Nuclear Hyperfine Interactions in W¹⁸², W¹⁸³, and Pt¹⁹⁵ as Studied by the Mössbauer Effect Citation Agresti, David George (1967) Nuclear Hyperfine Interactions in W¹⁸², W¹⁸³, and Pt¹⁹⁵ as Studied by the Mössbauer Effect. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XS89-6T82. https://resolver.caltech.edu/CaltechTHESIS:11022015-104645134 Abstract The Mössbauer technique has been used to study the nuclear hyperfine interactions and lifetimes in W 182 (2 + state) and W 183 (3/2 - and 5/2 - states) with the following results: g(5/2 - )/g(2 + ) = 1.40 ± 0.04; g(3/2 - = -0.07 ± 0.07; Q(5/2 - )/Q(2 + ) = 0.94 ± 0.04; T 1/2 (3/2 - ) = 0.184 ± 0.005 nsec; T 1/2 (5/2 - ) >̰ 0.7 nsec. These quantities are discussed in terms of a rotation-particle interaction in W 183 due to Coriolis coupling. From the measured quantities and additional information on γ-ray transition intensities magnetic single-particle matrix elements are derived. It is inferred from these that the two effective g-factors, resulting from the Nilsson-model calculation of the single-particle matrix elements for the spin operators ŝ z and ŝ + , are not equal, consistent with a proposal of Bochnacki and Ogaza. The internal magnetic fields at the tungsten nucleus were determined for substitutional solid solutions of tungsten in iron, cobalt, and nickel. With g(2 + ) = 0.24 the results are: |H eff (W-Fe)| = 715 ± 10 kG; |H eff (W-Co)| = 360 ± 10 kG; |H eff (W-Ni)| = 90 ± 25 kG. The electric field gradients at the tungsten nucleus were determined for WS 2 and WO 3 . With Q(2 + ) = -1.81b the results are: for WS 2 , eq = -(1.86 ± 0.05) 10 18 V/cm 2 ; for WO 3 , eq = (1.54 ± 0.04) 10 18 V/cm 2 and ƞ = 0.63 ± 0.02. The 5/2 - state of Pt 195 has also been studied with the Mössbauer technique, and the g-factor of this state has been determined to be -0.41 ± 0.03. The following magnetic fields at the Pt nucleus were found: in an Fe lattice, 1.19 ± 0.04 MG; in a Co lattice, 0.86 ± 0.03 MG; and in a Ni lattice, 0.36 ± 0.04 MG. Isomeric shifts have been detected in a number of compounds and alloys and have been interpreted to imply that the mean square radius of the Pt 195 nucleus in the first-excited state is smaller than in the ground state. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Boehm, Felix H. Thesis Committee: Boehm, Felix H. (chair) Chan, Sunney I. Davis, Leverett Mossbauer, Rudolf L. Defense Date: 26 May 1967 Funders: Funding Agency Grant Number Caltech UNSPECIFIED U.S. Atomic Energy Commission UNSPECIFIED Woodrow Wilson Foundation UNSPECIFIED Record Number: CaltechTHESIS:11022015-104645134 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11022015-104645134 DOI: 10.7907/XS89-6T82 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9265 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 03 Nov 2015 15:42 Last Modified: 11 Mar 2024 20:35 Thesis Files Preview PDF - Final Version See Usage Policy. 20MB Repository Staff Only: item control page

182 . NUCLEAR HYPERFINE INTERACTIONS IN w ' ' 183 AND Pt19 5 ' w ' AS STUDIED BY THE MOSSBAUER EFFECT Thesis by David G. Agresti , In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1967 (Submitted May 26, 1967) \ -.. _J ii ACKNOWLEDGMENTS Many people have contributed to the progress of this work. In particular, the author would like to thank: Dr. Egbert Kankeleit, who originally conceived and designed the experiments and provided needed guidance throughout all phases of the research. Dr. BtJrje Persson, whose close collaboration made the completion of these studies possible. Dr. Felix Boehm for his interest and support of these studies. Dr. Rudolf Mtlssbauer for many helpful discussions on the solid- state aspects of the problem. Dr. Edwin Seltzer for many illuminating discussions on nuclear theory and calculations of relevant nuclear parameters. Mr. H. E. Henrikson for his help with the design of the experiment. Dr. P. Duwez for his advice on metallurgical problems. Dr. R. Willens for suggestions related to the levitationmelting technique. Mr. Vagn Stephenson and Mr. Ellsworth ''Woody" Kiersey for their help in making parts of the apparatus. Mr. Granville "Glenn" Swanson for help with electronics. Finally, Miss Jerre Levy Basch, with whom the author has had many pleasant discussions on the final wording of this thesis. The author gratefully acknowledges financial aid from the California Institute of Technology, the U. S. Atomic Energy Commission, and the Woodrow Wilson Foundation. iii ABSTRACT The MtJssbauer technique has been used to study the nuclear hyperfine interactions and .lifetimes in w 182 (2+ state) and w 183 (3/2- and 5/2- states) with the following results: g(5/2-)/g(2+) = 1.40 ± 0.04; g(3/2-) = -0.07 ± 0.07; Q(5/2-)/Q(2+) = 0.94 + 0.04; T (3/2-) = 0.184± 0.005 nsec; T (5/2-) ;:_ 0.7 nsec. 112 112 These quantities are discussed in terms of a rotation-particle inter- · . · w 183 d ue t o C orio . l"is coupl"mg. F rom the measure d act 10n m quantities and additional information on y- ray transition intensities magnetic single-particle matrix elements are derived. It is inferred from these that the two effective g-factors, resulting from the Nilsson-model calculation of the single-particle matrix elements for the spin operators sz and 'S'+' are not equal, consistent with a proposal of Bochnacki and Ogaza. The internal magnetic fields at the tungsten nudeus were determined for substitutional solid solutions of tungsten in iron, cobalt, and nickel. With g(2+) = 0.24 the results are: IHeff(W-Fe)I= 715 ± 10 kG; lHeff(W-Co)j = 360 ± 10 kG; IHefiW-Ni)l = 90 ± 25 kG. The electric field gradients at the tungsten nucleus were determined for ws and WO~~· With Q(2+) = -1.81 b the results are:for 2 Ur. 2 18 2 WS , eq = -(1.86 + 0.05) 10 V/cm ; for W0 , eq = (1.54 ± 0.04)10 V/cm 2 3 and ri = 0.63 ± 0.02. 195 The 5/2- state of Ft has also been studied with the MtJssbauer technique, and the g-factor of this state has been de-· termined to be -0.41 ± 0.03. The following magnetic fields at the pt nucleus were found: in an Fe lattice, 1.19 ± 0.04 MG; in a Co lattice, 0.86 ± 0.03 MG; and in a Ni lattice, 0.36 ± 0.04 MG. Isomeric shifts iv have been detected in a number of compounds and alloys and have 195 been interpreted to imply that the mean square radius of the Ft nucleus in the first- excited state is smaller than in the ground state. v To Jerre vi From Jerre: David does physics from morning till night-From 8 in the evening till dawn's early light. Energy spectra confuse and perplex-No time for love and no time for sex. Tungsten 182 and 183 Interest him more than music or me. Magnetic dipoles, hyperfine interaction Act upon Dave like magnetic attraction. Typical people make love in the spring. Typical robins and sparrows will sing. Typical daisies and roses will bloom, But if you know David, you shouldn't assume That he is aware that it's spring and it's May. His thesis is due and he works night and day. However, I'm sure when he's post-PhD, He'll remember there's May and remember there's me. vii TABLE OF CONTENTS PART I. II. m. TITLE PAGE INTRODUCTION 1 1) Origin of the Spectra 2 2) Interpretation of ~he Spectra 6 a) Line broadening 6 b) Centroid shift 7 c) Magnetic hyperfine interaction 7 d) Electric quadrupole interaction 9 EXPERTh1ENT 16 1) Sources and Detectors 18 2) Absorbers 21 3) Drive and Data Storage 24 4) Special Equipment 24 RESULTS 33 36 1) Magnetic Hyperfine Interaction a) (2+ - o+) 100-keV transition in w 182 b) (5/2- - 1/2-) 99-keV transition in w 37 183 c) (3/2- - 1/ 2-) 99-keV transition in Pt195 38 39 2) Isomeric Shift a) w182 and w183 195 b) pt , 99-keV 40 3) Electric Quadrupole Interaction 182 a) (2+ - o+) 100-keV transition in w 41 42 b) (5/2- - 1/2-) 99-keV transition in w 195 . c) Ft , 99-keV 40 41 183 43 43 viii PART PAGE TITLE 4) Line Widths 182 a) w , 100-keV 183 b) w , 99-keV 195 c) Pl , 99-keV 5) Special Case: 47-keV Transition in w N. 44 44 44 45 183 45 DISCUSSION 77 1) Magnetic Fields 78 2) Nuclear Parameters for the 5/2- and 3/2183 States in w 195 3) Magnetic Moment of the 3/2- State in pt 81 REFERENCES 85 95 ix LIST OF FIGURES FIGURE PAGE I. 1 182 183 Level Schemes for w , w , and Pt195 12 I. 2 Dipole and Quadrupole Radiation Patterns 14 II. 1 Scintillation Spectra of Ta II. 2 Source Holder 29 II. 3 Cryostat and Drive System 31 m.1 Velocity Spectra for Ta m.2 m.3 m.4 m.5 Spectra for Ta III. 6 Isomeric Shifts in pt m.7 Spectra for Ta ID.8 Spectra for Ta m.9 Spectra for Ta m.10 Width-thickness Plot for 47-keV Transition of w IV.1 Internal Fields versus Host Magnetic Moment 87 IV. 2 Comparison of Electric Quadrupole Parameters . for w 183 89 182 183 Spectra for Ta 195 Spectra for Au Spectra for Au 195 182 182 183 182 182 , Ta183 , .and Au195 vs. W-Fe 27 47 vs. W-Co W-Ni and W 49 vs. W-Fe 51 vs. Ft-Fe 53 vs. Pt-Co, Pt-Ni, and pt 55 ' ' 57 vs. WS and WO 2 3 vs. Commercial WS 59 61 2 vs. WS and W0 2 3 63 183 65 x LIST OF TABLES TABLE PAGE m.1 Parameters for Magnetic Hyperfine Interaction 67 m.2 Results for Magnetic Hyperfine Interaction in W 69 m.3 Results for Magnetic Hyperfine Interaction in Pt 71 ill.4 Parameters for Electric Quadrupole Interaction 73 m.5 Results for Electric Quadrupole Interaction in W 75 IV.1 183 Magnetic Parameters for w 91 IV. 2 169 . 183 171 Effective g-factors for W , Yb , and Tm 93 j 1 L INTRODUCTION 2 L INTRODUCTION This thesis describes experiments performed over the past year and a half in which fundamental use has been made of a discovery made in 1957 by R. L. Mtlssbauer. l) Jn essence Mtlssbauer' s discovery demonstrated for the first time that certain y-rays emitted from radioactive nuclei in solid matter have an energy resolution very nearly equal to that corresponding by the uncertainty principle to the lifetime of the nuclear state from which the y-rays were emitted. This discovery meant an enormous improvement in the sharpness of such y-rays, and several new avenues of research were opened up. 2 The experiments described in this thesis ) utilized these very narrow y-rays in order to investigate nuclear hyperfine interactions in a number of materials. Structure in the energy spectrum of these Y- rays, slight broadening, and small energy shifts, all previously obscured because of the poor resolution, could now be readily observed, and valuable information was gained about the nucleus and its interaction with its environment. 1) Origin of the Spectra Previous to Mtlssbauer's work, the emission of y-rays from nuclei was considered to be a process that could be understood without reference to the properties of the solid in which the nucleus was imbedded. That is, the energy spectrum of the y-rays was supposed to depend only on the temperature of the material from which they were emitted but not on the fact that the emitting nuclei were bound together in a lattice. A free nucleus recoils after emission of a y-ray and the energy of the y-ray is reduced by an 3 amount, E 2 0 2 /2Mc , where E 0 is the energy of the y-ray and M is the mass of the recoiling nucleus. The energy spectrum emitted · from a collection ot nuclei at temperature, T, is centered on this value, and has a Gaussian shape with width, 20' = 2E JkT/Mc2 • 0 If the nuclei are in a solid, the above conclusion holds only if the recoiling nucleus has sufficient energy to be dislodged from its lattice site. If not, lattice vibrations will be induced, and the shape of the emission spectrum will depend on the shape of the phonon spectrum of the host solid. If the free-atom recoil energy is less than the mean phonon energy, the possibility arises that a certain significant fraction, the recoil-free fraction f, of y-ray emissions will not excite any phonon at all and will thus carry the full energy difference between the two nuclear levels involved in the transition. If both of these levels are degenerate, and the width of the energy spectrum is due to the finite lifetime, 'I", of the upper state, then the emission spectrum will be given by the Breit-Wigner formula (Lorentzian line shape), p(e) o: 1 [ 1 + -4 r2 ' 0 (I. 1) o r = 1r / -r = o.693" /T 112 , where and E (e - E ) 2 ] (I. 2) is the transition energy. If one or both of the levels is shifted or is split into a number of sublevels by interaction of the nucleus with its surroundings, the emission spectrum will take the form of a sum over Lorentzian line shapes, with the relative contribution of each Lorentzian depending on the relative emission probabilities for the different energies of the y-rays connecting the sublevels. Namely, 4 p'(e) cx: .l [l + _!__h(j)(e - E(j) ) 2 ] j r(j) (I. 3) • 2 The parameters, E, h, and r, appearing in Formula I. 3 contain valuable information about the nucleus and its environment, and the great value and interest in the Mtlssbauer effect arises because these quantities can be obtained from experiment. The energy spectrum for absorption of y-rays by nuclei in a solid without energy transfer to the lattice has exactly the same form as the emission spectrum, Equation L 1 or L 3, as appropriate. The thing that makes the Mtlssbauer effect so beautiful and so useful is that the emission (or absorption) spectrum may be modulated in energy by the experimenter as he desires. He does this by moving the source of y-rays in a controlled and predetermined fashion; for example, if the source is moved in the direction of emission of y-rays with velocity, v, then the emission spectrum is shifted toward higher energies by an amount, vEJc. He then records the number of y-rays that pass thru the absorber for various velocities of the source both toward (v > 0) and receding from (v < 0) the absorber. The counting rate will fall when there is large absorption (v ~ 0) and rise when there is no absorption (v >> er /E 0 ). In particular, if the absorption spectrum, Pa (e), is given by Equation L 3 and the emission spectrum, ps(e), by Equation I. 1, then the experimental, or transmission, spectrum will be P(v) = Jde • ps (e + vE ~ c ) p'a (e) (E (j) - E ) ] 2 • a o (I. 4) 5 By analyzing his data in an appropriate manner, the experimenter will be able to obtain all the r a (j) and the Ea (j) to within an additive constant and all the h(j). Of course, the resolution will be too bad to obtain these quantities with any precision unless r +r < s a"' E (i) E (j)I for all i and j. However, the resolution can be much J a a worse than this and one can still obtain accurate values for the peak positions provided a way can be found to relate the various E (j), a such as assuming magnetic dipole or electric quadrupole hyperfine interaction. There are two important restrictions on the transition that may be studied by this method, and these limit the number to extremely few cases, considering the total number of nuclear transitions. First, since an absorber is involved, the lower level must be reasonably long lived. In practice this means the ground state of a stable nuclide. Also, the absolute maximum change in counting rate is the recoil-free fraction of the source f s' so that f must be at least a percent or two for an effect to be observable. Tllis limits the transitions to energies of around 150 keV or less. The cross section, cr , for absorption by the resonant isotope of 0 y-rays having the proper energy is 21 . + 1 1 ex 1 E 2 2Igd + 1 1 + a. 1 1+ ~ • (I. 5) 0 In this formula, I ex and I gd are the excited- and ground-state spins, resp. , a. is the total electron conversion coefficient, and ~ includes all other processes available for de-excitation of the excited level, such as cascade via an intermediate level. For the absorber the mass absorption coefficient for zero-phonon processes is 6 1 tm N = f a cro A0 a. (I. 6) Here, A is the molecular weight of each molecule of the absorber, a is the fraction, by weight, of resonant isotopes, and N 0 is Avogadro's number. 2) Interpretation of the Spectra For the experiments reported on in this thesis we have chosen 5 transitions in 3 nuclei; the nuclear level schemes are shown in Figure I. 1. In order to obtain information about the nucleus and its environment, we have studied the shape of transmission spectra taken with various sources and absorbers. · Four mechanisms that affect the shape of the observed velocity spectra have been important for the present work. These are: a) Line broadening. Each component line of the spectrum is expected to have a minimum width of 2rc/E • This 0 is never realized in practice. First of all, the generally nonnegligible thickness, t, of the absorber results in a broadening according to Visscher's formula by an amount .6v = 0.135 2 rc t Eo tm • (I. 7) However, for t .:S 5tm , the distortion from Lorentzian line shape is not significant. Unresolved hyperfine splitting is also generally present and contributes to line broadening but the shape is frequently unaffected for practical purposes. Instabilities in the drive or th e mechanical mounting of the source and the absorber 7 can sometimes also cause line broadening . A special effect, which we have had to consider in the experiment on 183 the 47-keV level in w , is a broadening that occurs when the absorber is a powder and the size of the grains is _::: ~ tm. More will be said about this in Section m. 5. b) Centroid shift. This may be caused in several ways, such as by second-order Doppler shift or by gravitational effects. Only the isomeric, or chemical, shift is important for us here. From the formula, we see that for an isomeric shift to result, two conditions must be met: 1) the mean- square nuclear radii R in the excited and ground states must be different; and 2) the electronic charge density \*(0) j 2 at the site of the nucleus must be different in the source and the absorber. With this type of interaction, every component line . of the spectrum is shifted by exactly the same amount as given by Equation I. 8 •. c) Magnetic hyperfine interaction. This is the interaction between the nuclear magnetic moment, µ, and the effective -> magnetic field, H, at the nucleus, which may arise from the electrons in the solid or be externally applied by the experimenter. It has the Hamiltonian, -+ -+ -+ -+ J-l. M = - µ • H = - gµ n I • H , (I. 9) 8 and the eigenvalues, (I. 10) where g is the nuclear g-factor, µn the nuclear magneton, and m = I, I - 1, ••• , -I, is the magnetic quantum number. The interaction results in a splitting of the nuclear levels if I f 0 and resolved lines in the observed velocity spectrum if 2r .:S gµ H. n Resolved lines result because the energy difference between the excited state and the ground state is no longer unique, but has the discrete set of values, E mm I = E o - g' µ Hm.I + gµ n Hm. ' n (I. 11) where the primes refer to the excited state and m and m' run over all possible values. Each of the (21 + 1) x (21' + 1) ·lines in the magnetic hyperfine spectrum has a corresponding relative intensity that may be determined from the theory of ~adiative transitions. If the two states with spins I and I' are connected by radiation of multipolarity, L, then a photon has the probability, . I I' L 2 L · p mm'(e) 0: { m -m' ~m} z~ ,(e), of being emitted or absorbed at any angle, e, relative to the _, quantization axis (direction of H) in the transition between the substates, (I, m) and (I', m'). In the formula, { } is Wigner's 3j symbol, and Z has the ·following dependence on e: (I. 12) 9 z~ (a) = 1 - cos2 e (I. 13a) (I. 13b) z 02 (a) = 2cos 2 a 7 2cos4 a 2 1 2 4 (I. 13c) 4 z±l (a) = 3 - cos e + 3 cos a (I. 13d) z±22 (8) = -31 - -31 cos4 8 (I. 13e) These are the radiation patterns appropriate for dipole and quadrupole radiation, and have been drawn in Figure I. 2 for convenience. By using a ferromagnetic source or absorber and an external field of suffucient strength to polarize them, the experimenter can control the direction of the photon relative to the quantization axis. For example, application of a strong longitudinal 0 field fixes 8 = o , while a field applied transverse to the photon direction requires that 8 = 90°. Single crystal sources or absorbers also restrict the value of 8. If an unpolarized powder or polycrystalline source . or absorber is used in which the grains are randomly oriented, then all values of e are possible, and Formula (I. 12) reduces to I I' L ·2 p mm' oc: { m -m' t.m} • (I. 14) d) Electric quadrupole interaction. This is the interaction between the nuclear electric qUa.drupole moment, Q .. , and ... lJ the gradient of the electric field, V E = - 'V V V, at the site of the 10 nucleus, which is due to a nonspherical distribution of electric charge surrounding the nucleus. It has the Hamiltonian, J-l = - i I Qij (V iEj)nuc· (I. 15) ij The electric field gradient is a second rank tensor, but can always be brought to diagonal form by choosing the proper set of three mutually perpendicular axes, fixed relative to the crystalline axes, to correspond to the ij of (I. 15); furthermore, because of Laplace's equation, r: V .. = 0, only two of the V.. are independent. It is i ll ll customary to define eq = V and zz , the magnitude of the electric field gradient, v -v Tl = xxvzz YY , the asymmetry parameter, where the axes have been chosen so that IV I > IV I > IV I zz yy xx ' in which case, 0 < ri .:;;; 1. With these definitions and the conventional definition of the nuclear electric quadrupole moment eQ, the Hamiltonian takes the form, (I. 16) A where A A I ± = I x -+ il y • 11 If f1 = 0 the eigenvalues and eigenstates are obtained by inspection from Equation I. 16. Each substate (except the one with m = 0) is doubly degenerate and is specified by + m. However, when ri 'f O, Ji.Q does not commute with :J.i.M' the magnetic quantum . numbers are no longer valid quantum numbers for the substates, and one must solve the secular equation for J-l.Q separately for each different value of I. Jn the present experiments, only the 182 2+ level of w ~d the 5/2-level of w 183 showed measurable electric quadrupole interaction. The solutions for the secular equations for these two values of spin are presented in Table m. 4. The relative intensities of the transitions that result in these two cases are also presente_d in the .table. 12 Figure I. 1 Partial nuclear level schemes for w 195 182 , w 183 , and • Vertical arrows indicate the Mtlssbauer transitions. 183 For w the symbols K = 1/2 and K = 3/2 refer to the two Ft lowest bands. 13 Au19s 3- 2 - - - - - - 210 5- z 192d 130 3- z --i:----.-- 99 Tal82 ~- ~15d 4+----~ 329 z+ 100 ! o+ 0 wiaz Ta1s3 5.0d ~-~ 412 7 2 309 9- 5- 2 2 2 2 2 9 r 6 L2 207 5- 99 47 0 z 3zi 2 K = .!. 2 t * .w1sa 2 K =~ !, ---.----- ---/ ' I Figure I. 1 : 14 Figure I. 2 L Dipole and quadrupole radiation patterns Z m ( 9). 6 15 Am= O Am=O \ Am=± l I \ Am = :I: 1 f \ Am= :1: 2 t --00-1 ' r i L =l \ 0• L=2 Figure L 2 ' 16 ll. EXPERIMENT 17 II. EXPERIMENT This chapter will describe the equipment and the materials used in the performance of the Mtlssbauer experiment. There are certain general aspects that practically all Mtlssbauer experiments have in common. These are: 1) A source of y-radiation, generally produced by bom- bardment of stable nuclei with energetic particles, such as neutrons, protons, electrons, etc. The source may be used in the reactor during or just after production, or at a later date. 2) A detector, sensitive to the y-rays of interest and equipped with a discriminator for selecting pulses due to those y-rays. 3) An absorber or a scatterer, placed in the path of the y-rays. When Mtlssbauer absorption takes place, the counting rate decreases in the detector discriminator if an absorber is used since the absorbed photons are removed from the beam and increases with a scatte rer, because the detector is excited by photons emitted from the absorbing nuclei in the scatterer. 4) A drive, which moves the source or the absorber in a controlled and predictable fashion. 5) Recording equipment, which keeps a record of the number of pulses ( y-rays) appearing in the detector discriminator when the source or absorber is moving at a certain velocity. This r ec or d is the velocity spectrum (Figures m.1-5, 7-9) and is analyzed numerically to obtain the information sought from the e xperiment. 18 All of these features are present in the experiments described in this thesis. However, in our experiments, only absorbers have been used, and the drive motion has been imparted to the source. Other equipment used in our experiments include a specially constructed cryostat for cooling the source and the absorber and magnets for polarizing the absorbers. 1) Sources and Detectors As mentioned in the introduction (cf. Figure I. 1), we are concerned here with five transitions in the three nuclei 182 183 195 . . W , W , and pt • Extensive experiments were performed in only four of these, however, since the velocity spectrum for the 195 fifth, the 130-keV of Ft , could barely be distinguished from the background after 40 hours of counting. 182 183 Sources for the w and w measurements were 14 made by irradiating tantalum metal in a neutron flux of 3.3 • 10 2 n/ cm sec at the :Materials Testing Reactor in Arco, Idaho. Since 182 183 , and since irradiation of natural Ta produces both Ta and Ta 182 the 100-keV line from the decay of Ta and the 99-keV line from 183 the Ta decay cannot be separated by scintillation spectrometers (cf. Figure II. 1), precautions had to be taken to avoid a simultane182 183 ous measurement of recoiless absorption in w and w • For the w 182 experiments a 10-mil wire of Ta was used as source 182 since this was available from previous experiments on Ta with 183 the bent-crystal monochrometer at Caltech and since the Ta (5.0 days) had had sufficient time to decay completely. The absorbers were made with unenriched tungsten. 19 183 For the w experiments the sources were 4-mil Ta foils especially irradiated for the present experiments. After arrival from the reactor they were checked with a lithium-drifted germanium detector to determine the relative intensities of the 99 and 100-keV 182 y radiation (from Ta183 and Ta , resp.). Since some of the 183 higher energy peaks of Ta were easily resolvable from those 182 , and since the intensity ratios of these peaks to the 99 and of Ta 100-keV peaks, resp., have been previously determined, 3) the relative intensities of the 99 and the 100-keV peaks could be calculated. It was found that only about 0.015 y-ray of 100-keV energy 182 183 ) was emitted for every 99-keV y-ray (Ta (Ta ) at the time the source was removed from the reactor. However, the absorption coefficient (cf. Equation L 6) for resonant absorption by unenriched tungsten absorbers is 7.3 times 3a) as great for the 100-keV y-ray as for the 99-keV y-ray, and enrichment of the absorbers in w183 182 was necessa:ry to reduce the w contribution to the velocity spectra to a negligible amount. Because of the short lifetime of 183 Ta the time during which the source could be used was limited to about two weeks after removal from the reactor, since at the end 182 of this time the w contribution had grown to nearly 2% of the effect. 195 The source for the Pt experiments was commercially 195 prepared and was 2 mCi of Au activity diffused into a 1-mil pt foil. A sodium iodide scintillation detector (1-1/2" x 1") and a double-delay-line amplifier were used to detect the y-rays at a high counting rate. Since the detector was mounted close to the source and a superconducting solenoid (see Section II. 4) was used for longitudinal polarization of the absorbers, it was necessary to 20 compensate for the strong stray field ( F:;1 O. 5 kG) produced by the solenoid in order to avoid the use of a light guide which would have decreased the resolution of the scintillation detector. This was accomplished simply by surrounding the photomultiplier with a µmetal mantle and a compensating coil. Adequate compensation could be provided, and almost the same resolution was obtained as in the absence of the stray field. The window of the single- channel analyzer, set for the relevant photopeak, contained about 50% background from other lines for the 100-keV transition in w182 183 and about 80%, 85%, and 35% for the 99-keV (W ), 46.5-keV 195 183 (w ), and 99~keV (Ft ) transitions, respectively (see Figure II. 1). The 47-keV line was enhanced by the use of a critical 2 absorber of 180 mg/cm Tb 07" The precise position of the 474 ke V photopeak was determined by recording the difference between pulse-height spectra obtained with and without recoiless absorption, i. e. , with the source stationary and with the source oscillating with high velocity. All source material was mounted in a holder like the one shown in Figure II. 2. The tubular end of the holder fits firmly onto a rod that extends from the drive (as in Figure II. 3). Working with solid or powdered source material is made much easier with this design, since the material can be placed into the cap and the_ body screwed down tightly. When sufficient precautions are taken, the outside of the holder does not become contaminated and the material is completely and rigidly held in place. 21 2) Absorbers For the W 182 and W 183 . experrments the absorber material used included w metal, the compounds wo3, ws2, and alloys of W with Fe, Co, and Ni. As pointed out in the previous section it proved necessary to use enriched materials for all the experiments performed with the 99-keV radiation of w 183• The enriched tungsten was obtained as w and thus all the absorbers for the w 183 183 9 3 ,(82.5%w1 83 , 6.4% w 182), experiments had to be produced with the oxide as starting material. Since the nuclear moments of the 99-keV state were obtained as ratios to the 182 moments of the 100-keV state, the absorbers for the w experiments had to be made in the same way, but with unenr:iched WO as starting material. 3 Absorbers of tungsten metal powder used tungsten produced by the reduction of wo3 in a hydrogen atmosphere at 850°c. Tungsten sulfide, ws 2, was made by fusing a stoichiometric mixture of tungsten (produced as above) and sulphur in a pure nitrogen atmosphere in a sealed quartz tube at 900°C. 182 Experiments on w were also done with commercially obtained Wand ws • The velocity spectra obtained for the two types of 2 tungsten showed no significant difference, but the spectra for the tWo types of ws2 were in total disagreement, in spite .of the fact that their x- ray diffraction patterns were identical. (Compare Figures ID. 7 and 8 and see Section ill. 3a for further discussion. ) 182 183 The alloy absorbers for both w and w contained 1.8 at.% tungsten dissolved in ultrapure iron, cobalt, and nickel, except for the tungsten-iron absorbers used for the measurements on the 46.5 -keV transition, which contained 3.6 at.% tungsten. 22 (It was verified by Mtlssbauer experiments in w 182 that the effective fields were the same for the two concentrations of tungsten. ) The alloys were prepared by pressing tungsten powder (enriched for 182) experiments on the 99-keV level, natural for w into a small cavity in a pellet of the host material. By the use of the highfrequency field of a 5-kW ·induction furnace the pellet was levitated on a water-cooled silver boat and melted in an argon atmosphere. Then the melt was kept for around 5 minutes at a few hundred degrees above the melting point to homogenize it. The alloy was shaped by repeated rolling and tempering in hydrogen to obtain disc- shaped · absorbers, which were used mainly for measurements with transverse applied fields. For measurements without applied field and with longitudinal field the absorbers were usually prepared by grinding the tempered alloy on a fine india stone and dispersing the powder (average grain size: 3.5µ) in molten wax. However, this was not possible for the absorbers used with the 99-keV radiation of w183 , since one of the disadvantages of making absorber material starting from enriched material is that it is prohibitively expensive to obtain large amounts of the material. It was thus difficult to 183 grind the w -Fe alloy with the smali amount of material available, and it was therefore necessary to use the disc- shaped absorber for the experiment with no applied field. Only partial polarization was achieved however, as is evident from the velocity spectrum (Figure m. 3). Several experiments were also done with tungsten-iron alloy produced by another technique. It was prepared by arc- melting in an argon atmosphere and carefully annealing in hydrogen and resulted in a slightly smaller effective field than the ma~erial produced with the induction furnace (see Table ID. 2). 23 The pt 195 experiments used absorbers of pt metal, the commercially obtained compounds Pt 0, pt o , pt c1 , pt Cl , 2 2 4 and alloys of Pt with Al, Au, Fe, Co, and Ni. Most of the alloy absorbers were prepared similarly to the W-alloy absorbers by high-frequency melting, rolling, and tempering. A pt-Fe alloy was prepared by arc-melting and carefully annealing for several days, but no change in the velocity spectra was observed for the · two absorber preparations. All of the alloys for both the W and the Pt experiments were carefully checked by x-r.a y analysis, and it was verified that they were all solid solutions except for the Pt-Al alloy. In this case the x- ray analysis indicated intermetallic- compound formation, which is to be expected since a solid solution at room temperature can be acquired only by extremely rapid quenching. 5) , The absorbers were generally in one of three forms: solid plates or discs, powder dispersed in wax and shaped in a pill press to form a pellet, or powder held fixed in a plastic container. Tungsten and all the compounds were powdered absorbers, while Pt and the alloys were generally plates. Various reasons dictated the choice of the form of the absorber. For example, Pt is supplied as a foil; flat plates were used for the alloys with Fe, Co, and Ni to facilitate transverse polarization; on the other hand, for measurements without applied field powdered absorbers were used since this ensures that the orientation of domains is random. For convenience all powdered absorbers were in the form of wax pellets except those . 183 183 for the 99-keV experiments on W • The W o 3 and the W183 powders were held rigid in disc- shaped plastic containers rather than being mixed with wax for economic reasons. After the experiments were performed the powders were recovered for use in making WS 2 or W-alloy. 24 3) Drive and Data Storage The motion of the source was provided by synchronizing the motion of a transducer with a multichannel analyzer operating in the multiscalar mode, as has been described in detail elsewhere~) The transducer provided a velocity of triangular waveform to within 0.3%, as determined from the error signal. The electromechanical drive was calibrated by mea,suring the velocity spectrum of a single57 57 line Co source versus an absorber of Fe in Armco iron. An additional confirmation of the linearity of the velocity waveform was provided by taking calibration spectra at several different settings of the peak-to-peak velocity. Calibration spectra were measured with the source at 300, 77, and 4.2°K and the absorber at r .o om temperature. The relative positions of the lines were those of 7 Preston et al., ) which were used as the standard, to better than 0.4%. The data stored in the analyzer were punched onto paper tape, which was then converted into IBM cards for use with the computer program that analyzed the data. 4) Special Equipment Because of the high energies of the transitions .investi- gated, cooling of both the source and absorber is required to obtain a measureable resonant absorption except for the 47-keV experiments. Most of the experiments were therefore performed at liquic'.lhelium temperature in a cryostat as shown in Figure II. 3. The cryostat consists basically of two coaxial cylindrical containers ) The outer separated by an evacuated volume (10-7 - 10 -6 torr. container is made from an aluminum tube and the inner one from thin (7-mil) stainless- steel sheet. The inner one is wrapped with about forty layers of "super-insulation", a submicron glass paper 25 alternating with layers of 1/2-mil aluminum foil. Each layer of aluminum foil is separately connected to the inner container above the helium level so that the outer foils are connected to the upper warmer part of the contairier. With this arrangement the heat content of the outgoing gas is efficiently used. At the top of the cryostat is placed a set of thin stainless-steel plates, which serve the double purpose of radiation shields and separators for a number of gas layers, thereby reducing the convection. These reflector plates and the filling tubes are mounted to the plate covering the top of the cryostat. A center hole in this assembly allows the extended part of the drive system, containing the source and the absorber, to be easily inserted into the cryostat. The transducer itself rests on the top plate outside the cryostat. The construction of the cryostat is simple and inexpensive, and a helium consumption of about 0.13 -t/h is generally achieved. The transducer, the source, and the absorber are enclosed in a container that is easily removed from the cryostat. The lower extended part, the source tube, is made of thin-:walled (10-mil) stainless steel. It is surrounded by the liquid helium, but is closed on the lower end by a thin beryllium disc which serves as a window for the y- rays and allows the container to be evacuated and filled with an exchange gas for heat transfer. The drive motion is transmitted to the source by an extension rod (1/ 4" dia., 6-mil wall stainless- steel tube) which is centered by a spiral- shaped phosphor- bronze spring in the absorber holder, which is held firmly in place in the source tube by a stiff spring. By lifting off the cover to the drive container and pushing the exposed center tube of the drive (containing the drive coils) do:.wnward, the absorber holder is brought into the position where the centering spring is unextended. 26 A small carbon resistor mounted on the extension rod is used to monitor the temperature of the source and the absorber. The ease with which the source and absorber may be removed from the . cryostat, changed and re-inserted allows the use of strong sources. For the magnetization of the absorber in a direction transverse to the y-ray beam, a C-shaped permanent magnet is used and is mounted to the outside of the source tube. It provides a field of about 2. 5 kG in the plane of a disc- shaped absorber. Longitudinal magnetic fields of up to 50 kG at the absorber are supplied by a superconducting solenoid. Current leads to the coil and the heater for the superconducting switch are passed through a long thin-walled stainless- steel tube and end in four annular contact surfaces that mate with the solenoid contacts. It is important to avoid contamination of the contacts with films uf solid air or ice since the increased contact resistance causes unnecessary heating which results in excessive helium loss during the charging of the coil. Current to the coil up to 30 amperes is supplied by a simple transistor circuit powered by storage batteries. The velocity spectra for the experiments with the 100182 keV radiation of w (Figure ID. 1) demonstrate that the polarization of the absorber was just as expected: longitudinal, transverse, or random, as appropriate. We were thus assured that complete polarization or randomness was obtained in the absorbers 183 195 used for the 99-.keV experiments in w and Pt even though we were not able to verify this fact directly because of the poor resolution of the velocity spectra in these cases. 27 Figure II. 1 Nal(Tl) scintillation spectra for the Ta Au 195 182 , Ta 183 , and sources. The solid lines represent the full scintillation spectra, and the dashed lines the discriminated peaks. The hatched areas indicate the background included in the peaks. The number on the ordinate is a typical rate in the discriminated peak with the absorber in place. 28 Ta1az u ....-x ray <ll (/) "0' ...... x 0 N Ta1as - \ u Q) (/) x ray "0' ..... x 47keV I.I) ""' N Au195 u - ~x 0 100 Q) ray (/) "0' ...... 200 keV y-ray Energy Figure n.1 · 29 Figure II. 2 Source holder. The source material is placed in the cap and the body is screwed down with wrenches fitted to the flats. The body is. bored out to be fitted onto the drive extension rod, and the sides are slit to provide tension. . 30 .Figure II. 2 I 31 Figure II. 3 Schematic diagram of the cryostat and the drive system used in the experiment. 32 DRIVE 7-MIL SS WAL.L REFLECTORS SOURCE TUBE He L.EVE L. EXTENSION ROD SUPERINSULATION SOLENOID CONTACTS CENTERING SPRING SOLENOID Be -DISKS ~ > ~ ''''c''"~ COLLIMAT OR$ ~ M Figure IL 3 8 INCHES 33 ill. RESULTS 34 III. RESULTS Shown in Figures III. 1-5, 7-9 are examples of velocity spectra illustrating the various experimental situations encountered. Partially resolved magnetic hyperfine spectra have been obtained 182 183 , the 99-keV in w for the 100-keV transition in w , and the 99195 keV in Pt (Figures III. 1-5), and have been used to obtain Reff for W and Pt in Fe, Co, and Ni. The magnetic moments of the 99183 195 keV levels in w and Ft have also been derived. Spectra with structure originating in electric quadrupole hyperfine interactions (Figures III. 7-9) have been used to obtain the ratio of electric 182 183 quadrupole moments Q(2+)/Q(5/2-) for w and w and also the gradient of the electric field eq for ws2 and eq and the asymmetry parameter Tl for wor An isomeric shift has been identified for 19 the first time in Pt (cf. Figures III. 4-6) and has yielded information about the first-excited and ground-state radii. An estimate has been made for the lifetime of the 99-keV state of w 183 , but because unresolved broadening is present in the corresponding 183 spectra, the error is quite large. The 47-keV transition of w is so broad that structure cannot be resolved. We have treated this case specially (cf. Figure III. 10) in order to obtain a value for the magnetic moment and the lifetime of the 47-keV state. The spectra have been analyzed on the Caltech IBM 7094 computer by fitting them with the least-squares method to a sum of Lorentzian- shaped lines (Equation I. 4). The interpretation of the spectra is based on Section 2 of the Introduction, and the application to each particular case will be made as we discuss the analysis of each spectrum. A number of variable parameters determine the positions, intensities, and widths of the lines. These parameters 35 are: background B; slope of the background S; total dip of the 195 spectrum (% effect) H; peak width w; center shift (Pt only) c; parameters used in specifying the peak positions e(j) when magnetic dipole or electric quadrupole interactions are present; and additional parameters used when it is desired to vary the relative intensities h(j) of the component peaks in the :f itting procedure. The formula we used in fitting the spectra was based on Equation L 4, · and has the form 6 S H N h(j) } (III. 1) R(v) = B • 10 { 1 + • v - - 2 \ 4 2 2 10 10 _l 1 + 2 [ v - c - e(j)] J=l w where v is the instantaneous velocity of the source, R is the counting rate in the detector, and N is the number of component peaks. The formula represents the sum of a slanted baseline and a number of Lorentzian peaks. The slanted baselines are thought to be caused by phase shifts in the pulse electronics. A spectrum was taken with a nonresonant absorber to verify that the baseline was linear. The h(j) are normalized by requiring ~ h(j) = 1. 195 Sometimes, and particularly for the Pt-Fe spectra of Ft , a considerably improved determination of essential parameters can be achieved by a combined fitting procedure in which several different spectra are analyzed together ·in one single least-squares procedure. A parameter in the function assigned to fit any one of the spectra might also be used in the functions for other spectra. An example of this is the line width corrected for absorber thickness. Therefore spectra measured under different but complementary conditions (e.g., applied magnetic fields) and fitted together usually determine a common parameter more precisely than the same spectra fitted 36 mdividually. If a combined fit of several spectra is possible, systematic errors might be revealed if present in one spectrum but not in the others. 1) Magnetic Hyperfine Interaction For three transitions partially resolved magnetic hyperfine interaction was observed: the (2+ -0+) 100-keV of w 182 , the (5/ 2- -1/ 2 -) 99-keV of W 183 , and the (3/2- -1/2-) 99..,keV of Pt195 • These spectra are shown in Figures ill. 1- 5. In each case the heavy solid line that runs through the experimental points is the fitted spectrum, and the lighter, smaller curves are the Lorentzian peaks that contribute to the resultant spectrum. The positions of the component peaks and their relative intensities are determined in accordance with the rules described in Section I. 2c. Formula (I. 11) gives the general relation used in fitting the peak positions; it is used in the following form: E In this formula E mm , = E o + gµ n H [ m - (g'/g)m' J • 0 (ill. 2) represents the experimental centroid shift of the spectrum, gµ. H is the splitting of the sublevels of the ground state, n and g, / g is the ratio of the g-factor of the excited state to that of the ground state. Thus if I I 0 (as in w 183 195 and Pt ), the magnetic parameters to be varied in the fit are gµn Hand g'/g. However 182 if I= 0 (as in w ), then · E mm' = E o - g'µ n H m' ' (III. 3) 37 and the variable magnetic parameter is g'µn H only. The relative intensities of the component peaks depend on the spins of the ground and the excited state, I and I', respectively, on the multipolarity of the radiat_ion, L, and on the polarization of the absorber. For "No Hext" (as used to designate the spectrum in the figures) formula (I. 14) holds. For " II Hext" or "1 Hext" formula (I. 12) must be evaluated. Table III. 1 gives the relative peak intensities obtained in this manner. Since the polarization of the absorber was known, the peak intensities were not allowed to vary from the values listed in the table. a) (2+ - o+) 100-keV transition in w 182 • The best resolved of the spectra obtained in this work are those of Figure m. 1. These 182 are spectra measured with a Ta source and tungsten-iron absorbers in various field configurations. The quality of the fit in each case demonstrates that for "II Hext" and "l Hext" complete alignment was '-~~hieved and for "No Hext" the alignment was completely random. These spectra were also subjected to a combined fit (Results in Table m. 2) by restricting the magnetic parameter g' µ n H as well as the widths of the individual Lorentzians to the same values for all spectra. S_m all corrections for the effect .of the external fields on the splittings (for II Hext) and for the differences in the effective absorber thicknesses due to different spectrum shapes were taken into account. The combined fit gave results and errors not signtlicantly different from the individual fits and thus served as further confirmation that the absorber polarization was as intended. The internal field at the tungsten nucleus was determined by adopting the value g(2+) = 0.24 for the g-factor of the ·2+ state, an average of several recent measurements, S) and consistent with the 9 value 0.25 calculated by Nilsson and Prior. ) 38 In Figure III. 2 are shown spectra taken with absorbers of tungsten dilutely dissolved in cobalt and nickel. Since systematic errors affecting the polarization of the absorbers were found not to be present for the experiments on W dissolved in Fe, the measurements were performed only with transverse applied field. The peak heights were taken in the fit to be those appropriate to the transverse polarization. To obtain Heff a value was adopted for g(2+), as above. A check on the reliability of the fitted spectra when they are composed of a number of Lorentzian peaks is provided by comparing the width of each component peak with the width of an absorber without hyperfine interaction, in this case tungsten. By referring to Table m. 2, we see that the width of the component peaks in the magnetic hyperfine spectra agree well with that measured for a pure tungsten absorber, after correction for absorber thickness. b) (5/2- - 1/2-) 99-keV transition in w 183• The observed 183 magnetic hyperfine patterns, shown in Figure III . 3 for a Ta source and enriched tungsten-iron absorbers in the various field configurations were subjected to a combined fit similar to that for 182 the Ta spectra. However, since a disc- shaped solid absorber was used for the measurement without any applied field and an experi182 ment with Ta and a solid absorber of similar shape indicated a partial magnetic alignment, a combined fit was also performed 183 excluding this Ta measurement. (The results of these fits are included in Table m. 2. ) For both types of combined fit, a determi-. nation of both the internal field and the g-factor of the 5/2- state was attempted, but due to the strong correlation between the two parameters the fits were very little affected by a change in the value of either of them, and both parameters could not be accurately 39. determined from the Ta 183 measurements alone. Therefore, the 182 internal field was fixed at the value determined from the Ta measurements, and as a consequence the value obtained for g(5/2-) . + . 182 depends on the adopted g-factor of the 2 state mW • Our results have been computed on the basis of the combined fit that excluded the no-field measurement, because the partial magnetic alignment of the absorber in the absence of an applied field resulted in a poorer fit when this measurement was included. The ratio g(5/2-)/ g(2+) = 1.40 + 0.04 is constant to well within the error for g(2+) within 0.2 < g(2+) < 0.3 and can be used to evaluate g(5/2-) when g(2+) has been consistently determined. It is possible to fit the present measurements also with a negative g-factor for the excited state, as well as the positive value we have been considering so far. The fit is, however, not so good as with the positive value, and the width of the fitted Lorentzians agrees not so well with the width determined for a tungsten absorber (refer to Table m. 2). A negative g-factor can therefore be ruled out. c) (3/2- - 1/2-) 99-keV transition in Pt 195 • The magnetic hyperfine patterns obtained for different field configurations and alloys of Pt with Fe, Co, and Ni are shown in Figures m. 4 and 5. The spectra show little structure, and the individual peaks are not resolved. But an isomeric shift is clearly observed for the alloys and will be discussed in the next section. The relative intensities of the peaks in the fits were taken to be those appropriate for a pure Ml transition. lO), ll) Fits to the individual spectra revealed a strong correlation among four parameters, namely excited- state g-factor g , effective field Heff' width w, and effect, i.e., dip of the 312 absorption spectrum. A unique determination of these parameters 40 was the ref ore not possible. However, the situation was found to improve markedly when a simultaneous fit was performed to the spectra for all three field configurations. The parameters g , 312 Heff' isomeric shift (I. S.), and width corrected ~or the difference in the absorber thickness were constrained to be the same for the six sets of data we had to fit. As a consequence the strong correlations among the four parameters, i. e. , the corresponding off-diagonal elements of the error correlation matrix, were reduced up to 50%, and unique and rather precise values can be quoted for these parameters. The results are presented in Table III. 3. The 12 . result ~or g is based on the value g = 1.21204. ) 112 312 As a check on the internal consistency among the individual measurements, drastically changed weights were assigned to them, and the simultaneous fits were repeated. The spread of the parameter values that resulted was compatible with the standard deviations. In fitting individual spectra minima for Q 2 could some- times be obtained for different sets of parameters. With this in mind we repeated the simultaneous fit searching for other minima, L but none was found. Figure III. 5 shows spectra from measurements with transverse applied field on Pt-Co and Pt-Ni absorbers. By constraining g to the value obtained from the fit to the Pt-Fe 312 data, Heff could be determined for the other alloys. The results for the fits are presented in Table III. 3. 2) Isome ric Shifts a) w182 and w183 • No evidence for an isomeric shift has been found in the measurements reported here (upper limit: 182 0.05 nim/ sec in w ). 41 b) pt 195 , 99-keV. Isomeric shifts are clearly observed for Pt in Fe, Co, and Ni (see Figures III. 4 and 5). In addition to these alloys, shifts were measured also for 20 at. % Pt in Au and O. 7 at.% Pt in Al. The shifts are plotted in Figure m. 6 versus the electronegativity of the host metal. Isomeric shifts have also been observed in some compounds of Ft; namely, PtO (-0.34 ± 0.11 mm/s), Ft0 (-0.40 ± 0.08 mm/s), PtC1 (-0.1 ± 0.2 mm/s), 2 2 and FtC1 (-0.3 ± 0.3 mm/s). 4 From Figure ill. 6 it is seen that the isomeric shift for the alloys decreases linea:i;ly with decreasing electronegativity13) of the host element. (Pt-Al should be disregarded since it was not a solid solution. Refer to Section II. 2). This trend is opposite to that 197 13a) . observed for Au by Barret et al. If we adopt the lme of reasoning that decreased electronegativity of the host material results in an increased electron density at the impurity nucleus, it follows that 195 the mean square radius of the Pt nucleus in the first-excited state is smaller than that in the ground state. 3) Electric Quadrupole Interaction 182 Only the (2+ - o+) 100-keV transition of w and the 183 (5/2- - 1/2-) 99-keV transition of w yielded measurable electric quadrupole interaction. The observed spectra are shown in Figures ill. 7 - 9. The positions of the component peaks in these spectra are gl.ven generally by Equation I. 16, since the ground states are unsplit by the quadrupole interaction. For I= 2 and I= 5/2 Table ill. 4 gives the energy levels E resulting from the electric quadrupole interaction, the substates w, and the relative transition intensities T from the ground stat e expected for a polycrystalline absorber with randomly 2 oriented crystallites. In the table e qQ is the electric quadrupole 42 splitting factor, and it was varied in the fitting of the spectra. For fitting wo 3 spe ctra, ri was also variable. In several cases the relative peak heights given in the table did not provide a good fit, and were therefore allowed to vary. a) (2+ - O+) 100-keV transition in w 182• The observed electric quadrupole patterns for the 100-keV transition in w182 are . shown in Figures ill. 7 and 8. The analysis (results in Table ID. 5) of the tungsten disulfide spectra was performed with TJ = 0 since ws 2 is axially symmetric. l 4) It was found that fixing the relative peak intensities at 2:2:1 (cf. Table m. 4) did not give a good fit. They were therefore allowed to vary, and the fit improved. The 2 analysis of the velocity spectrum for the interaction energy e qQ was found however, to be insensitive to the relative intensities. Spectra were taken with absorbers of commercially obtained and laboratory prepared (see Section Il. 2) WS • The peak 2 heights fit tQ the spectrum for the commercially obtained ws 2 deviated more strongly from the expected 2:2:1 ratio than the home prepared material, and the deviations of the peak heights for the two preparations were of opposite sign. X-ray and spectroscopic analysis showed no difference between the two materials. In view of the exceptionally high magnetic susceptibility of tungsten disulfide, the measurements on the commercial material were repeated at 1.5°K with the absorber in a magnetic field of 50 kG to check on a possible magnetic interaction. No change in the anomalous spectrum was observed. At 77°K a quadrupole pattern with peak intensities in the expected ratio of 2:2:1 was obtained (Figure m. 8), which contradicts an explanation in terms of an anisotropic Debye-Waller 5 factor. l ) So far, no explanation for this effect is available. 43 In view of the difficulties encountered in the study of the quadrupole interactions in tungsten disulfide, a similar study of tungstic oxide was performed to obtain an independent determi182 nation of the ratio of the quadrupole moments for w and w 183 • The symmetry at the site of the tungsten nucleus in tungstic oxide is known to be low and implies a non-axially symmetric electric field gradient, i. e. 11 f 0, at the tungsten nucleus. As is demonstrated in Table III. 5 and Figure III. 7, a reasonable fit to the 182 measured velocity spectrum for the transition in w requires a large asymmetry parameter, contradicting previous results. 16) 183 b) (5/2- - 1/2-) 99-keV transition in w • The 183 velocity spectrum obtained for a Ta . source and an absorber of enriched tungsten disulfide shows very little structure, as seen from Figure III. 9. Therefore, the analysis of this spectrum is not very sensitive to the relative intensities of the peaks. Since the compound was prepared by the same technique as that for the 182 w measurement, the relative intensities of the lines were inferred from that measurement and were kept fixed in the least2 182 squares fitting procedure. The parameters e qQ for w and 183 w in ws2 could therefore be directly compared and the ratio Q(2+)/Q(5/2-) obtained. In fitting the velocity spectrum obtained with the wo absorber, 11 was fixed and set equal to the value 3 182 determined from the w experiment. The resulting ratio of the quadrupole moments is in good agreement with that determined from the tungsten disulfide experiments. c) Pt195 , 99-keV. An attempt was made to observe an electric quadrupole hyperfine interaction with this transition. 44 Absorbers of ptC1 , ptC1 , PtO, and pt0 were used but no 2 2 4 statistically significant quadrupole interaction was seen. 4) Line Widths Each spectrum fitted is assumed to be one Lorentzian dip or a com position of several, all of the same width. For each transition studied the widths of component peaks of the composite spectra were not significantly different from the width obtained for the unsplit absorber when the broadening effects due to absorber thickness were taken into account. Because these widths matched the width of the unsplit absorber, our confidence in the correctness of the fits was increased. Factors contributing to the widths of the peaks are discussed in Section I. 2a. 182 a) w , 100-keV. The widths obtained from the · · t s on the (2+ - o+) t rans1·t·10n m · w 182 are m · good various exper1men agreement with the width observed using a tungsten metal absorber. The mean of the experiments, corrected for absorber thickness is 2.30 ± 0.06 mm/sec. A smaller value for this width, 2.0 ± 0.2 mm/ sec, has been quoted elsewhere. l 7) The discrepancy might be due to source broadening and to some extent to noise produced by the boiling liquid. . good agreement b) W183 , 99-keV. As for W 182 , there is 183 among the widths determined for the (5/2- - 1/2-) transition in w • These widths do not, however, correspond to the natural width, 183 because of source broadening. After the decay of Ta the source 182 was checked in a w experiment, and the width observed with an 2 absorber of 20 mgW/cm was 3.5 mm/sec. In spite of this broadening 45 the spectrum shape was practically Lorentzian; hence the analysis 183 of the w (99-keV) spectra in terms of Lorentzian components is justified. One can estimate the lifetime of the 5/2- state if one corrects for the source broadening by assuming it to be caused by distributed electric field gradients. Then the width is 3.9 + 0.4 mm/sec, which corresponds to the half-life T 112 (5/2-) = O. 72 ± 0.07 nsec. c) Pt 195 , 99-keV. The width, corrected for thickness broadening, taking an average over several of the experiments is 18.0 ± 0.3 mm/sec, which implies an lower limit for the lifetime of this state of T > 0.154 nsec. This agrees with the electronically 112 measured lifetime of T ~ 0.16 nsec. 18) 112 5) Special Case: 47-keV transition in w 183 A determination of the lifetime and the magnetic 183 moment of the 3/2- state in w was attempted. The dependence of the absorption spectrum on the thickness of tungsten metal and tungsten--iron alloy absorbers was studied. For absorbers of uniform thickness, the half width of the nearly Lorentzian velocity spectrum 19 is expected to depend !~nearly on the thickness of the absorber ), and the width corresponding to zero thickness can be determined by linear extrapolation, as demonstrated in Figure m. 10. Fine powder (average grain size ~ 0.5 and s=:::1 0.02 recoilless resonant absorption lengths for Wand W-Fe, respectively) dispersed in wax was, however, used for the absorbers. It was found for the tungsten measurements that the widt hs measured are affected by the absorber granularity to 19 the extent that Visscher's formula ) cannot be used to determine the 46 natural line width. The effects of absorber granularity have been 20 treated in detail elsewhere. ) The correction to the extrapolated width is approximately proportional to the grain size measured in units of the recoilless resonant absorption length (t of Equation I. 6). m In Figure m. 10 estimations of this correction to the tungsten measurements are indicated, from which it is inferred that the corresponding ·correction to the tungsten- iron measurements is negligible due to the much smaller grain size. To avoid granularity effects, and since sufficiently thin tungsten metal foils could not be obtained, solid absorbers of tungsten-nickel alloy were used for the determination of the natural line width of the 46.5-keV transition. magnetic interaction is negligible. Line broadening due to From a combined least-squares fit to the observed velocity spectra for six absorber thicknesses, restricting the fitted widths to be proportional to the thickness of the absorber, the width for zero absorber thickness was determined to be 32.0 .± 0.8 mm/sec, which corresponds to the half-life (3/2-) = 0.184 + 0.005 nsec. Similarly, the vel9city spectra 112 obtained for tungsten-iron absorbers were fitted in one least-squares T procedure. The value 32.0 ± 0.8 mm/sec was taken for the width corresponding to zero absorber thickness, and the ground- state splitting was fixed to a value in accordance with the measured internal field. The magnetic moment of the 3/2- state was then determined by the fit: g(3/2-) = -0.07 ± 0.07 or g(3/2-) = 0.2 ± 0.2. Only negative values for g(3/2-) are, however, consistent with other experimental quantities (cf. Section IV. 2) • A fit to the W-Fe data with variable width for zero absorber thickness was also possible and gave values in agreement with the above, but with somewhat larger errors. 47 Figure ID.1 Recoilless resonant absorption spectra for the o+ - 2+ 182 transition (100 keV) in w for tungsten dilutely dissolved in iron. The spectra correspond to various magnetic alignments of the absorber relative to the y-ray beam. The slightly slanted baselilles are thought to be caused by phase shifts in the pulse electronics. 48 1.00 •• .. 0.99 w1s2_Fe 11 Hext 1.00 0.99 w1s2_Fe l Hext 1.00 • 0.99 w1s2_Fe No Hext -10 0 mm/sec 10 FigureIII.1 49 Figure III. 2 Recoilless resonant absorption spectra for the o+ -2+ 182 transition in w for absorbers of tungsten dilutely dissolved in cobalt and nickel and of tungsten metal powder. The ferromagnetic absorbers were magnetized in a direction transverse to the y-ray beam. The slightly asymmetric velocity pattern for W-Co may indicate presence of quadrupole interaction. A somewhat better fit to the spectrum was obtained assuming combined magnetic and quadrupole interaction. The quadrupole interaction may be appreciable, but it turns out that the value determined for the internal magnetic field is practically not affected. 50 rnm/sec 0 0.995 • 1.000 w1s2_Ni .L Hext 1.000 w1s2 o.980 - -----::~---=jo~--'- -5 mm/sec 5 . Figure III. 2 51 Figure ID. 3 Recoilless resonant absorption spectra for the 1/2- 183 5/2- transition (99 keV) in w • A disk-shaped absorber of enriched tungsten dilutely dissolved in iron was used. The solid curves are the fitted functions for the three spectra simultaneous fitted by the least- squares method. The dashed curves correspond to the fit to the two spectra measured with applied fields. 52 1.000 0.996 wl83_Fe II Hext 1.000 0 .996 w1s3_Fe .L Hext 1.oooi- 0.996 wl83_Fe No Hext 0.992 -10 0 mm/sec 10 Figure Ill. 3 53 Figure ill. 4 Velocity spectra for the Au 195 source versus pt-Fe absorbers for the different field configurations. 54 • 99.8 • Pt-Fe No Hext 99.0 99.8 Pt-Fe l Hext 99.0 99.8 Pt-Fe 11 Hext 99.4 -5 • 0 • 5cm/sec Figurem.4 55 Figure III. 5 Velocity spectra for the Au absorbers of Ft-Co, Ft-Ni, and Ft. 195 source versus 56 99.6 Pt-Co 1 Hext 99.0 • 99.6 Pt-Ni 1 Hext 99.0 • • •• • • • •• •• 99.6 99.0 -5 5 cm/sec Figure III. 5 L__:;_~-1-~_L~---1.~--.__~ 57 Figure III. 6 Plot of the isomeric shift of platinum alloys versus the electroriegativity of the host element. The deviation for Ft-..A..l from the general trend might be because the platinum is not in a solid solution. In the insert isomeric shifts for some platinum com pounds are shown related to the valency of platinum. 59 Figure ID. 7 Electric quadrupole patterns observed for the o+ - 2+ 182 transition in w for absorbers of laboratory prepared tungsten disulfide and tungstic oxide. For ws , the solid curves 2 correspond to the fit obtained with peak intensities fixed to the ratio 2:2:1, and the dashed curves are obtained with independently variable peak intensities. For wo , the solid curves 3 correspond to the fit with variable symmetry parameter ri ; the dashed curves are obtained with ri = O. 1.00 0.99 1.00 .. · ·.. 0.98 -10 0 mm/sec JO Figttrem.7 .· 61 Figure ill. 8 Electric quadrupole patterns observed for the o+ - 2+ transition in w 182 for absorbers of commercially obtained ws 2 taken at nitrogen and helium temperatures. The solid curves correspond to the fits obtained with peak intensities fixed to the ratio 2:2:1, and the dashed curves are obtained with independently variable peak intensities. 62 1.00 0 .99 -- w1a2s 2 He Temp 1.00 . • .... ..•• • • • • • • •• r· • 0.998 •• •• • ••• ~ ••• -10 0 mm/sec . ro Figure III.8 63 Figure III. 9 Electric quadrupole patterns observed for the 1/2- - 5/218 3 transition in w · for absorbers of enriched tungsten disulfide and tungstic oxide. Solid and dashed curves cqrrespond to those in Figure 5. The lower spectrum is obtained with an absorber of enriched tungsten metal powder. 64 mm/sec - 10 1.000 I-. j 0 10 • •••• • 0.999 L • w1a3s2 1 1.000 • • • •• • •• 1.. ·... • •• • • wia3 0 . 3 0.998 L 1.000 •• • .. • .. . • w1a3 0 .9 95 •• - 10 0 mm /sec 10 F i gur e III. 9 65 Figure III. 10 The dependence of the measured width on the absorber 183 thickness for the (3/2- - 1/ 2-) 47-keV transition in w and absorbers of W, W-Ni, and W-Fe. Note the shifted scales for the widths. An experimental point indicates the width of the Lorentzian fitted to the measured velocity spectrum, and the error-bars correspond to standard deviations. One measure- ment for W-Ni corresponding to the point (15.3; 55.9 ± 2.4) is not shown in the diagram; the point falls exactly on the extension of the solid line. A solid line corresponds to the thickness dependence of the widt h of one single Lorentzian, determined by the combined fitting of all the measured velocity spectra for the particular absorber material. The error bars on the vertical axis give the standard deviation of the extrapolated width determined from the combined fit. For W the dashed lines give the width dependence expected for solid tungsten absorbers. They were obtained by correcting the fitted solid line for granularity effects. The average grain size ( ~ 3.5 µ) . was measured and the following values were assumed for the Debye temperature (e ) and for the total internal conversion 0 coefficient (at) : a) e0 == 360°K, ctt == 7.6, a.t == 8.4, c) 8 D == 280°K, ctt == 9.2. b) e0 == 320°K, For W-Fe the dashed line gives the width of the composite spectrum at half maximum determined by the fit. 66 50 50 300'--~---~--~----~~..._~...._~_._~_._~__......_~_.__~_.__~__,30 5 10 ABSORBER TH ICKNESS {mg w l83/cm2) FigureilI.lC 67 Table ID.1 Transitions between magnetic substates and relative transition intensities. The transition intensities are based on Equation I. 12 .o f Section I. 20, where the symbols are explained, and are given for e·ach field configuration used. Table III. 1 Transitions Between Magnetic Sublevels and Relative Transition Intensities -Nucleus w183: I' I L 5/2 1/2 2 Intensity Pt195: I' I L 3/ 2 1/2 1 Intensity w1s2: I' I L 2 0 2 Intensity m' m b.m 5/2 1/2 2 3/ 2 1/2 1 1/2 1/2 No H II H ext 1 Hext ext 5 4 4 4 3 0 m' m t.m 3/2 1/2 1 1/2 1/2 No H II H ext 1 Hext ext 3 2 3 0 3 4 m' m b.m No H II H ext 1 Hext ext 5 0 -1/ 2 1/ 2 -1 -3/ 2 . 1/2 -2 0 0 2 2 2 1 1 -1/ 2 1/2 -1 1/ 2 -1/2 1 -1/2 -1/2 -3/2 -1/2 -1 1 1 1 1 1 1 2 0 3 3 4 3 . 0 -1 -1 -2 -2 1 1 1 0 1 0 2 1 0 0 2 1 0 0 0 1 0 1 1 1 0 0 1 1 3/2 -1/2 2 1/ 2 -1/2 1 1 1 0 0 2 2 2 0 0 1 -1/ 2 -1/ 2 0 3 0 0 -3/ 2 -1/ 2 -1 - 5/2 -1/ 2 -2 4 4 4 0 5 5 m co 69 Table III. 2 Results from the study of the magnetic hyperfine interactions. Numbers within parentheses are standard deviations. The errors given are standard deviations increased to include the spread of the values and to take account of the uncertainties in the corrections as well as the precision of the velocity calibration. to Heff of the text • . H.int corresponds Table IlI. 2 Source I Ab~orbe r rhicknes: I ' h, j) jttinJ/µ eff Corrected Width Excited State Splitting 'Hint nun/sec rrm/sec mm/sec kG kG/mcgne t on 320 mgW/cm 182 Ta h) Fitted Width I W-Fe b) W-Fe 44 2.40 (0.04) 2.28 1.596 (0 . 008) 715 ± 10 32 2,45 (0.04) 2. 36 1.519 (0.009) 680 ± 10 W-Co 33 2 .43 (0 .11) 2.3'• 0 .806 ( 0.015) 360 ± 10 W-Ni 24 2.30 (0 .11) 2.24 0.200 ( 0 . 043) 90 ± 25 w 20 2.52 (0.0 6) 2.23 I * lol*-Fe W*- Fe W*-Fe w* lol -Fe Ta183 1.08 (0 .05) CF 0, 1, I!. 0.95 (0.04) 190 SF l 1.19 (0.14) 150 SF l 1.43 (0.14) SLF 0.95 (0.14) a) I . 1.19 (0.05) 0 .327 (0 .002) CF O,l,11 · 1.19 (0 . 05) g) 0.338 (0.002) CF l, II 0.92 (0.07) g) -0 . 237 (0.003) CF 0 1,· il· f) 1.4 7 (0.0 5) SLF 0.94 (0.14) 4.90d)(0.20) 4 . 55 0.89 (0 . 48) 48 5.0Bd )(0 .12) 4 . 73 1.57 g) 48 5.,12d) (0.12) 4 . 77 1.57 48 4 .6i> (0 .15) 4 . 30 1.57 22 5.35 4.67 4 , 7 ± 0.2c) g(5/ 2-,h,k) I CF 0 J l I j'I e) 48 (0 . 18) I _Y._ . li - n CF O, l, ji . c) 2.30±0.06 Ground State Splitting I 2 ,_."., I 400 ( 220) 0.53 (O. 26) 1 0. 34 ±a.Ole) CF - Combined fit; SF - fit to a single v e locity spectrum; SLF - fi t to a single Lore ntzian - shaped curve; ·o - No npplicd fie ld; l - transverse applied fie ld; II - longitudina l applied field . b) Alloy prepared by arc melting. c) The value is an average of t.he appropr iate separate determinations. d) The quot ed value corres ponds to the s pectra for t he transverse fie l d configurat ion. e) Attempted determination of both the i nternal field and the g-fac t or. f ) Attempted de t ermination of a negative value for the g-factor. g ) Determined fr 0tn the r esults for wl82. + h) The i;lven values correspon<! to adopting g ( 2 ) • 0. 24 1 see text. j) µ.,ff tnke n fr0tn Ref, ZS. k) g(S/2-) is independent o f the value of the width of th e component Lorentzians . Fixing this width to values differing by as n1uch as 30•t d ocs n ot affect g (5/ 2- ). *) Enriched tungste n was use d for the absorber --.i 0 71 Table ID. 3 195 Results from the study of the 99-keV level in Ft • The errors given are standard deviations. Hint corresponds to Heff of the text. The widths (W) are extrapolated to zero absorber thickness using e (Ft) = 230°K and the relation 0 e0 = e0 (host). J M(host)/M(impurity) • 72 Table III.3 Thickness (mg P t/ cm2 ) g3/2 Pt-Fe Pt-Co 30-60 50 -0.41 :1:0.03 -0. 41* Pt-Ni I, 50 I Pt I I 50 -0.41 * • ! I Hint (MG) l. 19 :1:0. 04 0.86 :1:0. 03 0.36 :1:0. 04 W (mm/sec) 17.4 :1:0. 3 18. 6 :1:0.4 17. 8 :1:0. 6 1 8. 0 :!:0 .4 -1.90 -1. 96 :1:0. 09 - 1. 65 :1:0.08 0.06 ±0. 17 0 .46 :1:0. 02 0.5 8 :1:0. 06 I. S. (mm / sec ) :ro. 11 ' Hint Ip eff (MG/magne:ton) 0.54 :1:0. 02 * Value adopted from the Pt-Fe results. 73 Table ill . 4 Electric quadrupole hyperfine interaction for the 182 (2+ - o+) transition in w and the (5/2- - 1/2-) transition in w 183 . Equation (I. 16) has been solved for the energy E and the form of the substates ~ resulting from the splitting of states with I = 2 and I = 5/2. The relative transition intensities T between these substates and the unsplit ground state are given as derived from Equation (I. 14). The quantity 2 e qQ is the electric quadrupole splitting factor. 74 Table m. 4 ri = 0 (as for WS ) 2 I= 2 E 2 -(1/4)e qQ -(1/8)e 2 qQ +(1/4)e2qQ I= 5/2 o/ T Io> .1 1±1> 1+2) 2 E o/ T 2 -(l/5)e qQ -(1/20)e 2 qQ I± 1;2> 1 I± 3/2> 1 I± 5/2> 1 2 2 +(1/4)e qQ ri f 0 (as for wo ) 3 I= 2 E 2 2 -(1/4)e qQ(l + ri /3) 1/ 2 T l+2)+j-2) 1 2 2 1 2 -V6/ri)Cl+(l+ri /3) 1 J jo> I+1> - 1-1> 1 -(l/8)e qQ(l - ri) l+l)+j-1) 1 2 I+2> + 1-2> I+2> + 1-2> 1 - (1/8)e qQ(l + ri) 2 +(1/4)e qQ 2 2 1/2 +(1/ 4)e qQ(l + ri /3) . 1 2 1 2 -V6/ri)[l- (l+71 /3) 1 J 10> I= 5/2 2 E. = (1/40)e qQ • (jth solution of the equation: J 3 2 2 x - 28x(3 + 71 ) - 160(1 - ri ) = 0 ) *j = aj I± 5/2 ) + bj I± 1/2) + cj I+ 3/2 ) T j = 1, j = 1, 3 75 Table ill. 5 Results from the study of quadrupole interactions. Numbers within parentheses are standard deviations. Table IlI.5 • 11 Absor ber ) Source I Fitted Width Ta Gredient e) Q(5/2-) eq Q(2 ' ) Ey mm/ sec 10 18 V/cm _,_ 2 Relative Peak Inte:-is it ies or Asyrrnctry Para!lleter I I d) 11.58 2 .12: 1. 96 : 0. 9 3 - 1 1.01 2 : 2:1 10.04 co.06) 't.'S2 I I 182 2.84 (0.08 3 I . I I -8. 7 3 (O. 09) 2:2:1 I -8. 23 (0 . 10) I -8.34 (0.05) I +l.54 ± o.04 I 2,76 (0.06) d) 2.42 (0.04) w*s2 I 8.18 2.12 : 1.41: 1.47 4.25 11 c 0.63 ± 0.02. 2.18 -.J ' ·o .93 4.8 (0 .3) 9 .45 (O . 40) 0.931 ± 0.038 4.7 (0 .3) 9.55 (0. 38) 0.939 ± 0.036 , l.06:0.99:0.95 d) 5 .1 (0 .3) -7 .92 (0. 37) 0.940 ' 0.050 Tal83 w*03 II I I I I a) b) c) d) e) 1~1 I I 10 . 07 (0.06) I -1. 86 ± 0.05 2.49 (0.04) W0 I I x2 I I ,.. 2.50 (0.04) ' Electric Field ! ce 2QQ_ m.'Tt/sec I I b) l: l : l I· . d) 0.63 d) Q(5/2-) = - (1.70) ± 0.07) barns e) The thicknesses were 50 mgW/cm2 and 22 mgW* /cm2/ where the symbol * stands for enriched. material. Not corrected for absorber thickness. 1'hc s tandard dev iation of X2 /(N - n) ~ 0.14 for nll the fits. K~pt fixed in the fitting procedure. Adop ting Q( 2+) = - (1.81 ± 0.05) barns, inferred from Coulomb excitation experimen ts (Ref, 30). 0.92 1.10 O' 77 IV. DISCUSSION 78 IV. DISCUSSION 1) Wiagnetic Fields The internal magnetic field (715 ± 10 kG; see Table ID. 2) at tungsten nuclei in dilute solution ill iron determined in the present work is in agreement with that (700 ± 70 kG) obtained in an earlier 21 MClssbauer experiment ) and the NMR result (635 kG) of Kontani and 22 Itoh, ) but is inconsistent with the value (430 ± 100 kG) determined 23 by the Coulomb-excitation technique. ) There is better agreement among the results of the present measurements of the internal fields for tungsten incobalt(360± lOkG)andnickel (90 ± 25 kG) and the fields 23 obtained in Coulomb-excitation experiments ) (Co: 330 kG; Ni: 60 22 kG). The NMR result for W in Co is 385 kG. ) The discrepancy between the values of the internal field in W- Fe obtained by Mtlssbauer and NMR experiments and the value obtained by the Coulomb-excitation technique is not at all understood. The discrepancy might be due to a dependence of the field on the concentration, since vastly different concentrations were used in the Mtsssbauer and the NMR experiments as compared to the Coulombexcitation experiments. However, for concentrations from 0.18 to 3.6 at.% tungsten we found no such dependence for tungsten-iron 24 alloys. Herskind et al. ) have found a similar discrepancy for Pd-Fe alloys, and they contend that the implantation technique used in the Coulomb-excitation experiments results in a different internal field from that obtained with a metallurgically prepared alloy. This may be because the nucleus recoilling into the lattice produces. local disturbances which are not present in the metallurgically prepared sample. Finally there may be a temperature dependence of the internal field, since both the MC1ssbauer and the NMR experiments 79 were done at liquid helium temperature, while the Coulomb excitation was done at room temperature. The internal field (1190 + 40 kG; see Table ID. 3) for pt in Fe obtained ill the present work is in rough agreement with the 22 NMR resuit ) (1280 kG}. There is better agreement between our results for pt-Co (860 ± 30 kG} and pt-Ni (360 ± 40 kG) and the NlVIR results (830 and 340 kG, resp.). Figure IV . 1 shows the variation of the internal field Heff for several elements in dilute solid solution in Fe, Co, and Ni as a function of the magnetic moment µ eff (µhost ) on the host atom. 25 Shirley and Westenbarger ) have attempted to explain the internal fields of transition elements dissolved ill magnetic hosts of the 3d transition series. Their approach assumes that the major portion of the field is due to a polarization of conduction electrons (CEP) by an exchange interaction involving the conduction electrons and the 3d electrons of the host atom. Their explanation predicts a linear dependence of the internal field on the host magnetic moment. As is seen in Figure IV. 1, the fields for tungsten and to a lesser extent platinum, deviate from this predicted linear dependence. Their explanation is :therefore incomplete~ ..A..lthough Shirley and Westenbarger mention other mechanisms that could possibly contribute to the internal field, they do not consider these to be important. However , the trend of our data for tungsten and platinum indicate that their premise is not valid. When an impurity element of a transition series is dissolved in a magnetic host of the 3d transition series, the spin of the host polarizes the spin of the d shell of the impurity, which in turn 26 polarizes the core electrons. After Campbell ), the polarization of the core (CP}, and the field produced by CP, is taken to be 80 proportional to the magnetic moment of the impurity, µ.impur1•ty • · · Thus, for Wand Ft, elements of the 5d transition series, both CEP and C P contribute to Heff' which may the ref ore be written as H e ff = a µ.impur1·t·y +b µhost· (IV. 1) The parameter a, which gives the contribution to the internal field from C P, is not expected to vary with the number of d electrons within a given transition series, because the core electrons are 27 predominately inside the d shell. ) By contrast the contribution to the field from CEP, given by the parameter b, varies markedly 25 within a given series, ) since the d electrons vary from element to element and provide variable shielding for the conduction electrons. Values for µ. ·t for a number of transition · impuri y 6) elements, including Wand Ft, in Fe have been derived by Campben.2 · from neutron diffraction data. For Fe, Co, and. Ni, µh t~ 2.22, . 28) 29) OS 1. 72, and 0.606 Bohr magnetons, resp. ' Our confidence in the validity of Equation IV. 1 is increased by considering the data presented in Figure IV. 1 for Au, Ag, and Cu. These elements are diamagnetic atoms at the end of each of the transition series. Since they have no magnetic moment.s , there is no contribution from CP. The internal field is then given by the second term alone of Equation IV .1, in agreement wit h the linear dependence evident from the figure. It is thus reasonable to assume that t~e deviation from the linearity that was predicted by Shirley and VI estenbarger is due to the additional contribution to the field from C P. 81 2) Nuclear Parameters for the 5/2- and 3/2- States in w183 This experiment provides the first measurement of the electric quadrupole moments of the 5/2- (99-keV) state in w 183 and of the magnetic moments of the 5/2- and 3/2- (46.5-keV) states. A value for the lifetime of the 5/2- state is estimated in this work, but large corrections had to be made which were based on assumptions that are not well established (see Section ID . 4b). A reliable measurement is made of the lifetime of the 3/2- state. Previous estimates for these lifetimes have been made based on Coulomb-excitation experiments30> and the Mtlssbauer e'x periment of Sumbaev et al. 31) However, the present result for the 3/2- lifetime represents a considerable improvement over the previous values. 183 The nuclide w is a strongly deformed nucleus whose level scheme consists of several bands (see Figure I. 1). The level structure and the Y- ray transition intensities in this nucleus cannot be well accounted for by an adiabatic rotational model for the nucleus. 32 A significantly improved description was obtained by Kerman ) as the result of mixing of states in the two low-lying bands, K = 1/2 and 3/2; by Coriolis coupling (the RPC model). More extensive band 33 34 mixing has been considered by Rowe ) and by Brockmeier et al. ) In this section a comparison of the experimental results with calcu- lations in terms of the RPC model will be made. The results of the work of Brockmeier et al. , namely the mixing parameters and magnetic matrix elements, and its notation will be used. The admixture of states of the higher bands into the low-lying levels is very small. The refore mixing of states in only the two lower bands is considered. Thus the moments and the Ml and E2 transition 4 probabilities can be described by the following eight matrix elements¥ ) 82 d Ql/2 1/2 0 1;2 1;2 G1/2 1/2b 0 1;2 3/2 0 3/2 3/2 Q3/2 3/2' an ' Q l/2 3/2', Ql/2 3/2bMl' E 2, , where G = K (gK - gR) and bMl = bo.f 2. The accurately determined ratio of the quadrupole Kx moments, Q(5/2-)/Q(2+) = 0.94 ± 0.04 (see Table ill. 51 suggests a comparison with accurately measured B(E2) values for Coulomb . w1a2 an d w183 • 30) The comparison . . present e d m . exc1·ta t·10n m is Figure IV. 2. In this figure Q(5/2-) may have been incorrectly derived. Our determination of its value depended on the derivation of Q(2+) from B(E2; o+ -+ 2+). In this derivation we assumed the correctness of the rotational model for w 182 • However, recent 35 186 Ml5ssbauer experiments )in,W and the theoretical calculations 36 of Kumar and Baranger ) have cast doubt on this assumption. Thus, the inconsistency apparent from the graph may be due to an incorrect value for Q(5/2-). In any case the diagram allows the determination 2 of Q1/ 112 = 6.5 ± 0.3b and Q 1/ 2 312 bE = -0.4 + 0.5b. 2 The measured magnetic moments, µ (3/2-) and µ (5/2-), and the measured half-life of the 3/2- state can be compared with values derived from the magnetic parameters of Brockmeier et al. The latter were obtained from the fit to a large number of relative 37 y-ray transition intensities ) with the assumption Q1/ 2 112 = 6.5b, which agrees with the value determined above. To calculate the magnetic moments the g-factor for the core rotation, gR, must be assumed and is here taken equal to the g-factor of the ground state 182 rotational band of w , since the contribution to gR from the odd neutron has been accounted for in the band-mixing theory. Contributions to gR due to higher bands and blocking effects are small compared to .the.uncertainty~ the g-factor of w 182• The comparison 83 is presented in Table IV. 1. It is seen that µ (1/2-) is well accounted for, but µ (3/2-), µ (5/2-), and B(Ml; 3/2- - 1/2-) differ from the predictions of Brockmeier et al. Recently, new~xperimental information on the w 183 38 39 nucleus has become available, ), ) which, together with the results of the present experiment, calls for a redetermination of the magnetic single- particle matrix elements. The data used are the results of the present measurements, the value of the ground state magnetic moment, and those B(Ml) values for transitions of predominantly magnetic character that can be determined most precisely. In Table IV. 1 are listed the experimental quantities used. These are fitted to 32 34 the theoretical magnetic transition rates and moments ), ) with the least- squares method. The fit is found to be insensitive to the parameters G 112 3/ 2 and G 3/ 2 3/ 2 • . The influence of various constraints on these parameters was investigated to determine the 1 2 1 2 reliability of the values obtained for the parameters gR, G 1 1 , 2 1 2 and G 1 l/ bMl. The results of such a fit are also included in the table. It was also found that these latter parameters do not depend sensitively on any individual experimental quantity. values are the results of the fits: gR Gl/2 1/2 Gl/2 1/2b Ml = 0.25 ± 0. 04 = -1.06 ± 0.05 = -0. 74 ± 0.06 • The following 84 The Nilsson model allows us to understand the values 1/2 1/2 1/2 1/2 .. of G and G bMl by the express10ns: a 1/ 2 l/ 2 :: (1/2)(gK - gR):;: (g-e, - gR) (1/2\jz\1/2) +(g~:-g-e,)(1/2\;z\1/2) (IV. 2a) G 1/2 1/2 . ~ . + "' bMl • /"2; (gK-gR)b0 :;: (g-e,-gR) (1/2IJ+\ -1/2)+(gs-g-e,)<1/ 2ls+ l-1/2) (IV. 2b) where, in the strict sense of the model, gz :;: g+ :;: g , the free nucleon s s s value, and gR. The bras and kets refer to single-particle states. gR :;: It is well known that the interaction between the spin of the odd nucleon . and the spins of the nucleons in the core reduces the spin contribution to the nuclear magnetic moment, and that this effect can be accounted for by the use of an effective value in place of g • It has recently 41 been pointed out by Bochnacki and Ogaza ) thatsthe component of the spin polarization of the core in the direction parallel to the symmetry axis of the nucleus might not be the same as that in a direction trans- . z verse to the symmetry axis. Therefore one may not assume that g A S + and gs are equal. The term (g -e, - gR) ( 1/2 I j+ I -1/2 ) is only 41 slightly affected by the spin polarization, so that gR ~ gR, ) and we have adopted gR :;: 0.24, an average of several recent measure8 ments. ) The matrix element ( 1/2 Ij \ - 1/2 ) can be obtained from the experimentally determined34) deco~pling parameter a A = - ( 1/2 I j+ ! - 1/2 ) • Since the odd nucleon is a neutron, g .e, = O. 0 Equations IV. 2 have been evaluated with various assumptions for the potential, 42), 43 ) and the effective single-particle g-factors, gz and s 85 g+, are then obtained by comparison with the experimental values s 1/2 1/2 1/2 1/2 . . . . for G and G bMl " The effective smgle-parhcle gfactors are quoted in Table IV. 2. For comparison, corresponding values for Yb 171 and 169 Tm have been calculated from available experimental data. 44 - 45 ) Since the primary experimental results have not been anaiyzed in terms of band mixing, one should in principle correct for the effects of band mixing on the experimental quantities gK, gR' and b • 47)' 48 ) 0 Such corrections have been estimated by assuming that only K = 3/2 47 bands mix with the K = 1/2 ground state. ) One consequence of the neglect of t he mixing of the K = 1/2 bands with the ground state is t hat no correction is obtained for the quantity (gK - gR)b 0 . In Table IV. 2 are given the results of two calculations of the effective gfactors gz and g+, one accounting for Coriolis mixing with the . s s K = 3/2 bands onl y and the other without Coriolis mixing. It is demonstrated in the table that in all cases the values derived for gz and g+ using recent Nilsson wave functions 42) s s differ from each other significantly. It should be pointed out that the values calcul ated for the effective g-factors depend on the potential used in the nuclear model. If the old Nilsson wave43 functions ) are used, markedl y changed values are obtained for 171 the effective g-factors for Yb , viz. gz/ g+ < 1, whereas there 183 fl s are only small changes for W and Tml69 3) 195 Ivlagnetic Moment for the 3/2- Level of Pt The val ue for the g-factor of the 3/2- state determined in this experiment (-0.4 1 ± 0.03) is in good agreement with that of Atac et al. 49) (-0.43 ± 0.10) and with the recently quoted value 86 5 (-0.4 0 ± 0.07) of Buyrn and Grodzins. 0) It is just outside the 51 limits (0.47 > g > - 0.60) giv~n by Benczer-Koller et ~l. ) who 312 assume I Hint I : :;: 1.39 MG for the Pt-Fe alloy. The core52 excitation model proposed by de-Shalit ) and Gal 53 ) should account 195 • Experimental information is for the low- energy states in Pt 194 54 55 available for the 2+ states in Pt ), ) so that a comparison of the predicted and measured values of the g-factor can be made. It turns out that calculations give values very near zero; hence present core-excitation models do not give an adequate description of the 3/2195 53 state in Ft . As has been pointed out, ) the discrepancy might be removed if configuration mixing is taken into account. 87 Figure IV. 1 Internal fields Heff at nuclei of atoms dissolved in Fe, Co, and Ni lattices, plotted against the host magnetic moment µeff° The values for W and Pt have been measured in this work. (See Tables III. 2 and III. 3.) The remaining values of Heff' as well as the values of µeff' are taken from a similar figure in Shirley and Westenbarger (Ref. 25). 88 - 1500 ,,.-,-------.---.----;---~ ··- I r t - 1000 :j - [ ~ © c -4oor - 300 j-~---o--~F~e--=o---o- - 200 ~- - 10~~ 0 1.0 E·cfeciiv e host moment 2 .0 (magnetons) ·Figure N.1 89 Figure IV. 2 Comparison of the electric parameters for w 183 derived from the ratio of the quadrupole moments, Q(5/2-)/Q(2+), measured in the present experiment and B(E2) values measured by the Coulomb excitation t echnique (Reference 30). The ratio of the quadrupole moments and 2 2 the B(E2, o+ .... 2+) = 4.00 ± 0.20 e b imply Q(5/:t) = 1. 70 + 0.07 b. The three quantities Q(5/2-), [ B(E2; 1/2- .... 5/2-)] 1/ 2 depend linearly on the quantities Q 1/ 2 112 , Q 1/ 2 3/2, Q l/2 3/2bE ' and Q3/2 3/2• It is . assume . d tha t Ql/2 3/2 = O·, 2 also Q3/2 3/2 enters only in Q(5/2-) and is there of little importance. 90 -H IN C\J S LO. .. . II (\j w __.... co I I C\J II ...-- ~ 0 -- C\J LLJ .0 C\.I ~ ~ 0 I C\J I --~~~~------~~~~--i~~~~~........J~~~~~-"'~ 91 Table IV.1 Magnetic moments, B(Ml) values, and magnetic parameters determined from these. The units for the magnetic 2 moments and the B(Ml) values are nm and (nm) , respectively. Column A gives the result of the fit with all parameters varied; column B corresponds to fixing the two parameters to which the fit is insensitive. Except where noted, the B(Ml) values are determined from the following quantities: 1) The ratio of the y- ray intensity of the appropriate transition to that of the crossover transition originating.from the same level (averaged from those of References 37 and 38). 2) The B(E2) value for the crossover transition (calculated . . .t he text); from the val ues of Q1/2 1/2 and Q1/2 1/2 bE given m 2 and 3) The mixing ratio for the direct transition (Reference 39). Table lV. 1 ........._~ .... - ··--9 Experimental Predictions of Value Brockmeier et a l. Fits to Present Data Quanti.ty - -· µ(1/2-) 0.117 µ(3/2-) -0 .1 1. 75 µ(5/2-) /µ(2+) a) ~ 1/2-, 46.5) ·- 1- ~ - -- ---- 0.123 0.117 0.117 ± 0.1 -0.28 -0.22 -0. 08 ± 0.05 1. 98 1. 79 1. 86 0.288 0 .176 0. 178 0.0316 0.0256 0.0263 0.245 0. 193 0.164 1.39 • 10- 3 0.98 • 10- 3 1.02- . 10- 3 0.209 ± 0.020 0.0239 ± 0.0017 B(Ml,5/2 - ~ 3/2-, 52.6) B(Ml,7/2 - ~ 5/2-, 107 .9) 0.216 ± 0.029 I (0.94 ± 0.26) ·10- 3 . B(Ml, 5/2 - ~ 3/2-, 82.9) B(Ml,3/2 A b) ...0 N - .. gR Gl/2 1/2 o. 24 c) 0.25 (0.04) 0.28 -1. 25 -1.06 (0.05) -1.06 Gl/2 l/2b Ml Gl/2 3/2 -0 .89 -0.74 (0.06) -0. 70 -0.21 -0.04 (0.13) -0.21 d)" G3/2 3/2 0.68 -0.2 0.68 d) "' a) b) c) d) .... -·-~·~...·- ·- (0.7) ··· 2 Calculated from T1/2(3/2\ with at== 8.4 (Ref. 40), and o == 0.006 (Ref. 39). Numbers within parentheses are standard deviations. 182 Adopted value, equal to gR of the ground state rotational band in W ; Brockmeier et al. use gR == 0.35. Fixed at the value predicted by Brockmeier et al. (Ref. 34). 93 Table IV. 2 Effective single-particle g-factors derived from the 183 ) and from the experiresults of the present experiment (Vv 171 mental data of References 45, and 46 (Yb ) and of Reference 169 44 (Tm ). The matrix element s of the spin operators have been calculated from recent Nilsson wave functions (Reference . 42), using the potential parameters x. = 0.0637 and µ = 0.42. The errors quoted are derived from the uncertainties in the experimental data only. 94 Table ·IV. 2 . l I r Quantity wl83 Ybl71 (1/2 j~ j 1/2) 0.281 -0.183 'I -0.35 6 (1/2jE,._,_j-l/2) 0.781 0.317 I -0.144 I : I ) z/ gs gs Tml69 a) 1.01 ± 0.02 a) 0.83 ± 0.02 b) 0.95 ± 0.09 b) 0.76 ± 0.03 a) 0.60 ± 0.01 a) 0.39 ± 0.05 b) 0.64 ± 0.03 b) 0 .51 ± 0.05 0.88 ± 0.04 i I· c + /g OS S 0.37 ± 0.03 a) Without correction for Coriolis mixing b) Corrected for Coriolis mixing with K; 3/2 band. 95 REFERENCES 1. The discovery was reported in: R. L. MUssbauer, Z. Physik 151, 124 (1958); R. L. Mtlssbauer, Naturwiss. 45, 538 (1958); and R. L. MUssbauer, Z. Naturforsch. 14a, 211 (1959). General references for the Mtlssbauer effect that the author has frequently consulted, and on which the Introduction is based, include: A. 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