) 4.0 U l 4 2 7 a" <> I F ( S R . t J . O . ) lit) 10 aa " R 1T E ( o, 1 1 J ) S S T O = l o 4 3 4a 4 5 1 0 ! 1 12 2 4 0 2 1 = S » ( S M , 1 3 2 2 = 3 0 R T ( ( 2 . • S * 3 . ) » ( S + l . ) * S * ( 2 . * S - l . ) / 5 , ) 3 " 1 = 3 . « ( S < 2 . ) « ( 3 + 1 . ) * S » ( S - 1 , ) A N G D 0 0 0 4 A N G D 0 0 0 5 4 6 a? 4 8 1 5 U 0<l2 = 5 . » ( o . * S * S t 6 , « S - 5 . ) O a 3 = 2 . » S t J R T { ( 2 . * S + 5 . ) * ( S t 2 , ) * ( 2 . * S + 3 . ) * ( S + l . ) « s * ( 2 . * S - i , ) « ( S - l . ) * ( ? 2 , « S - 3 . ) / o . ) A N U 0 0 0 0 6 A N G D 0 0 0 7 A N G D 0 0 0 8 4 9 5 0 5 1 1 5 16 17 N 1 = 3 + 1 ,1 N 2 = 3 + 0 , 6 N 0 = N 1 - N ? A N G 0 0 0 0 9 A N G D 0 0 1 0 A N G D 0 0 1 1 5 2 5 3 5 u 1 B 1 = 2 0 D O t o !\ = 1 , M 1 S.« = :< 3 M = S - S K 11 , A N G O O O 12 A N G D 0 0 1 2 A N G D 0 0 1 3 5 5 5 6 5 7 2 1 2 2 2 3 S M < ? = S M . S M C 2 ( n ) = 0 , C 4 ( M = 0 , ; A N G D O O l a 5 8 5 9 6 0 2 a 2 5 V ' 2 o 2 0 1 I F ( S . ' J E . 1, ) C 2 ( K ) = ( 3 , * S M 2 - , ) 2 l ) / g 2 2 "•RITE ( o , 2 0 i ) C 2 ( r O , C 4 C K ) F O R M A T C ' . 2 F I 0 . 7 ) 6 1 6 2 6 3 J 102 t o o * it CO i i i -» U ' J L ) • II V. O l II -J • m l TJ • O O • — s ru ; - T> i - f ' O Z O . II * • UJ G f\i • O III ^ m ru ro ru or cr _) - * -J 3 .t .r H -H - * •/) w w I II It i ru a O U . ti, r> "D; II It 76 R'EADCSvl'06)' A0,A90 lS2'4i " l 79' X0 = C u S ( A 0 )' /f-NB-O'O'O'l!* lias-80 X9 '0=C0S CA90)' ANG-BO'O'2'0' D2a-SI- r»-?tfs,-S-«<0*Cll»*X«7 A'NGD'0'02'11 1'2 7 S'2' S-u 0'= G-2 0 *' 0 7 .• * X 0 »' X 0 - 3', )>/« A-siGOO'0'22' I2a i 8 3' G290= ,b«X90«'('li,fX9 ' 0 )• A'NG-D'O'0-2 J 129 J 8a Ga90=G290* C7 »*X90 *X9'0--3v ANGOO'0'2* 130 as- *RtTE ( o , 1 0 7 ) A0,A9u,G2'0rG" :0VG29i0VGifW 131 C 1132 C 8!£rA VALUES K E A O 133 C l i t 6tv fa' R E A 0 C 5 t f 10 ,1 N 0 : 'l15- J IC r S T , S'PV N liM 135 6? * R r T E ( o , l o S ) 136- ' I F C I C . t O , 0 ) G O TO' f f A-NG-D0029' 1)37 by S-r = BETE/ST '< A-NGO0030 133' 9 0 S P = - JETt/S' ANGDO'0'31 139 11' RUNS = NU>1- 1 ANGD0032 i a o °2 O E L = ( S P - S T ) / R U Y S ANG00033 [« 9'5 T=0. 142 9 a 8 =100, 143 95 32 = C 2 l ' l ) f a<* 9 »• 8 a = C -J ( V ) I a 5 9 7 E2=rt2«u? iao-'•it, E 4 = c l i*ua j a ? 9=) * 0 1 , t f. 2 • E u 1 as 100 »90«1 ,-,S«Ea»,$7b*E<ti 149 JOV ^C0=1 , f G 2 0 « E 2 * 5 « 0 » E « 1-5 u-102 *C9 0 = l . - . 5 « G 2 9 c , «E2+,375«G490«E4 151 jos * R I T E ( c , l v 9 ) 3,T,B2,e4',HO,*90,«CO,i«C90 152 1 0 a 8 = 3 ? *NGOe0'3* I b i i os- 00 1'2 I s i , H U M ANGD0034 15a C 155 C * ( 0 ) , * ( 9 0 ) CALCULATION 156 C 157 io o Z=SINM(B«(S+.5))/SINH(B*,5) ANG00035 158 1 0 7 82 = 0 . ANG00036 159 10B S4 = 0 . ANG00037 160 109 00 13 K=1 , N 2 ANGD0038 l b l 1 1 0 S K = i< ANG00039 162 1 1 ; S K l S - S K - H , ANGP0040 163 112 X = 2 . « C 0 S " ( B « S M ) ANGDOOal 16a 1 1 3 52=S2*C2(« )'** A N G 0 0 C 2 165 1 14 13 i?/j = Ba + C4(«)*x ANG00043 166 1 15 IF(NO .E-'J.O) GO T O 17 ANGD0044 167 1 1 0 B 2 ; B 2 * L 2 ( N 1 ) ANGD0045 168 117 Ba = 3a + t u ( N 1 ) ANG00046 169 116 17 S2=82/Z ANGD0047 170 119 ANG00048 171 120 T i B E t t / B ANGD0049 172 121 E2 = 'J2«B2 173 1 22 i". « : ' J « « B 0 I 7a 123 hO=l.+E2*Ea ANG00052 175 12a -9(j = l , - . 5 * E 2 + ,375«Eu ANG00053 176 125 »C0=1. *G20«£2*Gao«Ea ANGD0054 177 1 2 B wC9o=l,-.5«G29o»E2+.37b*3U90*E4 ANG00055 1 78 127 »KiTE(o,l ( ' 9 ) B,T,f)2,B«»»IO»«90«'«CO»«C90 179 12b 12 3 = B * U £ L ANG00058 180 129 GO T O l a ANGD0059 161 1 JO 16 STOP ANGD0060 182 131 100 F O R M A T ( F U . 1 , F 7 , 2 , F 7 , U , 1 5 A 1 ) 183 • 1 0 ! * * * A R \ J i \ G * * * * w A R \ I N G * * * * n A P . \ I V G * * F O R M A T C 1 H 1 , 2 ' F I E L O = ' F 7 . 3 2 ! X , ' S E T A T E X P E C T I N G CO.". E X P E C T I N G COM E X P E C T I N G C O ^ 3 0 X , 1 5 A 4 / / H X , ' P A R E N T P A R A M E T E R S ! • / 2 1 X , • SP I Nn I fu , 1 / 2 1 X , 2 , ' K C - A U S S I / 2 1 X , ' M A G M O M t ^ T a ' F 7 , 4 , ' N U C L E A R M A G N E T O N S ! / I M E S TEMP ( I N M i O = ' F 6 , 2 ) B E T W E E N FORMAT I T E M S NEAR N= 5 E T w E E N FORMAT I T E M S NEAR 0 = B E T W E E N FORMAT I T E M S NEAR T = » * - A R N I N G « « E X P E C T I N G ' C O M M A B E T W E E N F O R M A T I T E M S N E A R )x I i i 102 r O R M A T ( I l , 2 F 4 , i , F 5 , 2 , F « , J ) 134 103 FOR i f lT 1 I H Q , i O X , ' U N O B S E R V E D T R A N S 1 T I ON 1 I 2 / 2 2 J X , ' F I N A L S P I N S I F U . 1 / 2 1 X , I R A U 1 A T I 0 N L' = T J A S 3 u A i < E U = < F 5 , 2 , ' ) ' / 1 6 X , ' T M E N U 2 = ' F B , ' 5 , 4 X , » « « I AR . \ I N G « « E X P E C T I N G C O M M A B E T W E E N F O R M A T I T E M S N E A R ON * A R .V I \ ' 0 « N A R \ I N G * E X P E C T I N G E X P E C T I M ; E X P E C T I N U C U M C j .-C 0 « * * <v A % I N G * * * * M A S S I N G * * * * « A K \ I \ G * * E X P E C T I N G E X P E C T I N G E X P E C T I N G to» COM COM U 5ETw «« 3 t T » ' _ A _ 9 E T _ ^ i A 3 E " ' I tA at i • A B E T E E N F O R M A T I T E M S N E A R IEN F O R M A T I T E M S N E A R E E N F O R M A T I T E M S N E A R I L N E E N E E N * « * A K1 \ I * * 1 3 5 1 0 4 * *Ji A f^ N I NG * * * * W A rr N I N G * * ft * ft A R .\l I N G * * ) 3b 1 0 5 F O R M A T I T E M S F O R M A T H E M S -F O R M A T I T E M S N E A R N E A R N E A R E X P E C T I N G F 0 * A 7 ( E X P E C T 1 N G E X P E C T I N G E X P E C T I N G F O R M A T ( C O M M A B E T W E E N F O R M A T I T E M S N E A R 4 = ' F 8 « 0 , 1 4 x ' 1 0 T A L U 2 s ' F « , 5 , 4 X , ' U « = ' r B , 5 C 0 M M A _ 6 E T w E E M row*T _I I E M S NE_AR_ H X ' J " « « B E T « E E N F O R M A T ' T T E M S N E A ^ " 2 = ' F B M A B E T W E E N F O R M A T I T E M S N E A R 4 = ' F B 10 X , ' O B S E R V E D G A M M A T R A M 5 I T I O N I / 2 1 X , C O ; C O f I t i O , F 6 X . 1 I N I T I A L S P I N s ' F 4 , 1 / 2 a , 1 , ' P I U S ' F 4 , 1 , ' ( D E L T U 4 = I F B , 5 ) 12 * * * A W \ I N G * * A K N I N G * * * * W A R N I N G * * * * * A R \ I \ G * * 2 / 2 1 X , ' F j N A i S P ) N = ' F U , 1 , / 2 1 x , r . M U L 1 I P O L E 3 E L T A : ' F 5 . 2 , • ) ' / 1 6 X , ' T M E N F 2 = ' F 8 . 5 , u x , <F<|« E X P E C T I N G C O M M A SE1KEE .N F O R M A T I T E M S N E A R i> I N I T I A L S P I N = ' F 4 , 1 = ' F 4 , 1 , ' P L U S ' F A | . 1, I (D ' K B , 5 ) = ' F 4 i -E X P E C T I N G COMMA B E T W E E N FORMAT I T E M S NEAR = ' F 4 E X P E C T I N G COMMA B E T W E E N FORMAT I T E M S NEAR = ' F 4 E X P E C T I N G COMMA B E T W E E N FORMAT I T E M S NEAR U 3 ' F u 184 185 18b 187 188 189 190 192 193 194 * * w A K v I >•{ • * * *> A M V J I ; \ * « ^ A R s l N 5 * * G * * • E X P E C T I N G C O M " A B E T W E E N F O R M A T I T E M S N E A R A = ' F 5 E X P E C T I N G C O M M A B E T W E E N F O R M A T I T E M S N E A R 2 = ' F 3 E X P E C T I N G C O M M A S E T « E F . N F O R M A T I T E M S N E A R a = ' F 8 . 1 3 7 13s 1 0 6 107 F O R M A T ( 2 f 7 , u ) F O R M A T ( 1 H 0 , 1 0 X , ' S O L I D A N C L E C O R R E C T I O N S ' / 2 1 X , ' A L P H A ( 0 ) = ' F 7 » 4 , ' R A D 2 J A W 3 ' / 2 U , ' A L P H A ( 9 0 ) = ' F 7 . 4 , ' R A D I A N S ' / 1 fa X , ' T H E N G 2 C 0 ) s ' F 7 , U , 4 X , ' G 4 195 196 197 * * * ' A R s I M G * * * * ( « . A R . \ I S G * * 3 ( 0 ) = 'F 7 . 4 / 2 I X , , 0 2 ( 9 0 ) = , F 7 , 4 , 4 X , ' G 4 ( 9 0 ) = ' F 7 . 4 ) E X P E C T I N G C O M M A B E T W E E N F O R M A T I T E M S N E A R = ' F 7 E X R E C T I . - J G C O > » M A B E T W E E N F O R M A T I T E M S N E A R ) = ' F 7 198 * « * A ~ \ ' 1 N G * * » * « A R N I N ' G « « » » « Af i N I Nu « * E X P E C T i N G C O M M A B E T W E E N F O R M A T I T E M S N E A R = ' F 7 E X P E C T I N G C O M M A B E T W E E N F O R M A T I T E M S N E A R i ' F 7 E X P E C T I N G C O M M A rfETwEEN F O R M A T I I E M S N E A R ) s l F 7 » « » A R M I .-« • 13R G * * 1 0 8 E X P E C T I N G C O M M A B E I w E E N F O R M A T I . I E M S N E A R ) = ' F 7 F O R M A T ( l i l O , 7 X , 4 M B E T A , 3 X , 4 H T E M P , 8 X , 2 H B 2 , 7 X , 2 H B 4 , 6 X , 4 H w ( 0 ) , 5 X , 5 M w ( 9 0 2 ) , s X , 4 n « i ( 0 ) , 5 x , 5 r ! W t 9 0 ) / ! 5 X , 4 M ( M K ) , 2 5 x , l 3 , R ( U N C 0 R R E C T E D ) ; 3 X , 2 4 H ( S O L I A N G D 0 0 7 0 199 200 1 i i ] 1 4 0 109 30 A N G L E C U R R E C [ I U N ) / ) F O R M A T ( l r i , 5 x , F o . 3 , 2 x , F 6 , 2 , 2 X , 2 ( F 7 . 4 , 2 x ) , 2 X , 2 C F 8 . 5 , l X ) ; 2 X , 2 ( F 8 , S , l 2 * ) ) A N G D 0 0 7 1 A N G D 0 0 7 3 201 202 2 0 3 1 ! 1 141 142 143 110 111 F O R M A T ( I 1 , 2 F 7 , 3 , I 3 ) F O R M A T ( l h O . F u , l , 3 0 H IS U N A C C E P T I B L E V » L U E OF S P I N ) E N D 204 2 0 5 2 0 6 i i I 1 U 4 F U N C T I O N T H R E E J ( J J 1 , J ' J 2 , J J 3 , M M J , M M 2 , M M J ) — A R G U M E N T S M U S T . H A V E T H E I R D O U B L E V A L U E S . F A C U L T I E S S E E F U N C T I O N F , T R E E 0 0 0 2 T R E E 0 0 0 3 2 0 7 208 j ( 1 145 1 4 6 C - — — U G N t K 3 - J - S T M S U L . E D M O N D S ( 3 , 6 , 1 0 ) AND ( 3 , 7 , 5 ) , C O M M U N / F A * U L C / F ( 6 0 ) D A T A N N / 2 / T R E E 0 0 0 4 T R E E 0 0 0 5 T R E E 0 0 0 6 2 0 9 210 211 | 147 148 1 4 9 I F ( N N , G T . 1 ) G O T O 4 1 J 1 = J J 1 J 2 = J J 2 T R E E 0 0 0 7 7 R E E 0 0 0 8 T R E E 0 0 0 9 212 2 1 3 2 1 4 I ( I S O i 151 152 ! 153 | 15 0 I 155 J 3 = J J 3 M1SMM1 M2=MM2 T H R E E J=o, I 1 = J 1 + J 2 + J 3 T R E E O 0 1 0 T R E E O O H T R E E 0 0 1 2 T R E E O O H T R E E 0 0 1 4 T R E E 0 0 1 5 2 1 5 216 2 1 7 218 2 1 9 220 r 15o 157 158 6 '1 = 1 1 * 1 I F ( N . G 7 , 6 C ) w R I T E ( 6 , 6 ) N FORMAT ( I b , 2 6 H I S OUT OF R A N G E ' OF F A K C N) / 1 H 0 1 1 9 ( 1 H * ) ) T R E E O O l b T R E E 0 0 1 7 T R E E 0 0 1 8 221 2 2 2 2 2 3 < **«AR'NlNG** E X P E C T I N G COMMA B E T W E E N FORMAT I T E M S NEAR 1H011 159 160 I F ( ' - i U D ( J l + j 2 + J 3 , 2 ) ,N£, 0 ) R E T U R N I f ( < J ! t J « - J 3 . L T , 0 ) . O K . ( J 3 - l A f e S U l - J 2 ) , L T t 0 ) , O R . C M l + K2 *M3 N E , 0 ) ) T R E E 0 0 1 9 T R E E 0 0 2 0 224 2 2 5 161 162 1 R E T U R N I F ( (M 1 , E O , O ) . A N U , ( M 2 , E O , O ) ) GO TO 3 N 1 = J 1 + J 2 - J 3 + 1 T R E E 0 0 2 1 T R E E 0 0 2 2 T R E E 0 0 2 3 226 227 228 • 163 1 o n 165 N 2=J 1-M 1 •J N3 = J l - J 2 - » J 3 t 2 N4=J2-M2+1 T R E E 0 024 T R E E 0 0 2 5 T R E E 0 0 2 6 2 2 9 230 231 I c o 167 168 N S = J 2 + J 3 - J 1 + 2 N6=J3-M3+i N 7 = J l + M ] + 2 T R E E 0 0 2 7 T R E E 0 0 2 6 T R E E 0 0 2 9 232 2 3 3 234 l e y 170 171 NH=J3 *M3»! N « = J 2 + M 2 * 2 Z = S S * T ( 0 , ! 2 5 « F ( H ) « F ( N I ) * F C N 2 ) » F ( N 3 ) * F ( N 4 ) » F ( N 5 ) * F t N 6 ) *> ( N 7 ) » F ( N 8 ) T R E E 0 0 3 0 T R E E 0 0 3 1 * T R E E 0 0 3 2 2 3 5 236 2 3 7 172 173 1 r INV) } >\HIN = MAXO ( ( . . ' 3 - J 2 - M 1 ) , 0) M KMAX = M ' l N 0 ( ( J l - . M l ) . ( J 3 + , < t 3 ) ) + l f R E E 0 0 3 3 T R E E 0 0 3 4 T R E E 0 0 3 5 236 2 3 9 240 1 7" 175 1 • I 7 b i! 0 2 K = K M I N , M-t A X , 2 N1=J1+MI+K; N 2 = J ! - M l - < + 3 T R E E 0 0 3 6 T R E E 0 0 3 7 T R E E 0 0 3 8 241 242 2 4 3 1 7 7 178 179 N 3 = J 2 f J 3-M1 - K + 2 N U s J 3 * M J-r< + 3 N 5 = J 2 - J 3 * M I t K + l T R E E 0 0 3 9 T R E E 0 0 4 0 T R E E 0 0 4 1 244 2 4 5 2 4 b 180 . 181 182 2 T R R E E J = F ( < t l ) » F ( N 1 ) * F ( . N 2 ) * F ( N 3 1 * F ( N 4 ) * F ( N 5 ) - T H R E E J T n R E E J = T « R E E J * 7 . I F ( M O O ( ( ( K K A x - i + M 3 - M i + J 2 ) / 2 ) , 2 j , N E . O ) T H R E E J = - T H R E E J T R E E 0 0 4 2 T R E E O 0 4 3 T R E E 0 0 4 4 247 248 2 4 9 183 1 6 4' 185 J R E T U R N I F ( 1 0 0 ( 1 1 , <i) ,NI , 0 ) R E T U R N 1 2 = 1 1 / 2 T R E E 0 0 4 5 T R E E 0 0 4 6 T S E E 0 0 4 7 250 251 2 52 i 1 8b 187 188 N ' , = T l - 2 » . J L T | N 2 = i i - 2 « J 2 * 1 N3 = I t - 2 * . I 3 t ) T R E E 0 0 4 8 T R E E 0 0 4 9 T R E E 0 0 5 0 2 5 3 254 255 183 190 I ' M N u = I 2 - J i » 2 N 5 = I 2 » J 2 + 2 N6=I2-J3+2 T R E E 0 0 5 1 T R E E 0 0 5 2 T R E E 0 0 5 3 2 5 b 257 2S8 192 1 « 3 i Qa T h R t t J = Si.'Rl ( . 1 2 5 * F (N) * F (NI ) * F CN2) * F ( N 3 ) ) * F (12 + 1) * F ( N 4 , I F ( ' i O U ( I 2 , 4),N£.o) T r ( R E E J = - T H R E E J R E T U R N * F ( N 5 ) * F ( N 6 ) T R E E 0 0 5 4 T R E E 0 0 5 5 T R E E 0 0 5 6 2 5 9 260 261 195 l ' s 197 u x = 1. v = . 1 2 5 00 5 L = l , 5 0 , 2 T R E E 0 0 5 7 T R E E 0 0 5 8 T R E E 0 0 5 9 262 2 6 3 264 193 199 200 F ( U = x F ( L + l ) = 1 , / x X = x * Y T R E E 0 0 6 0 T R E E 0 0 6 1 T R E E 0 0 6 2 2 6 5 266 267 201 2 0 2 2 0 3 5 v = T + , 1 2 5 N N = 0 G O T O 1 T R E E 0 0 o 3 T R E E 0 0 6 4 T R E E 0 0 6 5 268 2 6 9 270 i 204 END v . 2 2 F U N C T I O N S J X J . iIC-NER S I x . J - S T M f i O L . EDMONDS ( 6 . 3 , 7 ) , T R E E 0 0 6 6 271 V C 3 I X J / 0 0 0 1 S I X J 0 0 0 2 272 2 7 3 J o Cn . f f C ARGUMENTS MUST H A V E THEIR DOUBLE VALUES, C FACULTIES SEE FUNCTION F S I X J 0 0 0 3 s i x j o o o a 27a 275 205 2 0 a 2 0 7 FUNCTION S 1 X J ( J J 1 , J J 2 , J J 3 , L L 1 . L L 2 , L L 3 > C O M M O N / F A t u ; L C / F 160) L O G I C A L T S l . , M U S I X J 0 0 0 5 S I X J 0 0 0 6 S I X J 0 0 0 7 276 277 278 J 2o?. 2 0 9 210 T R L ( * , L , M j = C X . G T . L + M ) . O R . ( K . L T , I A B S ( L - M ) ) M O ( < , L , M ) : K O O K - I A B S ( L - M ) , 2 ) , N E . O D A T A NN/£/ S I X J 0 0 0 8 S I X J 0 0 0 9 S I X J 0 0 1 0 279 280 281 J 211 212 2 1 J I F ( N N . G T . l ) GOTO a ! J l s J J ' l J 2 = J J 2 S I X J 0 0 1 1 S I X J 0 0 1 2 S J X J 0 0 1 3 282 263 28a 1 2 ! a 2 1 5 21 e J 3 = J J 3 L 1 ='_L 1 L 2 = L L 2 S i x j o o i a SIXJOO 15 S I X J 0 0 1 6 285 286 287 2 1 7 21 e 2 1 9 L 3 = L L 3 s I x ; = o , ! F ( T R L ( J 1 , J 2 , J 3 ) . 0 R , T R L ( J 1 , L 2 . L 3 ) , 0 R , T R L : C L 1 , J 2 , L 3 ) . 0 R , T R L C L 1 , L 2 , J 3 S I X J 0 0 1 7 S 1 X J 0 0 1 8 S I X J 0 0 1 9 288 289 290 i I 220 221 1 ) ) Rt. TURN I F ( - ) U ( J 1 , J 2 , J 3 ) , 0 R . M 0 C J ! , L 2 , L 3 ) . 0 R , M 0 ( L 1 , 11 = J 1 » J ? » J W L 2 . J 3 ) ) RETURN S I X J 0 0 2 0 S I X J 0 0 2 1 S I X J 0 0 2 2 291 2 9 2 2 9 3 i 1 i 222 22 5 2 2 a I 2 = J l t L 2 + L 3 - 2 I 3 = L l * J 2 » L 3 - 2 I u = L 1 + L ? t J 3 - 2 S I X J 0 0 2 3 s i x j o o 2 a S I X J 0 0 2 5 2 9 a 295 296 ! 225 22e 227 N l = , l 1 * J 2 » L 1 • 1.2 + 2 •M2 = j 2 + J 3+l2 + L 3 + 2 N 3 = J . S » J 1 + L 3 + L 1 + 2 S I X J 0 0 2 6 S I X J 0 0 2 7 S I X J 0 0 2 8 297 298 2 9 9 2 2 6 229 250 HIN-2 = MA < 0 11 1 , 12, I 3 , 1 a )+2 MS < Z = » I N 0 ( N ) , N 2 , . M 3 ) - 2 1 F ( M A X Z + 2 . G T , O O ) GOTO 12 S I X J 0 0 2 9 S I X J 0 0 3 0 S I X J 0 0 3 1 300 301 30 2 -231 2 3 2 2 3 3 . N A l = J i + J 2 t j 3 + « N A ? = J I + J 2 - J J + 1 • N A 3 = J l - . ' 2 + j 3 + l S I X J 0 0 3 2 S I X J 0 0 3 3 SIXJOO 3 a 3 0 3 3 0 a 305 2 3 a 2 3 5 2 3 s Nf .a = .J2-J n J 3 + 1 N 8 l = J l » L 2 + L 3 » u • • 5 2 = J 1 + L 2 - L 3 M S I X J 0 0 3 5 S I X J 0 0 3 6 S I X J 0 0 3 7 306 307 308 237 2 3 8 2 3 9 NBJs J 1 - L 2 + I J + 1 l ,Ba = - J 1 + L 2 + L J + 1 N C 1 = L 1 + L 2 + J 3 + H S I X J 0 0 3 8 S I X J 0 0 3 9 s i x j o o a o 309 310 311 • j u o 2"1 2 « 2 N C 2 = U i L J - J J . ) NC3= L l - L 2 t J 3 + l NCa = - ! . W L 2 + J3+ l s i x j o o a i S i x j o o a 2 S I x j o o a 3 312 3 1 3 3 i a i 1 2 a 3 2 a ii 2 a 5 N 0 i = L i * J 2 - t L 3 + a N-D 2 = L I + J 2 - L 3 + 1 NO 3= L 1 - J 2 + L 3 + 1 S i x j o o a a S I X J 0 0 4 5 S i x j o o a s 315 316 317 j 2 a e 2"7 .NDi = - L l + J 2 1 L 3 + 1 U = 0 , 1 2 5 .(-],)**.M O O ( M I N Z/2,2) « S Q R T(FCNAl)»FtNA2 ) * F ( N A 3)*FCNAa) l < F ( N B l ) « K ( , \ B 2 ) « F c N 6 3 ) * F ( N B a ) * F ( N C l ) * F C N C 2 ) * F C N C 3 ) » F ( N C a ) * F ( N O ! ) S I X J o o a 7 S i x j o o a a S l x j o o a 9 318 319 320 2"3 2 « 9 2 »(• (N02 ) * F ( N O i ) » F t N o a ) ; 00 11 N = * I N Z , M A X Z , 2 NA1=N - I 1 S i x J 0 0 5 0 ' S 1 X J 0 0 5 1 S I X J 0 0 5 2 321 322 3 2 3 250 251 252 NA2=N-I2 N A 3 = .*.-I 3 •J A J = N - 1 U S I X J 0 0 5 3 s i x j o o s a S I X J 0 0 5 5 32a 325 326 253 25a 255 NPl=^l-»J N H 2 = N 2 - N NB 3 = N3-M S I X J 0 0 5 6 S I X J 0 0 5 7 S I X J 0 0 5 8 327 328 329. 256 257 S I X J = S I X J + U * F t N + 3 ) * F ( N A l ) * F ( N A 2 ) * F C N A 3 ) * F ( N A a ) * F C N B l ) * F ( N B 2 ) * F C N B 3 1 ) 11 U = - U S 1 X J 0 0 5 9 S I X J 0 0 6 0 S I X J 0 0 6 1 330 331 3 3 2 j J 258 R E T U R N 2 5 9 u x = l , S I X J 0 0 6 3 33U 2oO Y = , 1 2 5 S I X J 0 0 6 U 335 2 e l 0 0 S L = l , 5 9 , 2 S I X J 0 0 6 5 3 3 6 2 o 2 F ( L ) = X S I X J 0 0 6 6 337 20 3 F ( L » 1 1 = 1 ./X S I X J 0 0 6 7 338 2 6 U X=X«Y S I X J O O 0 8 339 2 o 5 5 Y - V + , 1 2 5 S I X J 0 0 6 9 3<I0 2ofe N N = Q ' S I X J 0 0 7 0 3« 1 207 GOTO 1 S I X J 0 0 7 1 302 2 6 8 12 * R I T E ! 6 , b ) . MAXZ S I X J 0 0 7 2 3 U J 2 o 9 b F Q Q M A 1 ( I 6 , 2 6 H IS OUT OF RANGE OF F A K C N ) / l HU 1 1 9 ( 1 H» ) ) S I X J 0 0 7 3 3 " " • « A ^ I \ - G « * E X P E C T I N G C O M M A BETWEEN FORMAT H E M S NEAR 1H011 270 .RETURN S I X J 0 O 7 U 315 2 7 j S I X J 0 0 7 5 346 30 AT A l . b 9 S U 1 5 0 0 . 0 0 0 0 0 0 0 0 , o 7 9 3 o s 5 0 , 0 0 0 0 0 0 0 0 , 1 1 322 7 7 i ) . 0 0 9 0 0 0 0 n_.j>_ 7 9 3 o h 5 0 . O O P OOOO 1 , 0 1 9 0 i 9 0 0 , 0 0 0 0 0 0 0 •. , 1 3 2 2 7 7 0 0 . 0 0 0 0 0 0 0 r * C O - 6 0 / F E , H = 2 8 7 , 7 0 K G , » | P A R E N T P A R A M E T E R S : | S P I N S 5 , 0 j F I E L D : 2 6 7 , 7 0 K G A U S S V, MCG wp»Enr= 3 . 7 5 4 0 N U C L E A R M A G N E T O N S  ' B E T A T I M E S TEMP ( I N MK)= 7 , 9 0 U N O B S E R V E D T R A N S I T I O N ' 1  I N I T I A L S P I N S 5 , 0 F I N A L S P I N 5 u ,o ' R A D I A T I O N L - i . o P L U S 0 , 0 ( P E L T A S Q U A R E D s 0 . 0 0 ) T H E N U2 = 0 . 9 3 9 3 7 g u : 0 , 7 9 7 7 2 T O T A L U 2 s 0 . 9 3 9 3 7 U Al = 0 , 7 9 7 7 2  O r i S E R v E O G A M M A T R A N 5 I T I U N I N I T I A L S = M , N S a . o  FINAL S P I N = 2 , 0 M U L T I P O L E s 2 . 0 P L U S 3 . 0 ( D E L T A S 0 , 0 0 ) T H E N F 2 s - o . 4 4 7 7 0 F 4 z - 0 , 3 0 4 3 3  S O L I O A N G L E C O R R E C T 10NS A L P . M A ( Q ) s 0 , 0 5 5 0 R A D I A N S  A L ? H A ( 9 0 )= 0 , 0 5 5 0 R A O I A N S T H E N G 2 ! 0 ) s 0 , 9 9 7 7 G 4 ( 0 ) - 0 , 9 9 2 5 G 2 ( 9 0 ) = 0 . 997 7 G u ( 9 0 ) s 0 , 9 9 2 5 S E T A T E M P 02 BU w ( 0 ) W ( 9 0 ) H ( 0 ) - W ( 9 0 ) I I K ) ( U N C O R R E C T E D ) ( S O L I D A N G L E C O R R E C T I O N ) 1 ! * * * * * * 0 , 0 0 1 , 6 9 8 a 1 1767 0 , 0 0 0 0 1 1 , 2 5 0 0 0 0 , 0 0 3 7 6 1 , 2 5 0 0 0 ! 0 , 7 9 0 1 0 , 0 0 1 . 0 0 7 7 0 , 2 4 1 2 0 , 5 1 7 6 5 1 , 1 8 9 9 3 0 , 5 1 9 0 5 1 . 1 8 9 6 1 0 , 7 8 2 1 0 , 1 0 0 . 9 9 9 6 0 2 3 6 2 0 . 5 2 2 1 7 1 , 1 8 3 7 4 0 , 5 2 3 6 b 1 , 1 8 6 4 3 0 , 7 7 a 1 0 . 2 0 0 , 9 9 1 9 0 . 2 3 1 1 0 . 5 2 6 7 a 1 , 1 B 7 S 3 0 , 5 2 8 1 1 I , 1 3 7 2 2 n , 7 o 7 1 0 . 3 1 0 , a S 3 9 0 2 2 6 0 0 . 5 3 1 3 4 1 , 1 8 6 3 0 0 , 5 3 2 7 0 1 , 1 8 5 9 9 0 , 7 5 9 1 0 , 4 2 0 . 9 7 5 7 0 , 2 2 1 0 0 . 5 3 5 9 9 1 , 1 8 5 0 5 0 . 5 3 7 3 2 , 1 8 4 7 a 0 . 7 5 1 1 0 . 5 3 0 . 9 6 7 5 0 , 2 1 6 0 0 , 5 a o 6 7 1 . 1 8 3 7 7 0 , 5 4 1 9 9 I , 1 8 3 4 6 0 , 7 9 3 1 0 . oa 0 . 9 5 9 1 0 , 2 1 1 0 0 , 5 4 5 4 0 1 . 1 8 2 4 7 0 , 5 4 6 7 0 , , 1 8 2 1 5 0 . 7 3 5 1 0 . 7 5 0 . 9 5 ( l n 0 , 2061 0 , 5 5 0 1 7 1 . 1 6 114 0 . 5 5 1 4 S , 1 8 0 8 2 0 , 7 2 7 1 0 , 8 7 0 , 9 4 2 1 0 , 20 1 1 0 , 5 5 4 9 7 1 , 1 7 9 7 8 0 , 5 5 * 2 4 , , 1 7 9 4 7 j 0 , 7 1 9 1 0 , 9 9 ft. 9'3 5 a 0 , 1962 0 , 5 5 9 8 2 1 . 1 7 8 4 0 0 , 5 6 1 0 7 , 1 7 8 0 9 J ! 0 , 7 1 1 1 1 , 1 1 0 . 9 2 a b 0 . 1 9 ) 3 0 , 5 6 4 7 1 1 . 1 7 6 9 9 0 , 5 6 5 9 4 , 1 7 6 6 8 i 0 , 7 0 3 1 1 . 2 a 0 , 9 1 5 6 0 , 1 8 6 5 0 , 5 6 9 6 3 1 , 1 7 5 5 6 0 , 5 7 0 8,5 , 1 7 5 2 5 0 . b 9 5 1 1 . 3 6 0 . 9 0 6 6 0 . 1817 0 . 5 7 4 6 0 1 , 1 7 4 1 0 0 , 5 7 5 8 0 , 1 7 3 7 9 0 . 6 3 9 1 1 , 4 9 0 . 3 0 7 5 0 , 1 7 b 9 0 , 5 7 9 6 1 1 , 1 7 2 6 1 0 , 5 8 0 7 9 , 1 7 2 3 0 0 , 6 9 0 1 1 , o3 0 . 8 6 8 2 0 , 1 7 2 2 0 , 5 8 a b6 1 , 1 7 109 0 , 5 3 5 8 3 , 1 7 0 7 9 0 , 6 7 2 1 1 , 7 6 0 . 8 7 8 a 0 , 1 674 0 , 5 6 9 7 6 1 . 1 6 9 5 5 0 . 5 9 0 9 0 , 1 6 9 2 a 0 , b o a 1 1 . 9 0 0 , 8 6 9 3 0 , 1 6 2 8 0 , 5 9 a 8 9 1 , 1 6 7 9 7 0 , 5 9 6 0 1 , 1 6 7 6 7 0 , 6 5 o 1 2 , 0 5 0 , 8 5 9 7 0 , 1 5 8 1 0 , 6 0 0 0 6 1 , 1 6 6 3 7 0 , 6 0 1 1 7 , 1 6 6 0 7 0 , 6 a * 1 2 . 2 0 0 , 8 a 9 9 0 . 1 5 3 5 0 . 6 0 5 2 8 l , l 6 a 7 a 0 , 6 0 6 3 7 1 , 16 a a a 0,64 0 1 2 . 3 5 ( l , b a 0 1 0 . 1490 0 , 6 1 0 5 3 1 , 1 6 3 0 8 0 , 6 1 1 6 0 , 1 6 2 76 0 , 6 3 2 1 2 . 5 0 0 . 6 3 0 1 0 , 1 445 0 . 6 1 5 6 3 1 . 1 6 1 3 9 0 , 6 1 6 8 6 , 1 6 1 0 9 i 0 , 6 2 a 1 2 . 6 6 0 , 820 ('• 0 . 1400 0 . 6 2 1 16 1 , 1 5 9 6 7 0 , 6 2 2 2 0 1 , 1 5 9 3 6 0 . 6 1 6 1 2 , 8 2 0 , B (. 9 7 0 , 1 356 0 , 6 2 6 5 4 1 , 1 5 7 9 2 0 , 6 2 7 56 , 1 5 7 6 3 0 . 6 0 8 1 2 . 9 9 0 . 7 9 9.4 0 , 1 3 1 2 0 , 6 3 1 9 5 1 , 1 5 6 1 4 0 . 6 3 2 9 6 1 , 1 5 5 8 5 0 , 6 0 1 1 3 , 1 6 0 , 7 6 R9 «, 1269 0 , 6 3 7 4 1 1 . 1 5 4 3 3 0 , 6 3 8 3 9 . l , i 5 a o a 0 . 5 9 3 1 3 . 3 3 0 , 7 7 8 3 0 , 1227 0 , 6 4 2 9 0 1 , 1 5 2 4 8 0 , 6 4 3 8 7 1 . 1 5 2 2 0 0 . 5 6 5 1 3 , 5 1 0 , 7 b 7 6 0 , 1 185 0 , 6 4 8 4 3 1 , 1 5 0 6 1 0 , 6 a 9 3 8 1 , 1 5 0 3 3 V 0 . 5 7 7 1 3 , 7 0 0 , 7 5 6 7 o, 1 143 0 . 6 5 4 01 1 . 1 4 5 7 1 0 , 6 5 a 9 a i , i 4 6 a 3 J 109 » K l K l O J 3 i n i n ^ 3 £ 3 ru o io a a 3 a cr o o ru o o* m m ru a- L P to -o cr -« r^. m ru ru ru; » ^ i 7 -X) m — i o xi -c! ru — -V o flic ru —»| —« x>j fl -cr — —• o o o o cr =i x> fl >n rr o c 3 o c ^ » -o t cn co m o LO so m J1 fU o r-. r- ^ © © o a O 'J> -in x> ru ;r ."u o fl fl c o o O to -o O -n m in m O O O l o m o K M C — o m 3 o o o 33 o in —• A r\j ;? cj o o o ;n a- s | O rj -fl 3 M -n m tn o o o fl 3 O —• O cr -a ' fl co r\j ru — - - • —< O O O; O O O fl —« A d O ~7 ru o a —• —< o o o o |m -o nj tv o *n O ^ 1 " N ^ D-£ X l N S (O I I fl fl A A A -c o o n j l ^ i ^ ru o ."vi. m \y\J m-ir. in >£\t~* 2*. o A njiso 3 c o ru to f t 3 ; ^ i n sDJ-O N r— r» r~j r- r~->r— r— i A o- ru Ln co a-3 O 0]0 O X i X D O O r~ -n ru " J Ki CO cO X> o ru o o i n « m cr m CO IO OJ r- m &• Ln A A CO I A x>| m —• fl M C B Xi CO CO i — rvj T) •tr*. o=cr ru * w O 17- O x> co o A 3 m|—• co rn ar> —omicrMVru o —* w k i <v M T o o- o cr fl -o ru Oftn o oo rn OD r ' l 3 3 o- o- o m o —.|A- cr Ln L-o.iritn-.-n v.o -<n ru fl o i 3 x> —*: i^n i n fllfl fl —-o- a- o- !o» a- cr r-- —• fl cn. o •<> C D o i I — I*- BO | o o o -o o o o o o |r— © —* x> ru ru if"*- O lO N f -j ) j nj o r , 3 3 3 3 o o o ru o HI - cr ^ co fl o o ©I© © © 3 m o i r u »*i ru o fl —•JT-- ru r-3 — o' fl cr — — — ©!c O 3 O O i o- m A —• fl © o fl cr' t> o a* o o o cr x> ru — .o fl r> (O » © o o ru r y i fl o m • n o * CO B N o o o o o o —• i n fl © m TI f l O o m x> fl © m •si ru fl fl fl o o o in i n in o o o o o o —• cr o o m r*. —• o J> |'J"» CT d © O © o o o o o o *n fl a cr i n ru fl cr ru m --o o o o o o o A —• O r- fl O r-~ m ru ru ru o o o o o © o o o m ir inl>o to —| rn _ :>,rs. LO cr ru ru —.1— — — © © © i © o o o o o O =1 CO a o cr ru o o-ru -o A rvj o O ru t> fl ci -*v; o m o fl ru x N N <D I ' fl fl fl fl fl fl 3 r> ,n o- o fl fl r-— fl 5>! © — ru N ru x 3 i n int fl ~~ ru ru c i n ct © fl * y a-fl © d CC o —. ru r> ir: A A in ru »o cr - H N ru -u tn OD co co m m in o i n •n cr x> xi cc ?n o ^ f i •n cr fl fl xi x> nj o o —* x> *n in o fl X ) co <o » n ru r- i n nj K ru r- m| cr a- © o x» ff-ct cr cr co m o o — — o o- o ru ru © cr o cr <\i ru *n cr o ^ ru ru o i o 2/ 3- cr cr- O O I\J c r\i!'n ^ m ?\} CT Cf I'M C" c» ru fl ©!cr r— —* •jy T. oO fl r» O 3- I o o o ru fl ru x> o O cr r-» © © © © © © m r u r u w i n s o -fl ru co cr © -* © © o o cr o o o o cr co r- m o 1' £ o fl "u O y i fl © n m mi n cr cr ^ o o in o © x i in -n rn: o ©; cr ru —| K I — o-m ?n rv o o o — m r- in tni ru ru ru © o © © o o © o o © C O m d in o co o © o o © o •fl co fl *f\ .nj o o o a rn K I | © C O © o o o tn —* ru ro ru: o o o o © o o o o j o cc> iri nj © o o o CO fl —» © ©I o o o o o o in cr Kll © o o| © o o © © C o © © © © © t— 4> cr —• fl o tn d nj © cr m ru — © x-o o o cr ru — © O- r-X LT m © nj cr r~. ct —• o cr U", IT' 'J' J". ^ cr xi in rv ru c LT". X» iT* ro © f> fl ru I fl r- o fl rv, ;i rv ci a a O ru| O O rC ru m in a i n ru o m -J 3 ^ 1*1 m rt o o -o| ru n i to —. m tn m •n rul fl X ) cr ru ru — o 0 o rvi ru o ru LT> i n i n cr c © ©• M cr c» cr rr TJ r- T ; | C C co rr fl IT- cr K \ ru tn in m tn i n in ^ I J I ; S c> rt m ci rf^-Tj —. —r ci cr TT , cr ca 3 n m »*-cr tn fri ru cr fl| " i ru fn m mi © rul a cr © o a j -o r- r. -n m ru|iv r\j ru • o i n x o o ru ru — o o © c © ; o o o l © © © o © o © © © o o o o o o 0 , 0 9 5 8 3 . 3 4 0 , 0 1 8 7 0 , 0 0 0 2 0 , 9 8 3 6 8 1 , 0 0 6 1 2 0 , 0 8 7 9 0 * 9 1 0 , 0 3 2 6 0 , 0 0 0 1 0 , 9 8 6 2 0 1 , 0 0 6 8 5 0 , 0 2 7 1 0 , 0 0 0 1 0 , 9 8 8 5 9 1 , 0 0 5 6 8 1 5 2 4 8 B Y T E S , A R R A Y A R E A = 0 , 0 7 9 1 0 0 , 0 0 C O R E U S A G E O B J E C T COOE= 0 , 9 8 3 7 2 1 , 0 0 8 1 0 0 , 9 8 6 2 7 1 , 0 0 6 8 3 0 , 9 8 6 6 1 1 , 0 0 5 6 7 420 B Y T E S , T O T A L AREA A V A I L A B L E : 1 0 2 4 0 0 B Y T E S D I A G N O S T I C S C O M P I L E T I M E : NUMBER Or E R R O R S : 0 , 3 b S E C , E X E C U T I O N T I M E : 0 , NUMBER OF W A R N I N G S ; 3 0 , NUMBER OF E X T E N S I O N S : 0 0 . 1 8 S E C , W A T F I V - J U L 1973 V 1 L 4 1 8 1 4 9 : 1 4 T U E S D A Y 28 OCT 7b i S TOR E X E C U T I O N T E R M I N A T E D S S I G I l l Appendix C The Nuclear Orientation Fitting Program NOFIT The Program: A program was developed which would f i t , by the least squares method, various Nuclear Orientation parameters to the experimental data points. The parameters which were to be f i t to the data were; f the fraction of nuclei feeling a unique hyperfine f i e l d . The remainder feel zero f i e l d . H the unique hyperfine f i e l d U2 F2 \ U4 F4 J . the UVFV coefficients The expression for the anisotropy was written as a Taylor Series Expansion of the form F(T, H+*H, 0 = 0°) = f[F(T, H, e - 0) + ?F<T> H ^ e = o) A H ( C l ) where F(T, H, 0 = 0) = A 2U 2F 2B 2 + A ^ F ^ (C2) and _3F (T, H, 6 •« 0) _ A2 U2 F2 dh • A4 U4 F4 3^, 9H ~ 3 H 8 H ( C.3) In Equations (C.2) and (C.3), the U 2 F2 and U^ F^ . coefficients are the 112 i n i t i a l estimates. Their best f i t values are found by varying the and multiplicative constants. Hence the best f i t values would be, (U2F2)'" = A 2U 2F 2 ( U 4 F 4 r - A 4U 4F 4 (C.4) A Restricted Least Squares Fitting method developed by Froese et.al. (1974) was used to f i t the parameter values to the experimental data points. The routine allowed the parameters to be varied individually, or any combination of them to be varied simultaneously. A Listing of the NOFIT program i s given. ir .T,,V!e C l , •MICHIGAN T E R M I N A L S Y S T E M F O R T R A N G C 4 1 3 3 6 ) M A I N 0 8 - 2 5 - 7 5 1 5 : 2 6 : 1 2 P A G E PO01 C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C * * * * * * * * * C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * N O F I T * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * _ G — * * * * * * * * * *.*-» * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 , 0 0 0 1 , 0 0 0 2 , 0 0 0 -STO - O J J -c********* C A F I T T I N G P R O G R A M T O F I T T H E H Y P E R F I N E F I E L D A N D T H E F R A C T I O N - C O F - N U C L E - I — F - F E L I N G - T H E - H - Y - P E R F - I - N E - F - I E L O - T - O - A - S E J - - — O F - E - X P E R - I M E N - T - A L -C D A T A P O I N T S . C - € - F U N C T I O N I S E - X - P - A N D E O A S A T A Y L U R S E R I E S OF T H E F O R M ; F ( x , H + D E L T A h ) = P C l ) » C F C X , H ) + C D F ( X , H ) / D H ) » P 1 2 > ) " H E R E P ( l ) IS T H E F R A C T I O N OF N U C L E I F E E L I N G T H E H Y P E R F I N E F I E L D A N D P ( 2 ) IS A N E S T , OF D E L T A H , P ( 3 ) AND P C 4 ) ARE C O E F F I C I E N T S - » " H - t C - H -A P-PE-AR—A-S—1 • C -c-c c -c-c c - C • • r C T H E Y ARE MEANT TO S O L V E FOR THE A T T E N U A T I O N C O E F F I C I E N T S OF ANY C O B S E R V E D T R A N S I T I O N , i - S T-ffE—S O B R 0 U-T-I-N E—=-A U-X-!!—, • C X IS T H E T E M P E R A T U R E IN M I L L I D E G R E E S K E L V I N AND H- IS THE F I E L D C IN K I L O G A U S S , P O L A R I Z I N G MUST BE ADDED TO H WHEN F I T T I N G AN _ C U N K N O W N - w Y P E R F I-NE—F-TELO'. : : :  w ( T H E T A ) = i * P ( 3 ) A 2 B 2 P 2 t P ( 4 } A 4 B « P 4 * A: ******************************************************************** ********* E N T E R . : S P I N , M A G N E T I C MOMENT IN N U C L E A R M A G N E T O N S , T I T L E FORMAT I F 4 , l , F 7 , 4 i 1 5 A 4 E N T E R : U 2 , U 0 , F 2 , F « F O R M A T : U F 1 0 . 7 E N T E R : S O L I D A N G L E D A T A ( H A L F A N G L E S IN R A D I A N S AT THE O E T C T O R S FORMAT : 2 F 7 . 4 . C E N T E R ' : NUMBER OF D A T A P O I N T S , NUMBER OF P A R A M E T E R S C I T E R A T I O N S , E P S I L O N , A X I S -6 F-OR-HAT i 3 1 2 , 2F 1.0,5 NUMBER OF 3 , 0 0 0 4 , 0 0 0 — 5 , 00 0 -6 , 0 0 0 7 , 0 00 — 8 - r O O O -9 , 0 0 0 1 0 . 0 0 0 -1-1 , 0 0 0 -1 2 . 0 0 0 1 3 . 0 0 0 -14-. 0 0 0 -1 5 , 0 0 0 1 6 , 0 0 0 -4-7 , 0 0 0 -1 6 , 0 0 0 1 9 , 0 0 0 -2-0,-0 00--2 1 , 0 0 0 2 2 . 0 0 0 - 2 3 , 0 0 0 -2 4 , 0 0 0 2 4 , 0 0 0 - 2 5 , 0 0 0 -2 6 , 0 0 0 2 7 , 0 0 0 - 2 8 , 0 0 0 -2 9 , 0 0 0 3 0 , 0 0 0 - 3 W - 0 0 0 -3 2 , 0 0 0 3 3 , 0 0 0 - 3 4 . . . 0 0 0 -3 5 , 0 0 0 3 6 , 0 0 0 -3-7-,-O-Oe-A X I S = 0 . 0 S O L V E D FOR A X I A L A N I S O T R O P Y DATA POI;NTS = 9 0 . 0 S O L V E D FOR E Q U A T O R I A L A N I S O T R O P Y D A T A P O I N T S C C - C • — C E N T E R : MODE I N D I C A T E S T Y P E OF W E I G H T I N G TO BE G I V E N TO T H E D A T A C P O I N T S D U R I N G THE F I T T I N G R O U T I N E . _j= F-ORMAT : 1 2 -3 8 , 0 0 0 3 9 , 0 0 0 -4 0 , 0 0 0 -4 1 , 0 0 0 4 2 , 0 0 0 _iL3-,.O-0-0-M O D E = - l , S T A T I S T I C A L W E I G H T I N G W ( I ) s , , / S I G M A Y ( I ) M O D E : 0 , E Q U A L W E I G H T I N G W ( I ) = 1 , 0 -MODE=~+-l —,—I-N s -T-R-OME-W J - A L — w E-I-5 H 3 - I N G — W -C-I-}=4-, I-G M A-Y-C-I-)-*-* 2 -W ( I ) = W ( I ) / W M E A N W M E A N = R C 1 ) + W C 2 ) - - - - - - - - - — - - ' + W C N ) - E - N ^ E S ; D A T A gg^N^T-S ) T EMP ( M i L L I X ) , AN I S04^0P-Y-*£R-ROFi IN A N I S FORMAT : 3 F 1 0 . 5 -E-N-T-E-R-j-rt-Y-PERF I-NE—F-I-E-L-D—E-S-T-I-MAT E- , -E-S-T-I -MA-TE-OF— F-R AC-T-I -BN-0F—NUC L-E-I-4 4 , 0 0 0 4 5 , 0 0 0 - U 6 , O 0 0 -4 7 , 0 0 0 4 8 , 0 0 0 -4-9-,-frOO-5 0 . 0 0 0 51 , 0 0 0 - 5 2 , 0 0 0 -M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 4 1 3 3 6 ) M A I N : : 0 8 - 2 5 - 7 5 1 5 1 2 8 1 1 2 P A G E P 0 0 2 0 0 0 2 - 0 0 0 - 3 -0 0 0 4 OOOS -O-ORrt— 0 0 0 7 0 0 0 8 - 9 < H H » -0 0 1 0 0 0 1 1 - 0 0 1 2 -0 0 1 3 0 0 1 4 - 0 4 M - 5 -0 0 1 8 - 0 0 1 - 7 -0 0 1 3 0 0 1 9 0 0 2 1 0 0 2 2 - O 0 2 S -0 0 2 4 0 0 2 5 - 0 0 2 6 -0 0 2 7 C F E E L I N G THE H Y P E R F I N E F I E L D . I N I T I A L E S T I M A T E OF D E L T A H C E S T I M A T E S OF THE A T T E N U A T I O N C O E F F I C I E N T S G2 AND G4 R E S P E C T I V E L Y C FORMAT : F 7 , 2 , S F 1 0 . 5 - £ P (1 ) I S THE FR-AC-T-I-O-N—OF-—NOC-U-E-I—F-E-ELING T H E — W W -B f^NE— F - J - E - I Q D E L T A H I S P A R A M E T E R P < 2 ) P ( 3 ) I S THE A T T E N U A T I O N C O E F F I C I E N T G 2 - P - ( - 4 - ) - I S-T-HE—A-T-TENUA T - I O N - C O E F F - I - C - I E N - T - G 4 -E N T E R : MO F-OR-HA-I 1 511 MD = 0 P ( I ) I S HELD AT I T S L A S T G I V E N V A L U E MD=1 P ( I ) I S ALLOWED TO VARY S U P P L Y — A S - M A N Y — D I F F ERE NT—MD—CARDS AS—YOU- ' - » - I -SH-E X A M P L E 0 1 P t l ) H E L D C O N S T A N T , VARY P C 2 ) , THEN MD CARD WOULD BE TO A N A L Y Z E DATA FOR MORE THAN 1 T R A N S I T I O N , PUT SEND B E F O R E THE DATA OF THE NEXT GROUP OF DATA TO BE A N A L Y Z E D , TG S T O P P R O G R A M , THREE E N D ~ O F - F I - L E S - A R E - N E C - C E S S A R Y ~ * It t* * * It** It* * ti ^* *it %1c* tt* * * * * * * * * * it*** 1c1t**^.k*1t**\*%tt*1i** it*it* * * * * * * * * * fc-X-TE-RN At—Ai4R< . D I M E N S I O N X [ 5 0 ) , Y C 5 0 ) , Y F C 5 0 ) , S I G M A Y C 5 0 ) , w ( 5 0 ) , ' P ( 5 ) , E 1 C 5 ) , E2 15 2 ) , F I R ( 6 ) , A ( 1 5 ) , M D C 5 ) COMMQN—A20-, A 4 o , -A2R0 . A49O , -S - , -0 - I -PM0M - , -HrA X - I S - , C 2 M - 0 - ) - , C4-I-1-0-) C O M - f O N / F A K U L C / F ( 6 0 ) L O G I C A L V E T . RT. -A-B - ( -5- , -HHM: :-N5J^ N s l , 1 5 - ? C A L C U L A T E THE C L E 8 S H - GORDAN C O E F F I C I E N T S S S = 2 , « S S R = A B S ( S S ) - A I N T ( S 3 ) -TF-fSR-rE-O , 0 . ) GO TO 24 W R I T E ( 6 , 1 1 1 ) STO= 1 0 - 2 « 0 2 i = S * (S+-1-,-) _ _ 0 2 2 = s a R r ( ( 2 , * S + 3 , ) * ( 3 + l , ) * S * ( 2 , * S - l , ) / 5 , ) « 4 1 = 3 , * C S + 2 , ) * ( S + 1 , ) « S * ( S - 1 . ) W = = r , - « 4 - b - , - « S - » S + 6 - , - * - S ^ 5 T - 4 -04 3 = 2 , * S O R T C ( 2 , * S + 5 , ) .*(S + 2 , ) « ( 2 , » S + 3 , ) * ( S + I , ) * S * ( 2 , * S * 1 , ) * ( S - 1 . ) » ( 2 2 , « S - 3 , ) / 9 . ) — « - l = S +1-, 1 : _ _ _ : " N 2 = S t O , 6 NO=N'l - N 2 -00—|-0-*=-l- , -N-l-Si< = K S-M = S - S K * 1 , - S * 2 = S M « S M 1 0 c C 2 ( K ) = 0 , C 4 ( K ) = 0 , - 0 0 2 8 -I F C S . G E . 2 , ) C 4 ( K ) = ( Q 4 1 - Q « 2 « S M 2 + 3 5 , * S M 2 * S M 2 ) / Q « 3 - R E AO C-5,1 O2-,-E-NOr-l-O00-)U2-f-U4f F-2-y-F^ 5 3 , 0 0 0 5 4 , 0 0 0 5 5 , 0 0 0 -56-^0-0-0-5 7 . 0 0 0 5 8 , 0 0 0 - 5 9 , 0 0 0 -60 , 000 b l , 0 0 0 -62-,-flO-O-6 3 , 0 0 0 6 4 , 0 0 0 - 6 5 , 0 0 0 -b b . O O O 6 7 , 0 0 0 6 9 , 0 0 0 7 0 , 0 0 0 - 7 1 , 0 0 0 -7 2 . 0 0 0 7 2 , 0 0 0 - 7 - 3 , 0 0 0 -7 4 , 0 0 0 7 5 , 0 0 0 - 7 6 , 000 -7 7 , 0 0 0 7 8 , 0 0 0 -7-9- rO40— 8 0 , 0 0 0 8 1 , 0 0 0 — 8 2 - , OOO-— 6 3 , 0 0 0 8 4 , 0 0 0 — 8 - 5 , 0 0 0 — 8 6 , 0 0 0 8 7 , 0 0 0 — 8 8 , 0 0 0 — 8 9 , 0 0 0 9 0 , 0 0 0 — 9 - 1 - . 0 0 0 — 9 2 , 0 0 0 9 3 , 0 0 0 — 9 4 , 0 0 0 — 9 5 , 0 0 0 9 6 , 0 0 0 — 9 - 7 - . - 0 0 0 9 8 , 0 0 0 9 V , 0 0 0 - 1 0 0 , 0 0 0 — 1 0 1 , 0 0 0 1 0 2 , 0 0 0 - U ) - i T 0 - 0 0 — 1 0 4 , 0 0 0 1 0 5 , 0 0 0 - 1 0 6 , 0 0 0 — ( M I C H I G A N T E R M I N A L . S Y S T E M F O R T R A N G ( « 1 3 3 6 ) MAIN 0 8 - 2 5 - 7 5 1 5 I 2 8 J 1 2 P A G E P 0 0 3 0 0 2 9 0 0 3 0 0 0 3 1 107 - 0 0 - 3 2 -0 0 3 3 0 0 3 « - 0 9 3 - 5 -0 0 3 6 0 0 3 7 - 0 0 3 8 -0 0 3 9 0 0 4 0 - 0 0 4 - 1 -0 0 U 2 0 0 4 3 0 0 4 4 0 0 4 5 0 0 4 6 -0 0 4 7 -0 0 4 8 0 0 4 9 - 0 0 5 0 -0051 0 0 5 2 - 0 0 5 3 -0 0 5 4 0 0 5 5 0 0 5 6 -0-05-7-0 0 5 3 0 0 5 9 -0060--00*+-- 0 0 b 2 -0 0 6 3 0 0 6 4 0 0 b 5 0 0 6 6 -208-H E A D ( 5 , 2 0 0 ) N , M , N I , E P , A X I 3 W R I T E ( 6 , 2 0 2 ) N , M , N I , E P -A-x-I-S = 0 - , -F -U S—AX-I-A t r - 0 E-T-E-C-TO R-= 9 0 , E Q U A T O R I A L ' D E T , I F ( A X I S , E O , 0 , ) GO TO 204 - « R 1 I E ( 6 , 2 0-3) 102 F O R M A T ( 4 F 1 0 , 7 ) w R I T E ( 6 , 1 0 3 ) U 2 , U U , F 2 ' , F 4 108 1 0 3 FORMAT ( 1 0 ' , 1 0 X , ' U C O E F F I C I E N T S ! I / 2 1 X , <U2=' , F 1 0 , 7 , 5 . x , IUU=I , F 1 0 , 7 / / l 109 2 0 X , J - F — C O E F - F - I C - I - E N - T - S . ' - 1 - / - ? - ! * ' - - ^ ^ ^ ^ 1-10 C C A L C U L A T E THE S O L I D A N G L E C O R R E C T I O N F A C T O R S 112 C 113 R E A D (-5, l-Ob-J— A 0 . - A 9 0 • : 114 X O = C O S ( A 0 ) • 115 X 9 0 = C 0 S ( A 9 0 ) 116 &2 0 = * X 0 - » - ( 4 - , - + * 0 - ) 1-17-G 4 0 = G 2 O » ( 7 , * X 0 * X 0 - 3 . ) / 4 , 118 G 2 9 0 = , 5 * X 9 0 « ( 1 , + X 9 0 ) 119 G4 9 0 = 0 2 9 0 • (7 , « X 90 » X 90 - 3 , ) At. • 1 20 w R I T F ( o , 1 0 7 ) A O , A 9 0 , G 2 0 , G 4 0 , G 2 9 0 , G 4 9 0 121 A 2 0 = u 2 » F 2 « G 2 0 122 _ A 4 0 = U<">'-4 » G 4 0 • 123 A 2 9 0 = U 2 « F 2 « G 2 9 0 124 A 4 9 0 = U 4 * F 4 * G 4 9 0 125 -C : : — : 126 127 12b —129 130 131 —132 133 134 - 1 3 5 136 137 - 1 3 8 139 140 —144-142 143 —1 44 145 146 —1-4-7-146 149 —150 151 152 —1-53 1S4 155 —1-56 157 158 —1-59 160 161 —162 GO TO 2 0 6 « R I T E ( & , 2 0 5 ) ~-I.F--(-N-,LE-,50-,0R-,-M-,-L-S-,-5) GO TO 2 0 8 -» R I T E ( 6 , 2 0 7 ) GO To 1000 - N P (S = N . MPARAMlt f H-vE—THE—D-A-T-A—T-HE-—AP-P-ROPRI A T E T Y P E : OF WE-IGHTINC R F A D ( 5 , 2 0 9 ) MODE - M O O E - S B E C - I F - I E S — T H E — T Y P E — O F — - R E 4 - G H - T - J J J G — T - 0 - & E — U S E - O - r — * Z = l . I F THE W E I G H T S A R E TO BE S U P P L I E D BY T H E U S E R , WZt - 5 - y * » o T 0 -1 , DO 2 i a I = 1 , N P T S R E A D ( 5 , 2 1 0 ) X ( I ) , Y ( I ) , S I G M A Y ( I ) - Y - C - I - ) = Y - ( B~i~» — C T H I S I S D U E T O T H E F A C T T H A T T H E F U N C T I O N B E I N G F I T T E D I S OF T H E 1 C F O R M ( w - 1 ) O B S = F * ( W - l ) I - F - ( - S I & M A ^ - B - r N E - r O - H - G O T O 24-2 : C I F S I G M A ( I ) = o , 0 , S E T T H E W E I G H T » 1 , 0 TO A V O I D T H E F A C T O R 1 / S I G M A c G O I N G T O . I N F I N I T Y , • R - I -T E - ( 6 , 2 1-1-)— I G O To 214 2 1 2 I F ( M O D E ) 2 1 3 , 2 1 4 , 2 1 5 - G S - T - A - T - i - S - T - I C - A L - — W E - f G - H T I N G G I V E N T O Y d ) . 2 1 3 W ( I ) = 1 , / S I G M A Y ( I ) GO TO 216 - E 0 U A E — w E-1G H T-I-N G—&-I-V E N — T - G — Y - H - J -000 000 000 0 0 0 -000 000 ooo-000 000 0 0 0 -000 000 0 0 0 -000 000 0 0 0 -000 000 0 0 0 -000 000 - 0 0 0 -ooo 000 0 0 0 -000 ooo 0 0 0 -000 000 0 0 0 -000 000 0 0 0 -000 000 0 0 0 -000 000 -oo-o-000 ooo 0 0 0 -000 000 0 0 0 -000 ooo 0 0 0 -000 000 ooo-000 ooo 0 0 0 -M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 4 1 3 3 6 ) M A I N 0 8 - 2 5 - 7 5 1 5 : 2 8 1 1 2 0 0 6 7 0 0 6 8 -00-6J3-0 0 7 0 0 0 7 1 - 0 0 7 2 -0 0 7 3 0074 -0*7-5-0 0 7 6 0 0 7 7 - f l 0-7-8-0 0 7 9 —008 0— 0 0 8 1 0 0 3 2 - 0 O 8 - 3 — ooeu 0 0 6 5 - 0 0 6 6 — 0 0 8 7 0 0 8 8 - 0 0 8 " — 0090 - O O R 4 -0 0 9 2 0 0 9 3 — 0 0 9 4 -0 0 9 5 0 0 9 6 211 C -2-1-5-2 1 6 2 1 7 C w ( I } = 1 , GO T 0 2 1 6 I N S T R U M E N T A L W E I G H T I N G G I V E N TO Y C I ) » ( I ) =-)-,-/3-I-SAU-Y ( I ) » » 2 S U M Z S U M + W ( I ) w M E A N : S U M / F L O A T C N P T S ) - 0 0 - 2 1 7 - I = - l - , N R - T s — W I I ) = W ( I ) / w M E A N - W E - A 0 - I - W - 4 ^ E - J - N 4 - T - f A - b - £ S T I M A T E S OF' FRAn - T i m-nt E I . T L A T T I C E - - • - - * » . w w-u i w - r — r " i »> L ' x OHN —y-p— r w v f c - t _ ± — L A T T I C E C S I T E S ANO H Y P E R F I N ) F I E L D B E I N G F E L T BY THE N U C L E I , T H E D E L T A H I N C THE T A Y L O R S E R I E S I S P ( 2 ) AND THE F R A C T I O N Of N U C L E I I S P ( l ) - C P « - > - * ^ O - P . ( . u - ) _ A R E - - T . H E - A ^ - T . E - N U A . T - I . 0 A U C - 0 E - F - F - , ~ G 2 - A N 0 - S < l - R E S P E C - T - I - V E L - Y R E A D ( 5 , 2 1 8 ) H , C P 1 1 ) , I = 1 , M P A R A M ) KR-I-T-E-C-6 R 2 - 5 W - H - r - W - I + r - l J S + r ^ A * AM 1 R E A D IN THE C A R D S A L L O W I N G T H E P ( I ) ' S TO VARY 2 1 9 R E A D C 5 , 2 2 0 , E N D = 9 9 9 ) MD M 0 C H C K = M D ( 2 ) - C A L L - 0 R R L - 0 F -(X ,-Y- rYF-,-w-,-E-l-,E2- rP- p*Z; H, *, Ht rHOr&^Ml* i MD-)-i M f ' a i ' U C W T _J CIV n , -1 V o ... w . , .r- .. w „. . . . - - _ _ . I N C R E M E N T ri BY P C 2 ) ONLY WHEN YOU A R E ! A L L O W I N G P<2) TO VARY I F ( M O C H C K . E O . I ) H = H t P ( 2 ) -WR-I T E - ( 6 , 2 2 1 - ) W R I T E ( 6 , 2 2 2 ) 00 2 2 3 K = l , M P A R A M • * R S T f ( o , 2 2 - ) * T P ( < ) , E 4 < « - ) - , E 2 - < * ) ! : 2 2 3 C O N T I N U E I F ( N D ) 9 0 1 , 9 0 1 , 9 0 2 - 9 0-1 WRI-T E-( 6 , 9 0 5 ) GO TO 2 2 9 9 0 2 W R I T E ( 6 , 9 0 6 ) -2-2-9 GO—1-0-2-1-9-C 9 9 9 R E A D A N O T H E R S E T OF MD V A L U E S AND V A R Y T H E P A R A M E T E R S A G A I N -P-R -1 - .NT-OU-T-T-Hfi -F-I -AiAL—RE-SLH^S-^F—I-MJi-iim - I -NG . K R I T E ( 6 , 1 0 0 1 ) Ri^t-t&-^_yo-)_p-4-l_j_ w - R I T E ( 6 , 2 2 5 ) H W R I T E ( 6 , 2 5 0 ) P ( 3 ) , E 2 ( 3 ) , P C 4 ) , E 2 ( 4 ) -WR-I TE ( 6 , 2 2 6 ) — DO 2 2 8 K = 1 , N P T S Y C K ) = Y (K ) + 1 . 1 6 3 , 0 0 0 16(1 ,000 1 6 5 , 0 0 0 —J-46-,-004-1 6 7 , 0 0 0 1 6 8 , 0 0 0 — 1 6 9 , 0 0 0 -1 7 0 , 0 0 0 1 7 1 , 0 0 0 —1-7-2,-0^00-1 7 3 , 0 0 0 17<l ,000 — 1 7 5 , 0 0 0 -1 7 6 , 0 0 0 17 7 , 0 0 0 - 4 - 7 8 , 0 0 0 -1 7 9 , 0 0 0 1 8 0 , 0 0 0 1 81 , 0 0 0 -1 8 2 , 0 0 0 1 8 3 , 0 0 0 - 4 8 4 - r O 0 O — 1 8 5 , 0 0 0 1 8 6 , 0 0 0 - 1 8 7 , 0 0 0 -1 8 8 , 0 0 0 1 8 9 , 0 0 0 - 1 - 9 0 , 0 0 0 — 1 9 1 , 0 0 0 1 9 2 , 0 0 0 - 1 - 9 3 , 0 0 0— 1 9 4 , 0 0 0 1 9 5 . 0 0 0 -1-9 6 , 0 0 0 — 004-7 !CEJ.*_)=Y|.- ( K ) i i 0 0 9 8 c C-T H I S IS TO C O R R E C T FOR T H E - F A C T T H A T T H E ' P O I N T S B E I N G F I T T E D WERE A C T U A L L Y Y ( I ) - i , o AND NOT Y C I ) — O T F F - . v f . K l - , , . i : . ( . K j 0 0 9 9 0 1 0 0 2 2 8 g w R I T E ( 6 , 2 2 7 ) K , X ( K ) , Y ( K ) , S I G M A Y ( K ) , W ( K ) , Y F ( K ) , D I F F , M O D E C O N T I N U E . c c C A L C U L A T E S T A T I S T I C A L D A T A 04 OS — N F . B F F - ' = N P - T - < ! - M P f t R A i 1 _ 1 1 9 7 , 0 0 0 1 9 8 , 0 0 0 - 1 9 9 , 0 0 0 — 2 0 0 , 0 0 0 201 , 0 0 0 - 2 0 2 , - 0 0 0 2 0 3 , 0 0 0 204 , 000 - 2 0 - 5 , 0 00 2 0 6 , 0 0 0 2 0 7 , 0 0 0 -208,-00 0 2 0 9 , 000 2 1 0 , 0 0 0 -2-1-1-, 0 00 2 1 2 , 0 0 0 2 1 3 , 0 0 0 •24-4,000 2 1 5 , 0 0 0 2 1 6 , 0 0 0 2 1 7 , 0 0 0 -P A G E P 0 0 4 J W 117 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O O O O o o o o o o o o o o o o o • ^ ^ f u r \ i f \ i r v i r \ i f u r u r \ i ^ j r u ' / i i * l ' ^ r O K i f A i r y r u f \ i r \ j f \ j ^ j r y . A j r w f u r v j r > j f \ ) f \ j r u f \ j in o H-rn »n -n . ry ,\ oil * o o o o o O o o o o o o o o o o o o o o o o o o o o o * o O O O O O O O O O O O O O O O O O O O O O O O O O * O * - * o o o o o o o o o o o o o o o r> o o o o o o o o o « *• cr » - * . . * r> o o -< • \ i 3 r- if/ > o -< (M ro 3 'ji B r - - x a - o r ' ' ^ " ^ 3 * r n o ct c t c t c r c r c r c r c r c r ^ t f i i i l i T i t r i P l O J i i n u l i r i £J}j)-OJ> > - o j r u r u r y r \ j r v j r u r u r v i r \ i r \ i f u r \ i r \ i r ^ ry ' r u ry ry ru co •j* o #5 in UJ at x x < cr —' I -eo x •f - © >r o v. > UJ UJ LU UJ cr cr u. 3- Z *— II U. U. »-» o O It II rp a to a_ w v. Z + O! *. o cn • o — m — : * 11 -fi r, c o x O l II tj tl I »- O II o » « « a to i U-Kltf) Ml rr «* x c o n i u • If) q i " *T* U J II s: »--< z fx UJ UJ <t ** — ru J= I >c ru « -O —• o cr * t (J t u © --* k U_ cr -f* II 1 ° . > rx ri- -- o o *• : u_ i * . x. at rr. o tjj o o o 3 » o o © o o c S nj m cr tn fl rl rt w " rt T O C l o o o 3> • ^- X U. : O - ) l » (_J I ' X -fl — o • -v o *-r* * «* * re r co CD < »— or i z < 1- o o « DL n_ -|* nc J u j iL o ' u — k a_ u> * - J •* ru II co Z - i z ^ US C^ l <J Z X z H UJ < tn * to * _i cr <t o Z CC <s rr •tt x * f L o II • Z w d» * UL ru * «. * O ru £ — m 6 ~ r-t_> < < *-« tc :r -cr o o O U . l l . * * « * t-4 k « « « u_ -J * * < * 7 -:2 « O O O ru U. © CO • to f I -f) J : x < ui rr fl rr k n 3 cr k _ l a o o u co rr 3 rr ul z t- UJ 4. CO X l * _ U J 4 « _ J »— Iff Z CO » o U J a M x co J . i— :r uL i_> -I Q UJ < UJ Lu t i t M U f X I UJ tO Z »-* U_ X T O li or fl rt ». UJ k_ w a. - j UJ —» -v o i i n X A - • L >-f » O z 1\ x a l - j ru i t U. cO ru O Ul »— 3 O X » *> (O CO i )— K CX LiJ l U . •5 i -J -i 1 x - H u > o o cr o © i- cr *- *~ >~ *- i-< a J < < < < • 3: »^  r z 3 x : rr «-f» tr -r rr or O O O O C U_ ix. U. U_ L 1» * ru m m * o o o < * < S rt z ri: n a < < <r «t < «a < . y, j i y i s x 1 • 4 " m in r»- cr < o o o o • ro ru rv m ( - x - u . uL - or ut co o — ru c» o i n * ru ru ru r\j rn fu ru ru ru ru rv ru ru rv m o o o o o o O O O O ( M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( « 1 3 3 6 ) M A I N . 0 8 - 2 5 - 7 5 J 5 t 2 « U 2 P A G E P 0 0 6 O I U O 0 1 U 2 - 0 4 - « 4 -0 1 « a 0 ! " 5 2 F I E L 0 = ' , F B , 2 / 1 O x , ' F R A C T I O N OF N U C L E I F E E L I N G H = ', F 8 , 5 / 1 O X , ' A T T E N 2 8 5 , 0 0 0 3 U A 1 I 0 N C O E F F I C I E N T S ; G 2 = ' , F 8 , 5 , 5 X , ' G U = ' , F 8 , 5 / 1 0 X , t ? C 5 J = 1 . F 8 , 5 ) 2 8 6 , 0 0 0 3 1 5 F Q R H A T C ' O ' , ' S T A T I S T I C A L A N A L Y S I S OF R E S U L T S ) ' / 1 O X , ' D E G R E E S OF F R E 267 , 000 2 E 0 l l M = - L f . I 2 / - 1 . 0 X , J . W E - I 5 H T E O - A V E R A G E - O F - V A R I A N C £ S = : l . , F 4 0 , 5 / 1 OX ,-l C H I _ 2 6 8 , 0 0 0 -i S O ' J A K E D s i , F 1 0 , 5 / 1 0 X . ' R E D U C E D C H I - S Q U A R E D : ' , F 1 0 , 5 / i O X , ' V A R I A N C E OF 2 6 9 , 0 0 0 4 F I T = t , F 1 0 , 5 ) 2 7 0 , 0 0 0 - J J 5 FORMAT. ( J - 0 - l - , J - * « t » 6 R R O R * * * D E G R E E - S - O F — F - R E - E 0 O M - = - l - , - 1 3 , - i — C H E C K - F - O R 27 1 , 0 0 0 -2 F A U L T B E F O R E C O N T I N U I N G | i ) 2 7 2 , 0 0 0 9 0 5 F O R M A T ( i o 1 , 1 * * * * * E Q U A T I O N S rfERE.NDT S O L V E D S U C C E S S F U L L Y t * * * * l ) 2 7 3 , 000 - 9 0 s fq)MMA-T-(-J.o-L,-L*j>^-*-»_E.Oi;^-l-I.0NS—wE-RE— S O L - V E O — S O C C E S S F U L L - Y — *-«.» *•*-!-) 2 7 u, 0 0 0 -910 FORMAT ( M M , 275 , 000 lOo i F O R M A T C M ' END OF F I T T I N G R O U T I N E , M / V ' T H E R E S U L T S OF 2 7 6 , 0 0 0 2 _ T H E - - F - M - T - I - N C - A R E — H - ) 2 7 7 , 0 0 0 -END 2 7 8 , 0 0 0 I D , E B C D I C , S O U R C E , N O L I S T , N O D E C * , L O A D , N O M A P MAME—=-MA-IN fc-I-Nt-GNT—= 5-7-0 1 U 6 • O P T I O N S I.N E F F E C T * —4 -9R.T-J .QMS—j N - E F F - ' t G I-*-• S T A T I S T I C S * S O U R C E S T A T E M E N T S = 1 1 6 , P R O G R A M S I Z E = 6 7 1 2 • S T A T I S T I C S * 008 D I A G N O S T I C S G E N E R A T E D , H I G H E S T S E V E R I T Y COOE IS 0 S_j< A R N T N G - E R R O R S-4-N—Mi-I N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X I - C C C C n i c ^  -f"> • m i - * 9 ~ * -^i iln O IT. j* » S5f; ,0 o 3> «U o ru w XJ O H It 1-.-- O m < ui • II » I t) O O O rt UJ •— >r-* » * <: XJ r» * A ru •+* o ru » * — j> Q ru ru •O + O o » • O UJ * U l t i I * " •ii c in — 1° ? Si o c c o C " rt -~ y £ W -n r]n .-• o _ ~n c ru TI p* TO it n ^  • rj a z £= r\j O o o o o ^ o o o o o o c o o o o O O O O O O O O O O r p o C I O O O ru ru ru r v n j r v j r v t t - t — i-4 , ,-** J*-*'*~*-" <r — <^ ~*1 V — ^ ^ o e ru o • o o m • * * x U i CC tr> ' t- rtj < , » (/lO f l i» • rn rf ! z Ai X: -4 * i^ n o * » r> ru - n n tn ^ c M o fv r\j T J J> I C is I o C -O s~ r <L • Z * V : K. I A O C I II II II I II i rv </>;*. ru o • * cn T o o o o o o o o o 0 0 ^ 3 0 0 0 0 0 0 o o o a o o o o o o a ' It It II II II II II • rt x x CD Z ^ ! O - ' i ' O * * . z. 0= o; C E a CJJ ir * u: c ru t M o it M « **v N. + + • V + 1 r - j r - s i o o m o o t J^ ru c P rv t rt ^, » , t k z o j<. A : A o C ru ti I) II A *-* O O u« •! ~ CO TJ » + k * » o ru ui i « w S » i n r i t O :< M a ^ 3-n n o ru (A O II II —< •• Z CO 7 C - + X UJ I o * LT ~Z» ( X U"! (V Q" * c* CO O-CO i n * p z n o " n o c II X X z ru .a -» O rt x O l d * >-C SI ! I ! I I ! i I I ! I I • I W N M O ^ O i 7 . a i r c ^ r u ^ o £ c» - a ^  J ; w r u * - o c C B - I a i / , c ^  i v - o * a. >; o L n c i ^ r u ^ o ^ * ^ a u n ^ w r u * - ^ o ^ o ^ ^ o o *o o o ^ "c "o c o o "o O O o c V "o o - - - - - o 0 o < = o o o o o o o o o o o o c o o o o o o o o o o o o o o o o o o o o o o o o o o o o o p o o o rtrt^^^^rt^QOfpOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO O O O O <_> w O O O O O O O O O O O O O O 611 120 Testing NOFIT: In order to test NOFIT, the parameters f , H, and U^F^ were least 60 square's ^ fitted' < t • to theoretical and pseudo-experimental data for Co , The pseudo experimental points were generated for standard deviations in the anisotropy of 0.010 and 0.020. The pseudo-experimental points had a random-normal distribution about the theoretical data. A l i s t of the theoretical and pseudo-experimental data points for ten temperature values is given in Table Cl. These values are for a l l nuclei (f = 1.00) feeling a hyperfine f i e l d of 287.7 kilo&auss. Table Cl fin Theoretical and Pseudo-Experimental Data Points for Co Anisotropy (c0= o.} Temperature m i l l i °K Theoretical Experimental o = 0.010 a = 0.020 10.00 0.51905 0.513 0.506 11.63 0.58583 0.591 0.596 12.05 0.60117 0.603 0.605 14.08 0.66616 0.677 0.688 15.38 0.69483 0.695 0.694 20.00 0.79109 0.779 0.768 25.00 0.85190 0.842 0.831 29.41 0.88686 0.873 0.859 34.48 0.91414 0.910 0.907 50.00 0.95650 0.968 0.979 These points are generated for a detector which subtends 0.055 radians, therefore the anisotropies are those which can be seen by the detector. Best Fit to Theoretical Data a) The data of Table Cl was used to f i t the values of f and H. The UvFv values were !kept fixed at the theoretical values of U2 F2 ~ ~ ° * 4 2 0 5 6 a n d U4 F4 = -0.24281. Only and H were allowed to vary; The order of variation was , H, then and H simultaneously. The results were f = 0.9931 ± 0.0119 H = 289.71 ± 3.06 •kilogauss In this run i t was necessary.to give a l l points equal weighting, since no error was associated with the data. The results are plotted in FIGURE Cl (a). b) The data of Table Cl was used to determine the best f i t values of U2F2 and U^F^. The parameters and H were fixed at the values 1.000 and 287.7 kiloGauss respectively. Only ^-^2 and_U^F^ were allowed to vary. The order of variation was ^2^2 U 4 F 4 , then ^^2 and U^ F^  simultaneously. The best f i t to the data was U2 F2 = - ° ' 4 2 0 5 6 x (1-00640 ± 0.00713) U.F. = -0.24281 x (0.94561 ± 0.06794) 4 4 A l l data points were given equal weighting for reasons given above. The results are plotted in FIGURE 3.1 (b). 123 Best Fit.to Pseudo-Experimental Data for std- Dev. = 0.010 a) The pseudo-experimental data was used to obtain the best f i t values of f and H. The U0F„ and U.F, values were 2 2 4 4 -0.42056 and -0.24281 respectively. The order of parameter variation was the same as that in C l (a). Best f i t values to the data were f = 0.9345 ± 0.0582 H = 306.57 ± 16.96 kilogauss X 2 = 6.15 The results are plotted in FIGURE C2(a). b) The pseudo-experimental dtaa was used ot obtain the best f i t values of ^2^2 and U^ F^ . The parameters f and H were fixed at 1.000 and 287.7 kilogauss respectively. Parameter variation order was the same as in Cl (b). The best f i t values to the data were, U2 F2 = - ° - 4 2 0 5 6 x (1.03726 ± 0.03660) U4 F4 = -0.24281 x (0.66264 ± 0.34862) X 2 = 7.00 The results are shown in FIGURE C2 (b). 125 3) Best Fit to Pseudo-Experimental Data for Std. Dev. = 0.020 a) These pseudo-experimental data pts, were generated with a larger standard deviation (a = 0.020) than those of section C2. The sitti n g procedures were identical to Section C2 (a). The best f i t to the data was obtained with f = 0.88001 ± 0.11529 H = 324.6 ± 38.1 kilogauss X 2 = 6.65 The results are shown in FIGURE C3 (a). b) The pseudo experimental data was used to obtain the best f i t values of U 2F 2 and U^ F^ . The f i t t i n g procedure was identical to that of Section C2 (b). Best f i t values were obtained with U 2F 2 = (-0.42056)(1.06714 ± 0.07319) U4 F4 = (-0.24281)(0.39755 ± 0.69713) X 2 = 7.00 The results are shown in FIGURE C3 (b). Table C2 Tabulation of the results when f and H were varied Temp, mi l l °K w(e) Theory W ( 0 ) EXP. a = 0.010 W ( 0 )EXP. a = 0.020 Data Best F i t T;Data Best Fit Data Best F it .10.00 0.51905 0.51879 0.513 0.523 0.506 0.526 11.63 0.58583 0.58530 0.591 0.586 0.596 0.586 12.05 0.60117 0.60056 0.603 0.601 0.605 0.600 14.08 0.66616 0.66514 0.677 0.663 0.688 0.661 15.38 0.69483 0.69958 0.695 0.697 0.694 0.693 20.00 0.79109 0.79008 0.779 0.786 0.768 0.781 25.00 0.85190 0.85102 0.842 0.845 0.831 0.842 29.41 0.88686 0.88609 0.873 0.882 0.859 0.878 34.48 0.91414 0.91351 0.910 0.910 0.907 0.907 50.00 0.95650 0.95615 0.968 0.979 0.979 0.952 128 One of the problems in the testing of the program NOFIT was the generation of the pseudo-experimental data points. If they were truly random, the sum of the differences between the Theoretical and pseudo-experimental anisotropies would be very close to zero. In the case of the data points generated for these tests, the sum of the differences was +0.045 for a standard deviation of 0.020. These points exhibited smaller anisotropies than the theoretical values they were generated from. For the lower temperatures these points exhibited a larger anisotropy than the theoretical data. The effect of these p^teuelo-experimental points w i l l be to generate a hyperfine f i e l d which is larger than that of the theoretical value and a fraction f which i s lower than the figure of 100%.used in the calculations. This effect is demonstrated in FIGURE C4. 1/T °K W(9) FIGURE C4 Exagerated effect of f and H on the f i t to the data. 129 This effect explains the results of least squares f i t t i n g of f and H to the psuedo-experlmental data. In both cases a fraction f < 1 and hyperfine f i e l d H > 287.7 kiloGauss was obtained. The effect i s quite apparent in the comparison of FIGURE C2 and C3 with FIGURE C4. 130 Appendix D Calculation of the Coefficients The Uv coefficient can be written in terms of the Wigner &J' symbols as Uv - [(2I X + 1) (2I 2 + 1)] h (-1) 2 L where the bracketed term i s the SIX-J symbol. Here 1^  is the i n i t i a l spin of the unobserved transition, 1^ is the f i n a l spin, and L is the multipolarity of the unobserved transition, A l i s t i n g and the output of the values used in these experiments follows. This program i s a modified version of one developed by P.W. Daly (1973) to give the angular distribution for gamma radiation from oriented nuclei. S C O M P I L E C » « * « . . . . . . . . * * * * * . . . » * , , * * » * * , * , * » , « » , , * * , « * . . » « , , » „ „ „ , „ , , , « * * « * * * * * * * , , , C T H I S PROGRAMME C A L C U L A T E S T H E U C O E F F I C I E N T S D E S C R I B I N G U N O B S E R V E D C P R E C E D I N G N U C L E A R D E C A Y S , C c E-N-T-E-S-i—I-N-I-H-Afc-S?IN,-F-INAL— S P I - N 7 - L - l - , - L 2 , - W H E R E - L ~ l - & - C - a - A R E - T - H E M U L T I P O L A R I T I E S OF T H E D E C A Y , ( L 2 D E F A U L T S TO L I • i ) - F O R M A T * - 4 F U , 1 -c * * * * « « * « . • * « * * « « * * * * * » » * , » * * , * , * » , * * * * . * » , » , , « » * , * » » » * » » , , , , , , , , , , , , , , , , , , , , , , , 2 J - « 1 — 6 3 7 —e 9 10 -1-1 12 13 - 1 <t 15 16 -J-7 5 -18 4 19 - O - I M E N S I O N - F - I - R (•«>-) C O M M O N / F A K U L C / F ( 6 0 ) * R I T E ( 6 , 1 ) — F O R M A T ( ' 1 1 , 5 X , I T H E UK C O E F F I C I E N T S A P P E A R AS U K ( L I , L F , L 1 ) , WHERE 1 — 2 / 1 5 X , ' L l I N I T L S P I N ' / 1 5 X , ' L P = F I N A L S P I N I / 1 5 X , ' L I = M U L T I P O L A R I T Y OF J 1 H E T R A N S I T I O N ' ) — RE AO ( 5 , 3 , F N ! ! : 1 0 0 0 ) 3 1 , S 2 , E L 1 , E L 2 F O R M A T ( U F a , 1 ) I F ( F L 2 . L T . 0 . 1 ) E L 2 = E L 1 + 1 , — 1 1 = 2 . « S 1 1 2 = 2 . « S ? L = 2 . * F L 1 — D 0 - 4 - I = !-,-? I F ( I , G T . 1 ) L = 2 , « E L 2 0 0 5 N u = 4 , 8 , u — N = I + N U / 2 - 2 — WW = S I X J ( I 1 , H , N U , I 2 , I 2 , L ) F l R ( N ) = W K * S 0 R T ( ( 2 , * S l t l , ) . ( 2 , * S 2 t l . ) ) - I F - C M O D ( - ( 1 2 + L - ) / -2- r2->-rNE-rO )-F-I-R-(-*-) s - F - I - f t - W -20 - 2 1 -22 23 - • ? « -25 1 0 0 0 7 C O N T I N U E w R I T E ( 6 , 6 ) S l , S 2 , S l , S 2 , E L l , F I R ( l ) , S l , S 2 , E L l , F I R ( 3 ) , S l , S 2 , E L 2 , F I R ( 2 ) - 2 , S l , S 2 , E L 2 , F I R ( « ) - - - - - - - - - -F O R M A T ( ' 0 ' , F < 4 , 1 , 1 X , F « . 1 , 2 ( 1 X , I U 2 ( I , F « , 1 , , , I , P « , 1 , , , , , F « , 1 , ' ) = I , F 1 0 2 f 7 , 2 X , l u « C ' , F u , l , r , > , F U , l , l , ' , F U , l , ' ) = l , F 1 0 , 7 ) ) — G O - T - 0 - 2 • W R I T E ( 6 , 7 ) F O R M A T ( ' 1 1 ) - S T O P — -END - V . 2 2 F U N C T I O N S I X J < IG N E R - S •! X - J - S Y M B 0 L - r - E D H 0 N D S—{ 6T -3 T - 7 - J - r -S I X J 0 0 0 1 - S - I - X J 0 0 D 2 -C - A R G U M E N T S MUST H A V E T H E I R D O U B L E V A L U E S , F A C U L T I E S S E E F U N C T I O N F S I X J 0 0 0 3 C S I X J 0 0 0 4 26 27 - 2 6 -2 9 30 - 3 1 — 32 33 -3«-35 36 - 3 7 -38 39 -ao-F U N C T I O N S I X J ( J J 1 , J J 2 , J J 3 , L L 1 , L L 2 , L L 3 ) C G M M 0 N / F A K U L C / F ( 6 0 ) - L - O G I C - A L — T R L - r M O -T R L ( K , L , M ) = ( K , G T , L t M ) , 0 R , ( K . L T , I A B S ( L - M ) ) H O ( K , L , M ) = M O D ( K - I A B S ( L - M ) , 2 ) , N E , 0 — D A T A - N N / 2 / I F ( N N , G T , 1 ) GOTO U . 1 J 1 = J J 1 -J2=-J-02 — _ J 3 = J J 3 L ! = I . L 1 - L 2 = L L 2 •— : . L 3 = L L 3 S I X J = 0 , - I F - ( - T R L - ( - J l - r ^ 2 T i ) ^ ^ R T ^ R W - h - L - 2 T t 3 + T 0 R T ^ R t S I X J 0 0 0 5 S I X J 0 0 0 6 - 3 I X J - 0 0 - 0 - 7 -S I X J 0 0 0 8 S I X J 0 0 0 9 - s i x j o o i o -s ix joo i i S I X J 0 0 1 2 - 6 IX J00-1-3-S I X J 0 0 1 4 S I X J 0 0 1 5 - S I X J 0 0 1 6 -S I X J 0 0 1 7 S I X J 0 0 1 3 - S I X J 0 0 - 1 9 -6 7 3 9 1-0— 11 12 1 3 11 15 1-6— 17 18 19 -20 21 — 2 2 — 23 2 a . — 25 — 26 2 7 — 2 8 — 29 30 _ . J 1 — 32 33 _ . 3 4 35 36 — 37 — 38 39 11 42 — 43 44 45 — 4 6 47 48 49 50 - 5 - 1 -52 53 - 5 4 -5S 56 -5-7-58 59 - 6 0 -61 62 - 6 3 -132 — ru O O O O O O XXX 00 CO CO —• ro n in yo N to a g g g g g g g g g g g g S g g g g i f i S S S S S S S S S S S S S S *><~~*-222333*-232 3 3 2 3 3 3 3 3 3 3 2 2 2 3 2 3 2 2 M S [> O t n m m * O O O o O O o o ~i "3 ~0 X X X X -r* OJ f l -o -o o o O O O O o o o o *T> -3 —> x x x x •€ N CO O" -O >C ^) ~c o o o o o o o o o o -> - a r> *-> -> X X X X X I I O — r u r f i t f i ^ o o o o o o o o o o o o ~3 ~0 "> -3 -> -i X X X X X X - I zrowr a : *-j ~> . z> - • fr- —• ru t UJ ~> _ • : » - ' + . O — -« X -> -II I ru ru i v » +- + + rvj r ru K> - H ; > r u r u r u r t j _ j _ j _ i •C 3 ^ « OC(\.'fli(\|(\J«jj.j_ ij 11 2 U-* f ru i % ro A J X. V . tsl U. rt 2 * rt rt I Kl Q O 2 " O U_ f x u, * : •* * « rt . ^ * rt KI : H*I •*! rt ro o - - • • ct 2 r - — 2 : + ru ru rv ru ru ru ru ru ro ru ru ru i o u. • -> ~> " 5 w u. * : a o t a t / > c o t o c r j ( O E O c o ( O t o « c o c a c o w < / i e o e o I =r —• — . =T — .U ^ —.1 + * — r\j K> J -> ~3 -> II If M — r u r i ' Z Z 2 II II « -»-J r^j r II i Z >c C- « r *--« * * U_ is -•* LTI r u ; J -J _J nj ~ o Ii ii ii II II if II ti ti H it | | | , " t ^ w | ! f\J K l g o v u . J C O O O I I U . • ( : 2 2 2 2 ID # ( I ru » " 5 >^ _ l _» . 2 2 2 2 2 ; - r u HI 51 2 : * i I — r 2 2 2 2 : 11 II l i H i : < < < fti C 2 2 2 2 ; u. o LT> _J X ru II » — in rt 4. -» _J X >-* <- II II . . X >- . :-r — *r -z uj -a a o >- 3: z> «»-i»M>-,»r>.h.f_ (• M C s « s i , a: « K a a v v i j : - A I. J j T H E UK " E ^ j C i e N T S ^ P P E A R AS UK ( L I , LF, L 1), WHERE L F s F I N A l S P I N U s M U L T I P O L A R I T Y O F T H E T R A N S I T I O N ~ 7 T O 5 - r O - U 2 - ( - 7 T 0 - » — 5 T O ~ 2 T O - ) = - « T 9 2 9 5 5 3 5 U U < — 7 - r O - r - 5 - j - O v — 2T0 - > » - 0 7 ; 7 M82HI -U 2 ( — 7TOT-*-|-OT - 3 T0 - > o-0 - s - 7 - l - 9 6 2 8 8 — 0*K—7 - r O i 5 . 0 , 3 t 0 4 = 0 , 1 9 2 9 6 5 5 7 , 0 U . O U 2 ( 7 , 0 , U . O . 3 , 0 ) = 0 , 8 7 2 2 5 9 1 UU< 7 . 0 , U , 0 , 3 . 0 ) = 0 , 6 1 5 7 0 0 1 U2C 7 , 0 , 4 , 0 , 8 , 0 ) = 0 . 5 U 5 1 6 2 0 UU ( 7 . 0 , U . O , a , 0 ) = - 0 , 1 5 3 9 2 5 a 7 , 0 3 , 0 U 2 ( 7 . 0 , 3 . 0 , u , 0 ) = 0 , 7 6 9 1 1 7 3 UUC 7 . 0 , 3 , 0 , U , 0 ) = 0 . U 1 9 5 2 9 U U 2 1 7 , 0 , 3 , 0 , 5 , 0 ) = 0 . 2 9 5 9 1 9 U UU C 7 , 0 , 3 , 0 , 5 , 0 ) = - 0 , U 5 U U 9 0 5 — 6 T 0 — 7 T O - U 2 C 6 . 0 , 7 v O v — i ~ r i H > -g - 0 T 9 69 22 5 - 7 — U U t - 6 - r O 7 - , - 0 - « — 0 - ) =-0-,-8 9 7 U 0 3 - 7 - U 2 (—6 T 0 , - 7 . 0 , — 2 T 0 - ) = - O T 8 a 8 0 - 7 -2 - 7 — i K K - 6 - , ~ 0 - r - 7 - t - « r - 2 - ,-0-) •=—0-r5 2 3 a 8 u 6 -6 , 0 5 , 0 U 2 ( 6 , 0 , 5 , 0 , 1 , 0 )= 0 , 9 5 8 0 3 3 d U U ( 6 , 0 , 5 , 0 , 1 . 0 ) = 0 , 8 6 3 0 5 9 2 U 2 ( 6 , 0 , 5 , 0 , 2 . 0 ) = 0 , 7 9 3 7 9 8 9 U K 6 , 0 , 5 , 0 , 2 . 0 ) = 0 , 3 6 8 5 9 7 2 6 , 0 U . O U 2 ( 6 , 0 , U . O , 2 , 0 ) = 0 , 8 9 9 9 5 1 1 U U ( 6 , 0 , U . O , 2 , 0 ) = 0 . 6 6 6 0 8 8 8 U 2 ( 6 . 0 , 1 , 0 , 3 , 0 ) = 0 , 6 1 0 6 8 1 2 UU C 6 , 0 , U . O , 3 . 0 ) = - 0 , O U 9 0 0 6 1 - 5 T « : — 7 T O - ' J 2 ( — 5 T 0 7 — 7 - T 0 T — 2 t 0 - ) = - 0 y 9 2 8 5 5 3 5 — U U ( — 5 . 0 , - 7 .0 , - 2 . - 0 )=-0-r7 7-i 82 l - « ~ U 2 - < — 5 - , - 0 - r— 7 , - 0 3 T 0- ) = - Q - r 7 - t 96288—UU(-S,+r-7-r<}-,—$l:<yi^-rl?2<>~rS?— 5 , 0 6 , 0 U 2 ( 5 , 0 , 6 , 0 , 1 . 0 1 = 0 , 9 5 8 0 3 3 d U U ( 5 . 0 , 6 , 0 , 1 , 0 ) = 0 , 8 6 0 0 5 8 5 U 2 ( 5 , 0 , 6 . 0 , 2 , 0 ) = 0 . 7 9 3 7 9 9 6 UUC 5 . 0 , 6 . 0 , 2 . 0 ) = 0 , 3 6 8 5 9 6 9 5 , 0 5 , 0 U 2 ( 5 , 0 , 5 . 0 , 1 , 0 ) = 0 , 8 9 9 9 9 3 5 UU C 5 , 0 , 5 , 0 , 1 . 0 )= 0 . 6 6 6 6 6 U 3 U 2 ( 5 , 0 , 5 , 0 , 2 , 0 ) = 0 . 7 1 0 2 S U U U U ( 5 , 0 , 5 , 0 , 2 , 0 ) = 0 . 1 5 3 6 U 5 U - 5 T 0 < r r O - t f 2 - t - ^ 5 T ( > T — * T O — t r O - ) - = - 0 T 9 5 9 3 - 7 2 U U U - ( — 5 T 0 > — U T O . - I - T O ) = - 0 t 7 9 7 - 7 21-U - U 2 ( - 5 ,-0 , - U , 0 - , - 2 f 0 ) o - - 0 T 7 0 U 5 2 7 6 - - O - U - < - ^ . - 0 7 - « - i - 0 - 7 - - 2 T e ^ = - - 0 - r « 2 J » « 9 — -5 , 0 3 , 0 U 2 C 5 , 0 , 3 , 0 , 2 , 0 ) = 0 , 8 H « 8 3 U - UU t 5 . 0 , 3 , 0 , 2 , 0 ) = 0 . 5 U 3 5 5 5 U U2C 5 , 0 , 3 , 0 , 3 , 0 ) = 0 . U 2 U 9 1 6 6 U « ( 5 , 0 , 3 , 0 , 3 , 0 ) = - 0 , 3 6 2 3 7 0 3 1 , 0 U , 0 U 2 ( u , 0 , U . O , 1 , 0 ) = 0 . 8 U 9 9 9 7 9 U U ( U . O , U , 0 , 1 , 0 ) = 0 . U 9 9 9 9 8 2 U 2 ( u , 0 , u , 0 , 2 . 0 ) = 0 . 5 7 3 3 7 U 7 UUC u.o, u,o, 2 , 0 ) = - 0 , 1U93U99 j H T T ^ K T T . - v Z " ' - ' ^ - ± - — - - I t 1 2 . [ Z Z 134 Appendix E Hyperfine Distribution Fitting Program HYPFIT This program f i t s , by the method of least squares, experimental data to a Gaussian distribution of hyperfine fields. The anisotropy for such a distribution i s given in Equations (3.4) and C3.5). A variable fraction of nuclei which f e l t this distribution of hyperfine fields was also included. This allowed the distribution centroid, distribution width, and fraction of nuclei feeling the distribution to be determined from the data. A l i s t i n g of this program is given. M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G(«l336) M A I N 0 6 - 0 8 - 7 5 15135!59 P A G E P 0 0 1 H Y P E R F I N E F I E L D D I S T R I B U T I O N , ********************** 0001 0002 -0Trx3~ 0 0 0 1 0005 T O W " 0007 0008 -oco^ -0010 OOP. -0-0T2-0013 0014 -TTOTS-0016 0017 0019 0020 -002T-0022 0023 -0 0 28-c********** c C T H I S R O U T I N E . F I T S , B Y L E A S T S O U A R E S , A G A U S S I A N H Y P E R F I N E F I E L D ~ C D-mR ' I-etntO^ ^ T - 0 ^ t f C L - £ ^ ^ ^ V - f l R - K 1 l l ^ ^ ^ ^ ^ ^ - » ) - ^ | - D ^ ^ T A ( ri ( T - H E - T ^ ^ T E M P T — ) — ) - ; A FRACTION P ( l ) OF THE NUCLEI FEEL'' A GAUSSIAN F I E L D DISTRIBUTION CENTERED ABOUT A MEAN F I E L D P C 2 ) OF' WIDTH P(3 ) ' , THE. REMAINING "NUCtEI ARE AS3BMeO-T-O-F-E-et-ZERO-F-I-g'tD7- •  :  J O B C A R D S I N ORDER A R E : C E N T E R T E M P ( M l L L I D E G R E E S K E L V I N ) , H ( 0 ) , ERROR IN W ( 0 ) C FORMAT 1 3 F 6 . 3 "C E - NTE R - 1 N I T l A f - E S T I H A T E ' S — 0 F - ^ M E — P AS-ArM E-TERS7- ~r-C P ( l ) = F R A C T I O N OF N U C L E I F E E L I N G H Y P E R F I N E D I S T R I B U T I O N , C P ( 2 ) s MEAN V A L U E OT T H E G A U S S I A N P I E L D D I S T R I B U T I O N IN - C K I L 0 6 A U S S - ; -C P ( 3 ) = F I E L D W I D T H I N K I L O G A U S S , C . F O R M A T t 3 F 1 0 . 5 ~ C E N T E R - M A X I - M U M - N U M B E R - O F — r r E R A - T T O N S T — g P - S I L O N I P E L T A P f P 7 C F O R M A T ! I 3 , F 5 , 3 C E N T E R M O V A L U E S , A / H O L D S T H E P A R A M E T E R F I X E D A N D T H E U A L L O W S T H E -c PAR-AM ETEK—ro-vTtRr; •  C F O R M A T 1 3 1 1 - 1 , 0 0 0 2 , 0 0 0 3 , 0 0 0 — * 7 * 0 0 -5 , 0 0 0 6 , 0 0 0 —7-,-oo-o-8 , 0 0 0 9 , 0 0 0 - W 7 0 0 0 -1 1 , 0 0 0 1 2 , 0 0 0 1 « , 0 0 0 1 5 , 0 0 0 - 1 - 5 70 0 0 -1 6 , 0 0 0 1 7 , 0 0 0 1 9 , 0 0 0 2 0 , 0 0 0 S E N D T E R M I N A T E S T H E P R O G R A M M E , T W O R E O U I R E D , W R I T T E N B Y P, R , H , M C C O N N E L L , J U L Y 2 3 , 1975 T t r r -r<r —ETTCRNAL AUX — DIMENSION X C 1 7 ) , Y ( 1 7 ) , Y F ( 1 7 ) , D E L T A Y C 1 7 ) . W T t l 7 ) , E l t 3 ) , E 2 t 3 ) , P ( 3 ) , M D 2 ( 3 ) — 0 AT A - N 7'M f w r r A T r r 7 7 T r l T 0 T 0 T 2 7 W T :  D O 10 1=1,17 R E A D ( 5 , 1 0 1 ) X ( I ) , Y ( I ) , D E L T A Y ( I ) —f-ORHArrSF*750 — — — Y ( I ) = ( Y ( I ) - 1 , 0 ) / A 2 «T(I)=1,0/0ELTAY(I)««2 — C B N T I N U E -2 2 , 0 0 0 2 3 , 0 0 0 2 5 , 0 0 0 2 6 , 0 0 0 102 R E A D ( 5 , 1 0 2 ) ( P ( I ) , 1 = 1,3) F0R*»T(3F10,5) RrAD-(STlTrt-rNTTEPS : :  103 F0RMAT(I3,.F5,3) »RITE(6,10tt)(P(I),I=l,3),NI,EPS . 2 b , a / 5 X , ' M E A N F I E L D = ' , F b , 2 , ' KILOGAOSS'/5X,'FI ELD WIDTHS',F6,2,1 K I 3L0GAUSS'//'NUMBER OF ITERATIONS ALLOWED (MAX) = ',13/IEPSILON=',F6,1 _ ; , , . . : . R E A D ( 5 , 1 0 5 , E N D = 1 U ) ( M D ( I ) , I = l , 3 ) F 0 R M A T ( 3 I 1 ) -CA'CC 0 P R t ^ F ' C X T T T r r p r f , E 1 ,E2,P;«Z,N,M,NI ,N0,EP3,AUX,MD? WRI T E ( 6 , 1 0 6 ) FORMAT( ' 0 ' , 8 X , ' P ( I ) ' , 1 6 X , ' E l ( I ) 1 , 1 5 X , ' E 2 ( I ) • ) -00-r2"-r=T73 : :  W R I T E ( 6 , 1 0 7 ) P ( I ) , E 1 ( I ) , E 2 ( I ) FORMATC ' , 3 ( 5 X , G 1 5 , 5 ) ) ~1F CND) 1 J n - J r i 1 — :  11 105 — 2 ? , 0 0 0 28,000 29,000 iO.OO-O-31,000 32,000 3 3,000 34,000 3 5,000 - 3 6,0 0 0 37,000. 38,000 3 9 , o-o-o-40,000 "t.ooo - 4 - 2 7 * 0 0 -4 3 , 0 0 0 4 4 , 0 0 0 -asrO 'Oir-106 12 107 16,000 17,000 -tt 87*00-49,000 50 ,000 -srrotur 52,000 53,000 ~S 17/0 00-M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G C U 1 S 3 6 ) MAIN. 08.08-75 15123159 P A G E P002 0 0 2 5 0 0 2 6 1 3 W R I T E C 6 . 1 0 8 ) 1 0 8 F O R M A T t 1 0 ' , ' * * W A R N I N G « * E O U A T I O N S I N THE PROGRAMME: D P R L Q P WERE 2 N 0 T S O L V E D S U C C E S S F U L L Y , ' / 1 4 X , ' P R O G R A M M E . W I L L - C O N T I N U E U S I N G THE N 3ETT-PA^wg^rar-iwri-A-'ri-ows M D , ' ) . : 1  0027 GO To 11 0 0 2 8 0 0 2 9 0 0 3 0 - 0 0 3 T -C -t C 1 0 9 0 0 3 2 0 0 3 3 - m r 0 0 3 5 0 0 3 6 - 0 0 3 7 -0 0 3 6 0 0 3 9 -o-o <rt-0 0 4 1 —PR1NT-^UT-THE—RES^t11^-OP-^E--L-ETm'3-m)7>-RE3 P I T . -W R I T E C 6 . 1 0 9 ) » —fTWnrT i 1 1 1 , ' THE HYPtfrFTNE—F -TELO PI3TRTBUTI0N RESULTS FOR B I - 2 0 6 / N I 2 U S I N G THE 1 7 1 9 KEV D A T A , I ) w R I T E < 6 , 1 1 0 ) — F O R M A T c ' — ' - r / r y - ' T E M P - M r L - u - i — K+rtKi^-t-xp1 <qx, ' H nT^yrr^*t*p-*rtrtrn-C H I S Q = 0 , 0 DO 1 5 1 = 1 , 1 7 —Y1 r - f r j -=TF-t-I - ) -«-A-2TtT0 : :  Y ( 1 ) = Y ( I ) « A 2 + 1 , 0 D I F F = Y ( I ) - Y F ( I ) —w R I-T E tDTi" i - i -> x-( I), Y c i t r r f m r H f r r -OtTtlt— 0 0 4 3 111 F O R M A T ( i 0 1 , 3 X , F 5 , 2 , 5 X , F 6 , 3 , 3 X , F 6 , J , U X , F 6 , 3 ) C H I S U = C H I S Q t D I F F * » 2 / D E L T A Y t I ) * * 2 " 1 5 C O N T I N U E A s P C H l I C H I 5 0 , 1 3 , 0 ) C « * * C H E C K FOR I N T E G E R OR F P 13 IN CHISQ, wRITE-(6Trl-2-)CHTSaT»-5 5 5 6 5 7 - 5 * 5 9 6 0 -frf 6 2 6 3 6 5 66 -tr7 68 6 9 - 7 0 -71 7 2 - 7 - 3 -7 4 7 5 , 0 0 0 , 0 0 0 , 0 0 0 TtrOD" , 0 0 0 . 0 0 0 TOiro-, 0 0 0 , 0 0 0 -o*o-, 0 0 0 , 0 0 0 7 0 0 0 -, 000 , 0 0 0 1 1 2 r O * 0 " , 0 0 0 , 0 0 0 7 00-0-, 0 0 0 . 0 0 0 -,-000-, 0 0 0 , 0 0 0 0 0 4 5 1 1 3 0 0 4 6 004 7 F O R M A T C ' 0 ' 1 ' S T A T I S T I C S ) ' / / ' D E G R E E S OF. F R E E D O M * 1 3 ' 7 " C H I " S G U A R E D »• ' 2 , F 6 , 2 / ' C H I - S Q U A R £ D P R 0 B A 8 I L I T Y s ' , E 1 3 , 4 ) — » R T T E ( - B T T » - ) - t - P r i ) , I - 1 , 3~) : — :  F O R M A T ( 1 0 ' , ' P A R A M E T E R V A L U E S j ' / / ' F R A C T I O N F = ' , F 7 . 5 / ' M E A N F I E L D = ' , F- 8 3 , 27,3,1 K I L O G A U S S ' / ' F I E L D WIDTH OF G A U S S I A N O.I S T R I BUT 10N= ' , F 7 , 3 , ' KI 8 4 , -SL-OGAyS3->-) — : 8 5 i S T O P ' 8 6 END 87 V00;0 -, 0 0 0 , 0 0 0 -fl-CD-000 000 , 0 0 0 , 0 0 0 -*-aprroNs I N irmr*—n>r&3i:i?ic,souRCE,NOtrr8Tr^ECK,LOAP,NOtrAi>-• D P T I O N S IN E F F E C T * NAME = M A I N , L I N E C N T = 57 • S T A T I S T I C S * S O U R C E S T A T E M E N T S = 4 7 , P R O S R A M S I Z E ; " TiT-AM-ST I C S * N O - D t A G N O S f l £ S ~ G E N E R - A - f e O ON 2454 NO E R R O R S I N M A I N 137 . __ p - i r . 1 r — i 1 1 1 r I 1 : x o o o 4 O O O ( O O O < ' o o o o o i O O O O O < O O O O < o o D o o o o o b o o o o o o o b o o p o o b o o o o o o o o o o o o o o o o o o o o o o p o o o o o 1 o o p o o b o o o o o o o - -p o o p o o o o o p o o o o o o p o o o o o o p o o o o o o p o o p o o i o o p O O t o o p o o i o o o o o o • &• o o 6 - o- o* t> ( X I < «* O w rt a * »— • - ' . J O X «1 « O u i rt ^ £K »*l z i - a. o •-« H U 3 Z CL « | TD x u_ #-• a: , r _»i JE u i . O O - I L > ~ < o o O -o i o o o in . O Q O I • • > O o O d •> • • II II > O O UJ X i II n UJ o > UJ O f t l 31 : z i x a . • O »- M I o o p a o i o O O 2 Jc -* o a. to CO p o o o o o o o o o O o o I > O O < > o o « eo c> p r u o o o o o p o o p o o { u u b u u u — i n a in o w t in o ° w t " " I K P IT 2 _ J O co co O U . M O O —• O « II II 11 >—« •—• o r toiw o IP io r~ oo O-o p o o o o a a a j o - i - * • O P o o f > o II t l II II O II X X X X X n co io cn ca I O co fu — —t ru ru f i r o I Q Q o a o i £ « i J i O * X * « * t > X I f - II « I t-« II (O T M L J CQ t rO > OD w : * Q_ * -h ^ : r o r u t — a. —* m rt a. v a. +• r u p i x CD II It » — r u r u r u p o o II X i- r u n 0^ K> CO O O H r u i-* r f\I f\J JO • Q O O t O X X X 3 • r> 3 r> ; X CO CO CO Cl U —• <\i • - r <o n j r u m •*-• O G O n i i l l II X X X E D D D ID CO CO CO CO --• r u — * - w r u m p o. o o O UJ K II D t -X 2 CO ZD — M If) •— o r u z x r O O t -O U S O — r u rO a -r u r u f u r u r u o o o o o o o p o o rgn *o r-- I ru ru ru p o o O O O I tfl & 1/1 JO OD r> o - « r u W r A r n 3 S a o o o o o o o o p o o o D M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G 1 1 1 3 3 6 ) AUX 0 8 » 0 B « 7 5 1 5 1 2 4 1 0 0 P A G E P 0 0 2 0 0 4 3 0044 . 0 0 4 5 > 004S-I 0 0 4 7 | OOuB j 0 0 f f » -I 0 0 5 0 i . 0051 —©•0-5-2--nr D 0 N E = D 0 N E + D 1 S U M * P H I D T W 0 = D T W 0 * ( O 2 1 S U M * D 2 2 S U M ) * R H I D T H R E E s O T H R E E * C D 3 1 S U M + D 3 2 S U M ) « P H I -CDN-MNUE-A U X = P ( 1 ) * B T W 0 * 0 E L T A H 0 ( 1 ) = D U N E « D E L T A H -0-{ -2-)-s Pt-m DT it a * D E:tT * H — 0 ( 3 ) = P ( l ) * D T H R E E * D E L T A H R E T U R N 143,000 14(4 ,000 145 ,000 -1-46x0-0-0-147,000 146,000 -6*0-• O P T I O N S IN E F F E C T * I D , E 8 C D I C , S O U R C E , N O L I S T , N O O E C K , L O A D , N O M A P • O P T I O N S IN E F F E C T * NAME = AUX , L I N E C N T = 57 - * S-TA-TI-STTC.S * S O U R C E—S T-A-TE M E N TS—= 5-2rPROg~RAM 3-TrZg—8 — -J-4-971WO -1 5 0 , 0 0 0 1 5 1 , 0 0 0 • S T A T I S T I C S * NO E R R O R S IN AUX NO D I A G N O S T I C S G E N E R A T E D -1-8-4-6-MICHIGAN TERMINAL SYSTEM FORTRAN GCH336) 8LK DATA 08-08»75 15121102 0001 0002 0003 B L O C K D A T A ''. C O M M Q N / B L / C R E A L . 8 C (13J/0,7928211,0,3961120,0, 0720719,-0,1801871,-0,3603711,--2 O T « SWfi 5 8 T « O T S O o 5-Jil ST-OTttt-S^BSBT^TS *niWT^t^^TVTttTtt<Wrxr— 33901120,0,7928211/ ' ' 0001 END toRT^OTS I?T~EF~P£'CT. rDTEljCDlCvSOURCST-NOtrtSTTN'ODECK, LOADrNWA-P-• O P T I O N S IN EFFECT. NAME = BLK D A T A , LINECNT a 57 ' •STATISTICS* NO DIAGNOSTICS GENERATED -CftR-im—r?r-8LK DATA- — _ _ 153,000 151,000 155,000 -tsa.uaa-157,000 158,000 NO STATEMENTS FLAGGED. IN THE ABOVE COMPILATIONS. hEXEC UT10 N T ER MI NAT EO" -P A G E P001 j I R O N H Y P F I T I E X E C U T I O N B E G I N S 140 BIBLIOGRAPHY Abragam, A. 1961. Principles of Nuclear Magnetism (Oxford University Press, London). Abragam, A. and Pryce, M.E. 1951. (Proc. Roy. Soc, London), A205, 105. Aeppli, H., Albers-Schonberg, H., Bishop, A.S., Fraunfelder, H. and Heer, E. 1951. Phys. Rev. 84, 370. Alburger, D.E. and Pryce, M.H.L. 1954. Phys. Rev. 95_, 1482. Alburger, D.E. and Sunyar, A.W. 1955. Phys. Rev. £9, 695. Allan, C.S. 1971. Can. J. Phys. 49, 157. Ambler, E., Grace, M.A., Halban, H., Kurti, N., Durand, H., Johnson, C and Lemmar, H.R. 1953. Phi l . Mag. 44, 216. Atlantic Equipment Engineers, 181 Reid Avenue, Bergenfield, New Jersey, U.S.A. 07621. Bacon, F., Haas, H., Kaindl, G. and Mahuke, E.H. 1972. Phys. Lett. 38A, 401. Balabanov, A.E. and Delyagin, N.N. 1968. Soviet Physics JETP 752. Bauminger, R., Cohen, S.G., Marinov, A. and Ofer, S. 1961. Phys. Rev. 122, 743. Beras, Harry. 1975. Physica Scripta 11, 167. Berglund, P.M., Collan, H.K., Ehnholm, G.J., Gylling, R.G. and Lounasmaa, O.V. 1972. Journal of Low Temperature Physics j5, 357. Biedenharn, L.C. and Rose, M.E. 1953. Rev. Mod. Phys. 25, 729. Bleane.y, B. 1951. Proc. Phys. Soc. A 64_, 315. Bowman, J.D. and Zawislak, F.C. 1969. Nucl. Phys. A138, 90. Brick, R.M., Gordan, R.B., Philips, A. 1965. Structure and Property of Alloys, Third Edition (McGraw-Hill Book Co., New York). Dabbs, J.W.T., Roberts, L.D. and Berstein, S. 1955. Phys. Rev. 98^ , 1512. Daniels, J.M,, Grace, M.A. and Robinson, F.N,H. 1951. Nature 168, 780. S i l y * P.W. • 1972. Ph,D„ Th°- ;c% University of B r i t i s h COWD'.^ V : . (--'.n^  iblished) „ 141 Daly, P.W. 1973, Ph.D. Thesis, University of Bri t i s h Columbia, Canada. Debye, P. 1926. Ann. Phys. 81, 1154. DeGroot, S.R., Tolhoek, H.A. and Huiskamp, W.J. • 1965. In <*,,£ , and y-ray Spectroscopy, Vol. 2, K. Seigbahn, editor (North Holland Publishing, Amsterdam), de Waard, H. 1975. Physica Scripta 11, 157. de Waard, H., Schurer, P., Inia, P., Niesen, L. and Agarwal, Y.K. 1971. Hyperfine Interactions in Excited Nuclei, edited by G. Goldring and R. Kallsh (Gordan and Breach Science Publishers, New York), Vol. 1, p. 89. Feldman, L., Augustyniak, W.M. and Kaufman, E.N. 1971. Hyperfine Interactions in Excited Nuclei (Gordon and Breach Science Publishers, New York). 1968 (North Holland Publishing Co. Ltd.) Vol.- 1, pg. 174. Ferentz, M. and'Rosenzweig, N. 1955. Tables of F Coefficients, Argonne National Laboratory Report #5324, Fraunenfelder, H. 1963. The Mossbauer Effect (W.A. Benjamin Inc., New York). Fraunfelder, H. and Steffen, R.M. 1965. <x,,J5 and 7-^ray Spectroscopy Vol. 2, K. Seighbahn, editor (North Holland Publishing Co., Amsterdam). Froese, E., O'Reilly, D. and Fowler, A. Febv 1974. 'UBC Curve' Subject Code 44.2. Computing Centre, University of British Columbia, Vancouver, B.C., Canada. Giauque, W.F. and MacDougal, D.P. 1933. Phys. Rev. 43_, 768. Gorter, C.J., Poppema, O.S., Steenland, M.J. and Beun, J.A. 1951. Physica 17, 1050. Halban, H. 1937. Nature, Lond. 140, 425, Hansen, M. 1958. Constitution of Binary Alloys (McGraw-Hill Book Co.,, New York). Hume-Rothey, William. 1936. The Structure of Metals and Alloys (Institute of Metals, London). Hume-Rothey, W, and Raynor, G.V. 1954. Structure of Metals and Alloys (Institute of Metals, London). Jeffries, CD. 1963. Dynamic Nuclear Orientation (Interscience Publishers, John Wiler and Sons, New York). Johnson, C.E.,Schooley, J.F. and Shirley, D.A. I960. Phys. Rev: 120, 1777. 142 Johnson, Matthey Co. Ltd., 73/83 Hatton Garden, London, EC 1, England, Johnston,,P.D., Kaplan,;M., K i t t e l , P. and Stone, N.J. 1974. International Conference on Hyperfine Interaction Studied in Nuclear Reactions and Decay, E.,Karlsson and R. Wappling, editors (Upplands Gratiska AB, Uppsala), p. 78. Kanbe, M. Fujioka, M. and Hisatake, K. . 1972. Nuclear Physics A192, 151. Kaplan, M. , Johnston, P..D. , K i t t e l , P. and Stone, N.J. 1973. Nucl. Phys. A212, 478. Kaplan, M., Johnston, P.D., K i t t e l , P. and Stone, N.J. 1973. Private Communication. Karlsson, E., Matthias, E. and Seigbahn, K. 1964. Perturbed Angular Correlations (North Holland Publishing Co,,.Amsterdam). Kearsley, M.J. 1957, Nuclear Physics 4_, 157, Kieser, Robert. 1974. Nuclear Orientation Studies of Spin Lattice Relaxation and Hyperfine Fields in Ferromagnetic Dilute Alloys, Ph.D. Thesis. University of British Columbia, Vancouver, B.C., Canada. (unpublished), Kistner, O.C. 1966. Phys. Rev. 144, 1022. Kistner, O.C. and Sunyar, A.W. 1960. Phys. Rev. Lett 4_, 412. Lindgren, I. and Johansson, CM. 1959. Arbiv For Fysik 15, 445. Manthurithil, J.C, Camp, D.C, Ramayya, A.V., Hamilton, J.H., Pinajian, J.J. and Doornebos, J.W. 1972. Phys. Rev. C6, 1870. Mantl, S. and Triftshauser, W. 1975. P.R.L. 34, 1554. Marshal, W. 1958. Phys. Rev. 10, 1280. Matthias, E. and Holliday, R.J. 1966. Phys. Rev. Lett. 17, 897. Mossbauer, R.L, 1965. In 'Alpha, Beta, and Gamma-Ray Spectroscopy' K. Selghbahn, editor (North Holland Publishing Co., Amsterdam). Mossbauer, R.L. 1958. 2 Physik 151, 124. Pound, R.V. 1949. Phys. Rev. 7_6,, 1410. Rose, M.E. 1965. In Alpha, Beta, and Gamma-Ray Spectroscopy, K, Seighahn, editor (North Holland Publishing Co., Amsterdam), Vol. 2. Rose, M.E. 1960, In Nuclear Spectroscopy, Part B, •-Ajzenberg-Selove, editors (Academic Press, New York). 143 Rose, M.E. 1953. Phys. Rev. 91, 610. Rose, M.E. 1949. Phys. Rev. 75, 211, Samoilov, B.N., Sklyaereuskii, V.V. and Stepanov, E.P. 1960. Soviet Physics JETP 11, 261. Schumacher, R.L. 1970. Introduction to Magnetic Resonance (W.A. Benjamin Inc., New York). Shirley, D.A. 1968. In Hyperfind Structure arid Nuclear Radiations, E. Matthias and D.A. Shirley, editors (North Holland Publishing Co., Amsterdam). Shirley, D.A. and Westenbarger, G.A. 1965. Phys. Rev. 138A, 170. Spedding, F.H. and Gschneidner, K. 1971. In Handbook of Chemistry and Physics, 52nd Edition, R.C. Weast, editor (The Chemical Rubber Co., Cleveland, Ohio), F171. Steffen, R.M. 1955. Adv. Phys. ,4, 293. Stolovy, A. 1960. Phys. Rev. 118, 211. Stone, N.J. 1971. In Hyperfine Interactions in Excited Nuclei (G don and Breach Science Publishers, New York), Vol. 1, p. 237. Stone, N.J. and Turrell, B.G. 1962. Physics Letters JL, 39. Strohm, W.W. and Sapp, R.C. 1963. Phys. Rev. 132, 207. True, W.W. 1958. Phys. Rev, 100, 1342. True, W.W. and Ford, K.W. 1958. Phys. Rev. 109, 1675. U.B.C. Metallurgy Dept., University of British Columbia, Vancouver, B.C. Canada. Vary, J. and Ginocchio, J.N. 1971. Nucl. Phys. A166, 479. Wheatley, J.C. 1970. Progress in Low Temperature Physics, Volume 6, C.J. Gorter, editor (North Holland Publishing Co., Amsterdam), Wheatley, J.C., Vilches, O.E. and Abel, W.R. 1968. Physics 4_, 1. White, G.K. 1968. Experimental Techniques in Low Temperature Physics (Oxford University Press, London), Yamazaki, T. 1960. Nuclear Data; A3, 1 (1967). Yates, M.J.L. 1964. In Perturbed Angular Correlations, E. Karlsson, E. Matthias, and K. Seigbahn, editors - (North Holland Pub. Co., Amsterdam), p. 453. 144 Zawislak, F.C. and Cook, D.D. 1969. Bull. Am. Phys..Soc. 14, 1171, Zemanski, H.W. 1968. -'Heat and Thermodynamics' (McGraw-Hill Book Company, New York). 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0093256/manifest

Comment

Related Items