Mössbauer Effect in Thulium 169

Citation

Cohen, Richard Lewis (1962) Mössbauer Effect in Thulium 169. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/F7HD-FD14. https://resolver.caltech.edu/CaltechTHESIS:07262011-095356834

Abstract

The recoil-free resonance absorption phenomenon has been used to study the 8.4 kev gamma ray which is emitted in the decay of the first excited state of Tm^(169) which is populated by the beta decay of Er^(169) . With sources and absorbers in various chemical forms, hyperfine structures which are strongly temperature dependent have been obtained. These have been studied with the aim of producing a source emitting an unsplit line. The observed absorption patterns are explained on the basis of a quadrupole interaction resulting from the interaction of the nuclear quadrupole moment of the excited state of Tm^(169) with the electric field gradient produced by the surrounding electrons and the crystal field. Arguments are given to show that the magnetic hyperfine interaction is expected to be negligible.

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Thesis (Dissertation (Ph.D.))

Subject Keywords:

(Physics)

Degree Grantor:

California Institute of Technology

Division:

Physics, Mathematics and Astronomy

Major Option:

Physics

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Public (worldwide access)

Research Advisor(s):

Mossbauer, Rudolf L.

Thesis Committee:

Unknown, Unknown

Defense Date:

1 January 1962

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Funding Agency	Grant Number
Atomic Energy Commission	UNSPECIFIED

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CaltechTHESIS:07262011-095356834

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https://resolver.caltech.edu/CaltechTHESIS:07262011-095356834

DOI:

10.7907/F7HD-FD14

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No commercial reproduction, distribution, display or performance rights in this work are provided.

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6546

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CaltechTHESIS

Deposited By:

Benjamin Perez

Deposited On:

26 Jul 2011 17:37

Last Modified:

28 Nov 2023 00:12

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The sis by Richard Lewis Cohen In Partial FUl'f'iUmenl". or the Hequi r ements For t he Degree o f !)Jeto r of Philo sophy CaUfornia InsUtute of Technology Pasadena, California 1962 Mnny people have contributed to tIle progre8sof these - experiments. In particular, the author would like to thank: Dr. Rudolf ~8s1>auer, wilo orig1na.lly suggested the experiments reported on and vho bas Binee continually advanced the theoretical and experimental investigations. I would like to thank him particularly for nuch invaluable counsel and for instilling in the author W'l increased awarenes8 of the need for - precision in experimental work. Drs. Ulrich Hauser and Felix Boe~ for many stbmllat1ng d,iscussiolUl and SlJ.ggestions in the early sta..~. of the experiment. Herbert 1';. Henr1kson~ "''hosc ingenul ty and skill in the design of experimental equip:Jent has enormously aided the progress - John M. Poindexter and Frank T. Snivel:y, for invaluable help with the experimental 1IOrk. Vernon Stevens, !>bUy E. COhen, Richard T. Brockmeier, - J. David Ilowman and M!1rshall Greer, far hel.p vith the measurements - and data analysis. Dr. Sten Samson, :tor JIIlch helpful 1nf01"lll8tion on the chem1stl";'! of thulium and erbium. Thia research "... supported in pert by the Atcaic - r..:nerC~t CorIIais81on. Abstract ~ssbauer Effect in Tml69 The recoil · f'ree resonance absorption phenomel¥JD haa been used t,o a t udy the 8.4 key g - . ray which is emitted in the deca,y (;f the first excited state of Tml69 which ia pOpllated by the beta decay of ~69 . inth sources and absorbers in various che1ll1cal forms, hyperfine structures which are strongly temperature dependent have been obtained . & These have been studied with the &1111 of producing source' emitting an unsplit line. The obaerved absorption patterns are explained on the basis o f & quadrupole interaction resulting from the interaction of the nuclear quadrupole Jlll)ment of the exc1 ted state of ~69 with the electric field ·gradient produced by the surrounding electrons and the crystal field. ATguments are gi "en to show that the magnetIc hyperfine interaction is expected to be negligible. Table of COntents Page I. Introduction 1 II. Theory A. - B. Elementary Theor.r 01' the f.fJs8ba.uer Effect 4 If.yperfine Structure and Energy Shifts in NUclear Transitions 6 -- I. The Q,ta.drupole Interaction 7 2. Cry_tal Fields and Perturbations 01' the 4f Electronic Shell in Rare Eatth Ions 10 3. In1'1uence ot Belexation Phenomena. 17 4~ The Effective ~pole Interaction 20 5. The E1"1'ecti ve Magnetic Interaction 26 6. The Nuclear Q.tedrupole }'b llent of rr.}-69 29 In. Experimental Procedures A. Experimental Equipaent 1. - 2. B. 31 VelocIty Spectrometer 32 Proportional Counters 35 3. Electronics 39 4: Source Oven and Cryoeta.t 41 Pr8paration of SOurces and Abeorbers 1. SOurce PrePQr&t1on 2. Absorber Preparation Page rv. 41 ?eaults A. . Measurements at Room Temperature B. - V. 1. Oxide Source and Absorber 46 2. Metal SOUrce and Abaorber 52 3. Metal Source and Oxide Absorber 54 4. 56 Studies of Other Absorbing Materials Measurements Above and Below 3rxP K 59 Discussion A. The Magnitude and Temperature Dependence of the Uyperfine Structure -- VI. 65 B. Size of the Reeonance };.'ttect 68 C. Line H1dths 69 8uJJma.ry References 73 75 -1 I. Introduction The discovery by R. L. If)ssbauer (1) of the phenomenon of recoil-free gemma ~ resonance emission and absorption has aade possible varlous studles in nuclear and 80lid state physics and ex~ perimental tests o f the theories o f relati vi ty. Jobst of these ex- periments have been performed using the isotope Fe5'T, while relatively little has been done using other transitions, particularly those in - the rare earth nuc lci. The unfilled 4f shell in the rare earths is the source of soma physical properties which distinguish the rare earth series f'rom most other element8. ~tis8bauer 8cattering expertments are particu- larly useful in studying the nuclear hyperfine splltting resultlng f'rom the interaction of the nuclear IIIOIIIente with internal fields produced by the atomic electrons. There are sev eral transitions In nuclei Of rare earth atoms that can be used for recoil-tree resonance absorption experiment8 (2, 3, 4). In the present work, the 8~4 key g. . . traneitlon in TIfil69 vu 8e1ected~ Thi8 particular transition, the character- istics of which are Pl"esented in fig. 1 . has the advantages that the recoll-f'ree fioaction is large e~en at very high t.emperatures (s_ :fig . 2) because of the low energy of the transition, tt..t the half life of the 1e-rel. is long enough to give a narrow 11ne width, and that euitable sources can easily be lIBde by neutron irradiation of EJol6e. - 2- 2• D 70 yB169 3 • 473 169 . . 6SER9 . 4D . 42% bKEV 58% 340 KEV 379 j36 316 .....+A-~....,.,-71 2 -""-..............+.5/ 2 -+--+-...........3/2 .-.01....01...._ _ 1 .. 12 FIGURE 1: DECAY SCHEME OF THULIUM 169 SHOWING 8.4 KEV TRANSITION STUD IE D IN PRESENT EXPERIMENTS ADD ITI ONAL I N FORMAT I ON~ NATIlftAL THULlU~1 IS 100% THULlUM 169 . GROUND STATE NUC LEAR MOMENT: - 0 .21 NM B.4-KEV TRANS ITI ON IS M 1~ E2 INTER NAL CONVERS ION COEFFICIENT M SHELL 69 M, O SHELL 37 8 .4 KEV STATE HALF LIFE~ 6 .9X10- 9S. w IJ.. o w >CJ 0,8 I ,CIi \ \ ",, ,, ""- ", , 250 750 "- TH4PERATURE (K ) 500 - - - METAL 90 : 160 K "- "" "" 1000 " 1250 ........ "" , 1500 RECOIL-FREE FRACTION AS AFUNCTION OF I ~MPERA TURE FOR THE 8 . 4 KEV TRANSI TIO N IN THULIUM 09 - - m(IDE 90 : 240 K , - .-.. ~ - 2: 1750 I \AI II. Theory A. Elementary Theory ot the ~s8bauer Effect The beels o.f all recoil-free" ~-ray resonance experiments 1s the discovery by lotissbauer that when an .tom 18 bound in • crystal 1ts mlcleus can make transitioDs 1n which the f'ull energy of the trans1t1on is g1ven to the em1.tted g. . - ray aDd practicaUy DO recoil energy 1$ given to the em! tUng or abeorbing 8ystem. There are two basic parts to the analys1e of the effect -- the part due to nuclear physics. vh1ch shows the or1gin and form of the resonance, and the part due to eo11d state physics, vhloh shows how the recoil-free transitions occur. The cross section for gaIIIII&-ray resonance absorption ls gi ven by the Brelt-Wigner formula, where Eo is the difference between the ground. and excited-state energles, E 18 the energy of the incldent gamma ray 1n the system of the absorbing nuoleus, , r::: ~T is the total width of exoited, Vho8e mean Ufe 18 the level be1ng 7: , Ie and Ig are the excited and ground state spins , and OCT is the total internal conversion ooefficient for the transition. * '!he name 1s sClllleVhat misleading. It .hould be noted that it is not thl! recoil which 1a eliminated, but the energy 10•• due to recol1. 5 If only recoil - free transitions are being considered, this c:ross ~ sect1on JIIl8t be IIIlltipl1ed by the recoil-free fraction f~ 1. Approximating the real vibration spectrum ot the crystal by the Debye spectrum, we obtain for the l"ecoll-:free fraction (1) _ . ~E8YE - eJXf (_ 6R [_ .1 . (L)\2[ 8,!r Td.t] ) ke if + e '4- et"-/ (2) whel"e R::F-o2/.2Nt!2 18 the recoil energy tor a freely recoiling atom of - Jll&8S 14, and k 111 the Eoltamann eonstent. This tOl'lll1la gives the recoil-:free .f raction for emission or absorption o-t. p - . r-.ve :t:rom a nucleus in a crystal with Debye temperature e, ¥ben the crystal. is at temperat ure T. -6B. IT.y-per .f'lne Structure and T':nerg,y Shi ft s in Nucl ear TransiHons In genera l, there are various effects whi ch s plit and s hift the line emi.tted from a r,tissbauer 30uree. In the prescnt exper1ments, the lare e natura l -l ine widt h o f t he transition beIng studied prevents the ob servation of t wo o f the possible effects. Theee are the second order DoJ)l)ler shift due to thermal vibrations of the atom about its equilibrium lattice position ( 5) and an i8011eric shift (6) which 18 . an electric interaction due to the interact ion of the nuclear charge distribut ion with the electron charge distribution inside the nuclear core, which c an be made different for source and absorber. The e ffec t s which are significant in the present study are t he interaction between the nuclear quadrupole moment and the electric field gradient a t the nucleus, . and the magnetiC dipole interaction between the nuclear magnetic moment and t he magnetic field &.t the nuclear sit e s produced by the a t omic electrons. These t wo effect s are considered separ ately in the f ollOWing s ections. The interaction o f the nucleus with macroscopic externally applied fi elds is not large enough to be observab le with the presently a vailable field s trengths . -71. The QIadrupole Interaction The quadrupole -interaction energy i8 a re8ult of the interaction o f the nuclear quadrupole moment with the electric ~ield gr&dient at the nucleus. in the form The interaetion Ha11lltoniancan be written H :::)=~ 'Qi • (VEX j ~ .i 0-2. Z. 1quadrupole tensor with component. (2), where ~ 1a the nuclear Q~:= 2;(~ r -I) (3I: - I (I +1) !I_ eQ -16 " Qz- 1[(2[-1) (I"iI~ +ItI~) ° , eG..~ ±2 (3) 2 Qlf2.I-O I t. 2 := where I:t and.Is are to be treated &8, operator" on the nuclear spin wave tun<:t1on I II"'> vh1ch has spin I arbi trarlly chosen II axis. and spin projection Illy along an I±and I z are de tined by ,l~ I! I I, m) = ( Ix r i ly} II) m> ::: [(I:;: 1'n)(I"!: m+!)J II, -m :!/> Ii/I,m>= in/lIm>. 18 a form of the electric field gradient tensor with components -- TI U~e -a =-{6I (UXl- ::t L UYe ) ! I (VE)z (v~):7._ 24 (U ~ XX (4) Uty ±2 i D.;<y) U vi th U the potential a t the nuclear site and , X}AXY 1. = d dX", ,)Xy U. .8. We are COIIPletely free in the choice of coordinate axes . Without the application ot external fields, the system that is lDOst con'Jfmient for calculation is that in which the Pl"incipe.l axes of the gradient tensor serve as the coordinate axes in which to write t he nuclear wave function. In this syst~ which we will call the (x', y', a') syst em, the gradient COIIIpOnents Ux'y' :: Uy'.':: Ux'l' : O. In addition, we will conform to the convention ot having the at axis along the strongest component ot the gradient tensor. introduce th,e parameters eq :: U. 'It' We further 1l : (try, y' - Ux ' x') / Us'.' and • 'Yl. and eq then cOIIIPletely describe the gradient teneor in the (x', y', It') sY8tem when Laplace's equation holds: We will nov proceed to calculate the quadrupole spl1 tting of the nal69 nuclear energy leveb in the (x', y', at) system. Since the ground state haG I : .~, there will be 1» CI'*'lrupole spUtting. The matrix elements tor the quadrupole perturbation of the I : 3/2 excited s t ate (e~4 key ) can be calculated using equations 3 and 4: 2 <IlmlJ-i~/I,m> = <I)m/tQ~-(VE);j Il)m)=A(3m -I(It-f)) -2 <I,m I /-jal l m')=- (I, ml L.. Q~ •(vE);jII,m') =11f(I}+ 1!- > A _~e2Q - 'fI{2I-/) -9The reaul. ting perturbation _tr1x 1& 1b, lI2. 1n '.. 3/3. 3/Z 0 0 , -3A 3A . -jz 0 - 'Yz. -{j'1.A 0 ° 3A ° ..fa 'Y[A -3A 0 -~ ,f3 flA - Y2. ,fiy[A 0 .An exact solution o f the secular equation of this _trix yields the energy eigen\~Ue8 E'!;3/2. = 3A (1+ 't~3) l. E f Y2. ==-3A (/-I- "l73) YZ Y2. the eigenfUnction8 of which are I 11,'!3h.)=A!3hI I ,!3h.> + B~Y2.IIJ !'i) II) : VzI= AN]) II (ba) ( {, p) Ct YJ. J ~ 'l'2) + D!"~/2. II,! 3/2.) ( the wave functions are identifIed by the I z .value t hey U8UJ118 ~. ~:.O) Thus vi thout performing the actual diagonallsation of the gradient tensor , we have shown that under a pure qua.1rupole interaction the I : 3/2 excited state ill 8pl1 t into twO levels regardless o f the complexity of the gradient tensor. The field gradlent a t the nuclear 81tes coaes ~ the surrounding lons and from distortions of the electronlc 8hella pro. duced by .the field o f these ions. The tirat step 1tl evaluating the field gradient, theretore, will be to look at the structure of' the crystal and the electronic states of the rare earth ions in the crystal electric field. -10- 2. Cl'ystal Fields and Perturbatione of the 4t Electronic Shell in Rare Earth Ions The rare earth series of elements is distinguished by the fact that the 4f electronic shell is partially fUled. The electronic ~onf1guratlon fOr all these elements ean be written (7) ls22s22p63s23p63dl04e24p64dl04rnSs25p65dO-16s2. In compounds or solutions, three electrons go -o ff (the two 68 electrons, the 5d electron, .it any, and a 4t electron if there is DO 54 electron), leaving a 3+ ion Yith a partially filled 4f shell shielded by the surrounding closed shells of 58 and 5p electrons. The magnetic properties of the 3~ ion are determined essentIally by the 4r electrons, since all tlle other electrons are in closed ehells. The free ion can usually be described accurately using L-S ... - . coupling of the 4f electrons; this gives a free ion ground state with J : L+ 8 whlch is 2J + 1 fold degenerate. If ve place the ion in the electric field generated by the surrounding ions in a crystal, we find that the shielding of the 4f electrone by 11 total of eight 5s a.~ 5p electrons makes the effect or the crystal field week in com- parison Yith the L-S coupling. so that J reaalne a gpod quantua number and perturbation methods can be used to evaluate the electron config· uration of' the ion in the crystal electric 1'ie14. Thi. i. in -.rked contrast to the iron transition element., vhere the perturbIng e1'fect of the crystal tield 1a strong In comparison with the L-S coupling and J Is DO longer a good. quantum nWllber. The effect of the crystal field is to partly or cClipletely remove the degeneracy of the f'ree ion ground state, depaDdlng on the -11- crystal field symmetry~* The crystal field aplits the energy levels of the tree ion ground state by less than 0~1 ev (,..,].2000 K) for ~(8~ vhUe the spacing bet-wen levels ot different J 1s ot the order of a fev e v ("'30,0000 K) (8). The:ref'Ore, in calculating the effect of the crystal field perturbation on the free ion ground state, in first order the existence of excited atatea can be neglected. :Because of the weak coupling ( .... 10. 5 ev) between the elec- tronic statea and nuclear momenta, the _hyperftne interaction can be neglected In calculating the electronic vave fUnctions. We shall proceed to calculate the form of the 4f electronic wave functions :reaulting t:rom the perturbation of the free ion energy levels by the crystal :field. Since in first order the cr'Jstal electric field eplita the ground state of the free ion into a manifold o f electronic states of the same J, 1t ia convenient to expand the potential in te1"!ll8 of spherical harmonica, This expansion hol48 inside a volume that baa no 1'ree charge, aDd 18 , restricted to reati vely few terms because of the a;y1llllletry of' the Cr"Jstal field. Table I contains the only value. of' the expansion pe.rametere n and -V which ocour inequat10n 7 tor .eoa- ot the eoII.pounds studied in the present experi.ent. * In TJD3+ , which has an even number of' electrons, there is DO Kremers degeneracy. .12,- Table I Signifioant Oonstant.s in t.he Expansion or the Crystal FIeld tor Various U!ttiee Symmetries HeXagonal close packed structure I Point symmetry D3h n -v 2 0 3 ±3 4 S 6 0 ±3 0, ± 6 Body-centered cubic structurel Point symmetry 02 -ov n 1 2 3 4 5 6 0, ± 2 0, ± 2 0, ± 2, ± 4 0, ± 2, ± 4 0, ± 2, ± 4, ± 6 Body-centered cubic structure. Point synnetry 031 2 -ov 6 0, ± 3, ± 6 -n 4 0, ± 3 -13 The -.trix elements of the potentl&.l operator ot equation 7 taken 1n the manitold of eigenstate. having the same J are given by V-m m': <Yi.m I V(f)/ Y{m.)=(~7nIL Any Y:r"YIJ'ffml (3) , ~v The wave functions r;, = r .,.,.., c(i.m 'If m (9) I for the different crJatal symmetries fol;1.ov :t'roIIl the solutions of the seeular determinant of equation 8~ _ Results for the ground stateo! Tm3+ are presented in Table II. As can be seen from equations 8 and 9, the aetual nllJllerical va l ues of the coeff1cients dim 1n Table II depend on the - values of Any which characterize the crystal field and on the expectation ',-'a lues of r1l~ We are concerned here only vtth some baaic characteristics of' the hyperflne interaction, which can be obtained without a numerical evaluation of the Ci1m~ This numerical e'laluation is di:rt1cult in most cases because values for Any are generallY not known. -3 _2 -4 2 1 -s .1 S V2-h v22 . V.24 v-2-2 V44 · V4-2 4 2 V3-3 V. 3) V.3-3 v33 3 v.4-4 V. 42 V-6-6 V0..6 V6-6 -6 ·4 .2 ·3 4 ) V-66 V-60 Voo v06 0 , -6 V60 v66 6 III 0 6 , m • Secular Determinant Point SY1l1lletry D)h -1 V!>-1 V.1S V.1-1 V~S S 1 V.!>-S V.$1 . V1-5 Vn -5 Seoular Determinant and Wave FunctioOll tor the Ground State ot Tlu3+ (Configuration 3H6) Table IIa i" I ....I ex 14164 +0(7_216-2 1 1 2 2 2 2 4 S 6 1 8 9 ex 8-,;16-' +CX 611l r; 1 CX 9,;16 +0: 9_116S . 1 C(9_,;16- +0< 9116 . 2 C( 1-416-h. +C(7216 ex 8,1/ +0:.8-116-1 +()(62 6 1 3 0:6-4 6 01. 64164 +CX6-216- 2 1 -4 1 2 1 2 V2 0 6 6 0(16 (16 + I t ) +()(.1016 6 0: 26 (16 + 16./)+ CXw~ o 0: 36 (Y/ + 16./) +CX)oy6 (Y/ + It) / (1/ - 16-3 ) / ~ 1 1 ° Wave Functtone DegeneracY' LeYel Number (Arbttra!Z) Wave Functions Table IIa (cont t d) r • ~ V26 V06 0 0 0 2 -2 -4 -6 0 -4 0 0 -6 ...5 -3 -1 V 'n v51 1 '-3-l 's..l 0 -1 -3 0 -S '3-1 '3-3 0 11 V1-1 V1-3 V1-5 V_IS '_1) V-u V_1-1 v_1-3 '_1-5 0 v_33 v.31 v_3-3 v.3-S 0 0 v.51 v..S-1 v.S-3 v.S-S V15 - '1) 1 'S3 '33 3 V 3S 5 3 '-It-6 V20 V2_2 V2-4 0 Voo V0..2 V0.. 4 -V0-6 V V , , -20 -2_2 -2-4 -2-6 '-40 v-4-2 V-4-4 V-60 '..6-2'..6-4'-6-6 v4-2 0 0 -2 v~ 0 0 V22 V 04 V02 V V -24 -22 0 V-42 24 V v40 v60 0 Secular Det8!'11d.nant S 0 V62 V 64 v42 2 4 vM v4h v66 6 , 4 iii 6 , •• around State ot Ta3+ (Configuration 386) Point Symmetr.r 02 Secular Determinant and Wave Functions tor the Table lIb ....• vt III I 13 12 11 10 9 13 7 6 5 4 .3 2 1 Level Number (Arbi trary) .. - Degeneracy -6r: l 4o CX9_1161 v0( 9_3I63 +CX 9_S~S '"""'1::l5J.6 'V '" 5. CX (X 12S rv 1 ex 113':::6 ~- 3, rv .". 1 CX "...1 0( -_3 0( ..-S 'V" \A 1l1 6 + 11_1)(6 + 11-3~6 + 11_5.1.6 .., 3... CX Y l ·.. CX ."..1,-0( 1-' "y- 3 0( ..-'5 1.)3"'6 r 131 6 -r 13-:r'6'" ;,-) 6 + 13-,"6 "i/+ CX12.3"'i.(?+CX 121Y61+CX 12-1I61+cx.l'2~3163+CX 12cSl6!l rv .., S. \A 115"'6 or CXlor;Yl+cx. lO~Y63+CXl01Y61+ CXlo_it61+ CXlO';3li+ CX lo_r;'!6S 3 S CX 9f/ 6 +CX 93Y6 +CX. 91y 16 CX SSY/ +CX 63Y / +CX olyl+ CX S_1161 +CX s_3163 'l-CX S_r:;'!6S t -6rt • -6"l6 f 6 2 4 0<. ')6Y.6 ';' CX 3!;X6 + 0( 32Y6'2 + 0{30"1.: +0( 3-2r'6 +0(3-h'!64 + ()( 3-6rt 6 2 CX h6"i6 +CX1,l;r6h 4o()( 42Y62 40CX 4016° -!rCX 1-,. 2'16 +0( 1,_4164 +()( h-6r:r: 2 4 4 ct.. r;6y +O( Sh"I6 +CX S2Y6'2 +CX ~OY.60 ':- ()( S_'2Y6 +CX 5-I.l6 +CX S 0 2 2 6 6 4 4 ()( 66h .... CX 6h"i6 +()( 62Y6 .... CX 60Y6 v ()(6_2Y'6 +CX 6-4Y6 +CX 6 6' 4 '2 0 ', 2 4 _oJ, ()( 76Y6 +()( 74'1"6 +CX n Y6 + 0( 70Y6 +CX 7_2 +()( 7-416 +CX 7_tl 6- 2 6 2 U CX 16Y6 +CX 1L Y6 +CX 12Y6 .~CX l0Y60 4o O( l _2Y6- +C( l_hY6- 4 +CX l -6'16-6 6 2 4 ()( -;i'l6 'l-CX 2476 +()( 22Y6'2 +0( 2016° -1-0( '2_'216 ·~0( 2_4I';}.! +CX 2 \"lave Functiona 'i'/uv e fu..l1Ct :i.OM Table In) (c:ont ' d) 6 0 0 0 -3 -6 0 -3 0 -6 2 V5-1 0 -1 -4 V 1 V 4 4 1 'zm -2-5 -2-2 -21 -24 V1_5 V1.-2 '11 v14 0 v4-2 v41 -2 -2 V . V -5 v.S-5 V-S-2 V-561 0 '25 '22 '2_1 V2_4 V-15 '-12 '-1.-1 V-1.-4 V V V 0 -42 -4-1 -4-4 $ 'SS '52 '3-3 0 '00 '0-3 '0-6 '_30 '-3-3 V.3-6 V-60 '-6-3 V..&.6 . v60 V)O 0 -S -4 -1 2 5 0 V63 v33 V03 '_33 V66 v)6 V06 • 6 , 3 3 6 • .- III Point Symetr,y C 31 Secular Determinant . Secular Determinant and Wave Functions tor the Ground State or 'l'lR3+ (Configuration 39 ) Table lIe f ,. 2 2 2 '2 7 8 9 Degeneracy 6 S 4 3 2 1 Level lumber {Arbltra!,l> ex l 2 4 S CX6-S16- +()(.6-216- +CX 61Y/ +0(61l6 ex Sex 2 -1 -h 7;r 16 . + 7216 +CX7_116 +ex 7- Jl6 1 CX7_S16-$ + (X,7-216-2 + CX n 16 + CX7h164 ex $ ()( 2 -1 CX -4 8,16 + 82Y6 + ex S-116 + . 8-416 C:J.. 8_Sy6- S + CX S-216- 2 +CX 811/ +CXS4164 $ 2 -1 -h 9S16 + CX 92Y6 + Cl..9_116 +<X9-1l6 ~_'Y6-S +CX 9-2Y6-2 +()(91y +0(94164 2 CX 6,1/ +CX 6216 +0(6-116-1 +CX6-hI 6-4 ° ex ° ex ° ex CX 56166 + ()(r;3Y63 + 01. '5016° + ex S-"l6-3 + CX r;..616-6 0 6 3 ex1.616 +(){131/ +(){lo16 +CX).,.)16- +CX l -616-6 CX 1 6 CX 1 3 -3 -6 26 6 + 23 6 +0(2016 +0(2_316 +CX 2-616 .3 ex -3 ex .- 6 ex 1 6 . 36 6 + 3316 + 3016 + 3-3Y6 + 3-616 ex 1 6 ex b6 6 + ZU163 + ex 4016 + 4-316-3 + ex 4-616-6 Wave functions Wave Functione Table IIC (cont'd) I I ~ a -17- 3. Influence of Relaxation Fhenomena "Ii In principle, each of the differept electronic states produces a different electric field gradient, lthich we will call -- ... (v E)l, and a different magnetic field, Hil end therefore a diff erent hyperfine 8plitting. " This would leed to a large number of nuclear levels in the nuclear excited and ground states, vb1cb would produce , .an exceedingly complicated. ~ spectrum. }i)wver, the I!Ipin~ latt1ce relaxation perfonns an averaging proceS8 vhich considerably simplifies the Hau.Us. When rare earth ions are bound in cryst6l8, there 18 a strong interaction betvetm the J of the 4f electrons end the lattice~ Because the orb! tal angular "IiICaent1.lll! is not quenched, "the electron spln.lattice r elaxat ion times are very sbort( substant1ally lea. than 10- 10 8 (9) at l"OOIIl temperature), 1Il1ch shorter than in the cue of the - iron transition elements. '!'hi, time is shorter than both the l1fet11le o f the nuclear state (""'lO~8 8) and the nucleu preceaa10n period (-10- 9 s). The nucleus does not 1"ollov the rapid reorientations of - .... the el~ t ronic spins because o f the veak coupling between I and J, and therefore experience8 a verage values of vi" and ii resulting from an ." a verage over the electronic states. This JllMn8 that ,.. can restrict the a~~raging procedure to the electronic states only. Assuming that the averaging proceat over the electronio states t akes place 1n times very much emaller than the nuclear llfet~ and. the nuclear precesa1O!1 period, we obtain the following a veragesl ~)I 'VE -\ H = (10 ) = L. ~(-£i~T) (J/J L where exp(-Et / kT) is the Bolta-.nn .pop.1l.atlon factor for the electronic otate with energy Ei .od T 1s the 1attice temperature. The averaging 18 shown 8ch~t1call.y in fig . - 3. -1.9- SP LI T BY CRYSTAL FIELD INTO t1ANY LE VELS - FREE ION 3H6 C'O FIGURATION .. NUCLEAR QUADRUPOLE SPLITT I NG AVERAGING PROCESS RESULTS IN 2 LE VELS IN I: 3/2 EXC I TED STATE rf..-tJ+-J--<====) ,._--- ELECTRON SPIN-LATT ICE RE.lAXAT I ON ~1AKES TRANSITI ONS AMONG THESE LEVELS AVERAGI NG OF QUADRUPOL E SPLITTING IN EXCITED STATE NO NUCLEAR QUADRUPOLE SPLITTI NG (1= 1/2) UNSPL IT GROUND STATE \ '- - - - - - - QUADRUPOLE SPL ITT I NG IN NU CLEAR GROUND STATE FI GURE 3: ILLUSTRATION OF THE AVERAGI NG OF THE QUADRU POLE SPLITTING BY THE SPIN-LATTICE RE LAXATION PROCESS. - 20- 1.. The ENectl ve ~pole Interaction The electric field gradient at the nucleus o~ an ion in an 10nlc crystal results ~ ~ principal eourcest a. the direct field gradient V~' due to the surrounding ions - b. the dl8tortlon of the tilled electronic shelle by the field ot the lIUr.l"OUl'lding ions c. the distortion o~ -partially tilled shells by the field of the surrounding ions resulting 1n d. ~ V E" the dbtort1on ot the f'illed ahells by the f'1eld reau! ting hom the psrt1ally filled shells, resulting in V "E'" ." These eomponenta vill be analysed in the above order. a. be shown, In iOM o~ the rare earth aeries, as vUl ~. VE itt relatively SJIIall aDd can be neglected. b. 'l'heaeeond effect 18 ealled "anUahield- 1n~~ since the net .trect of t he distortions of the eloeed ahelle i . .. , to increase the :field gradient V E reau!ting from the direct crystal f 1eld. The antlahieldlng e rteet caD be considered in eIther of two complementary ways. The 1'1rst viewpoint aasua. that the field due to the nuclear quadrupole DlOIDent defol"llll the electronic shelle of the atell, inducing a quad:rupole JlX)lbent. in them which 1. - If tt.. the nuclear quadrupole 1IDlIent: 'l'he quadrupole 1IIOIDent of the atom 18 then (1. ~) tIM. the nuclear quadrupole DIOIIent (if the induced ~t 18 in the .ame direc- tion as the nuclear moment). If' the atom 1& placed. ~ a perturbing field gradIent and the enet'gr ep11111ns betVII!MtD the nuclear orientations is measured, the direction. of the induced qtUIIdrupole IIlIMUt ohuges Vith the nuclear orientation, and the total quadrupole interaction is then g1"en by 1lQ : (~tom) • vi' : (1 - b')~uclear' V E' where VE' 1& the gradient tensor of the crystal field. The second viewpoint 18 that it an atoe is placed in en In- hoIIOgeneous electl"1c field, thia field will distort the filled electronic shell., and this distortion produces a gradient at the nucleus which au.glleDts or decreases the gradient rro. the extermil.ly applIed field. All baa been shown by Sternhe1mer (10) J theee two 'lrievpointa are equivalent in first order, 1.e., as long .. the t!e:fOl"lll&tion of the electronic shella 18 1I!IIIill, vh1ch is ~ the cue: Using the first of theae analyses, V'b.1oh b .moe general.1y uae:t'Ul and easier to deal Yith then t.h4t second; Stemhet.r (10) baa ealculated the etae of' thil'leffect 1"or ve:rioua closed ahell ion.: W- ean malte an ••tt.te o:f <! 1W' the c1.oeed sheUa of tbe tpe3+ lon by startinz with Sternbe1mer's value Of ~= -143 ± 1~ tor the CB~ lon, ¥bieh has the .... closed shells as the Ttt3+ ion~ '!'be existing cal- culations reveal a rough variation of' '( with 1/71- for a gtveQ cheU; Therefore we UtaUJDe a SOIiIe'What • Iller value of ¥ :for T,m3+ (z: 69) tlUlll tor CfJ+ Since vI I I a» (z :; 55): ¥::: ~lC1O in tul'tbel" ealeulations. We will use , we can neglect V ' e. ;\f l!; in ccmpIII.rieon with " 0 V..E f • !!.be distortion or the pvt1&ll.y tilled 4f' shell by the crystal tield 18 the _in source ot the eleetric neld grad1ent, and will 'be analysed In tome detail. All each or the differ- ent 1t t' electronic states produces & diN'erent 1'1e14 gradient at the nucleus, we .hall aepa.!'ately calculate the field gradient. ( V E)l 1'ar . each of' the cii rf'erent electronic substate.8 characterised by 'ft , the general w.ve function obtained earlier for the 4f' el.etron8~ We evaluate the gnd.lent toollOr ( V E)i &8 tollovai As8U.lll1ng that all the 4r electronic charge i . out.ide the 8~id of nucl.e&l" shape, rL (r) 'f where =/ p~r/)d r'= 2e! }t'(fl) ~(t)df' 'r- F'I I; - r/_, .~ (~) iI!I the potential in the neighborhood of' the nucleus fraIIl -:t is the'1&l"1able over vb1eh Yeintegre.te the 1 electronle eha.rge~ Expanilhg 11 - y r ln "phedeal 'Ila.l'1IDnlea ~ the 4f' eleet:ron8 and 1 dIfferentiating under the integral 8ign, we obtain the Cartee!u COUIPOnenta of ( V E)1 : -23- ¢Xy:: 2e(-iV7f (Yz~ ,(-2)<r 3) ¢x~= 2e <-I-lf (y~ + 'h-') ><r- 3 <r- ,e)Yr=2e(-i-fff(YzI- Ya-') ) 3 ). From thb we obtain that in the cu. of' the D:3h .~tl':Y('" page 14) ~xy : 1>Y'I : 1>... : 0: '1hle -.me that the prinoipal axea of' the f le14 gradient tensor lie along the eoordlnate eyartem \1MIl to expreaa t he Cry8tal field; this 1$ not true f'O!' the C1! Uld "31 sywDetriea: d~ (V 'E)"', the part of the field gJ:'tIdient resulting f'rom ~he distortion of the olosed shell. by the field of thAt 4r electron., 1& very dU'tleul.t to ealeu.late lir'ee1aely: In principle, it could be caleulated byperturblng the cloaed ehell wave :f'uncttOl'l8 vith t he potent.1al due to the 4t electron., but theextenaive overlap o r t he 4r wave funct ions nth the closed ahel! wave1\mcticma (vb1ch are t hela8elve8 not well known ft)r the rare earth eeriee) ak•• the integrals very di f ficult. However, we can give _ arguments to justU'y the assumption that VE"'« 4U&!itatlve vi", i.e., that the fIeld gredi.nt produced indil'e<:tly by the 4t electllClU through the . polarisation of-. the cloaed .hella 18 con81derably -Uer than the d1rect1'1eld gredient hom the !i.f' electJ"OGa: . It oan be .hown (U) the.t <r- tor · 3) the outer eheU. with J..:If 0* 1a aona1derably ....Uer .* S states are not per~ f,n f1rat order by the 4t e1.eetl"Oba, and shall DOt be COJ'W1dered • . (r- 3 ) for the 41' elect ron.: Since the gradient at the nuelear sites 18 proportional angUlar integrals < Yz"tn) (vhleh ~ 01' than to the t he eame order o f magnitude for all the shells) and propoTtlonal. to -3> . . < r I ~" . V E f t 1e ...uer thful Vl!i even tmdv .t~ de!'or-.t101ls o f the filled shells and viU be neglected. hereafter. ' Thu8, it ba8 been .bO¥n that the -.101" ooatrl'Wt10n. to the f le14 gradient at the nucleus CCJa t'l'OIl the ~try of . the ~1' eleetron shell and t he ant1ehle141ng o f' the eryetal neld:, ~ . 110 that 'V-' ~fT V E:: VE + V Et. 0 (12) Aa explained on ~ 11, when the apia ~lattlce relaxation t:lme '1. short, lie cannot obMrve the fie].4, gN41ente(v'E)i for each ..- :. " - - _. ~ ' eleetnmle sub.tate butratheir ObMJ"Ve an averase fte14 gN41ettt VE Which reault8 hom the M:tf'eJ'ent electronic etatetl wigbte4 acoording . to their Boltlllann t'aetor.• (~~ 10): '.!he totalett-.etlve field . g:ra41ent i8 then vi : v"E + b"V i' . tJ (13) ~V· E · 18 not intluenced by the .a veraging proces•• 0 ' "' ~VF: 18 e.eenti~l.y 1n4e}Ien4erlt o't the ~ture, eo that - - &I'lY t eaperat\ll'e vV1attonof. VE 00IDIt8 only :tnIrIDV 'E" ~ ' '!be tempe".---:. . . ·. t ure dependence of' thef'1elcl ~1ent V E is tho . . tol1ove, At wry . low tecrperatures (kT<<: El), only the loweteleetJ'GDle etate ia .. -:r; ..A.R - JOp1lated, and V E 1. V E1 -ro. the love.t eleot:nlllll0 ..tate. At in· tenDed1ate temperatures (ItT ~ Et), au tlw electronio state. are ---:i'; JIOpllate4 and. ' V E . . . - 18 gi van by the avenge frClllquatlon 10. At high temperature. (kT»Et) all the .e leetron 8Ubatatea Yi1l be ~ ~ 25· popllated, which .ena that there rill be DO pref'ened orlentat1orl of ~~. J. 'lll1. re8Ultis in a net eharge dietr1butico of apher1eal. syIIBIeUy wb1ch produces a cere field gradient at the nucleus. The QUadrupole interaction produced by the 41" electron. rill therefore approach ,el"O at high temperatUJ"es. !bvevel', by D!t&D8 o£ the ant1ahielding effect, the 4r electrons atUl eontdbute a 88*ll f1e1d. gra41ent which can be calculated by tre.ating the 4fshell ... a charge dlatribution Of spherical 8;y111l1etl"'J, like the closed ahelle. Thue, at big,.1 temperatures, the ~in1ng et'f'eotive 1'1e14 gradient is approx1ately ~V E' ~ -265. The Effective Magnetic Interaction The magnetic byperrine interaction is given by ... ~ Hat : ; ffn . H (14) .... vhere jUn is the nuclear magnetic moment end H is the magnetic rield at the nucleus. In the absence of an external MgDetlc field, the field at the nucleus results from the spin and orbital angular momenta of the atomic electrons in partially filled shells, in our caee the 4t shells. Under the assumption of pure L-S coupling, ecpation 14 can be revritten (11) (15) where the constant K contains such things as radial 1ntegrala, electronic charge, and g- factors. - - If' the coupling bet ween I and J is usu.d negligible (see page 17), the only significant term in equation 15 is KI.,Tz, 110 that (16) Aa in the case of the quadrupole interaction, evaluate '1M first (lIm )f'or each of the ditf'erent electronic s t ates. It 18 necessary to treat the degenerate and non~degenerate states separately. For the non-degenerate eleotronic levels, lie can show that the magnetic interaction 1s aero in each .tate. The non-degenerate electronic vave fUnctions are real except tor a trivial phase factor . because the crystal field Hamiltonian (eq. 7), which does not contain magnetic interactions, 18 invariant under t1JDe reversal. Thus the electronic wave functions contain equal admixtures of ~ and y,? : -21 - (Jz ) : 0 for states of t his torra; thus the magnetic hyperfine interaction vanishes for the non-degenerate electronic levela. If the electronic states are degenerate, the situation i8 more complex. fUnctions It we cona1der a doubly degenerate state nth wave IfA and 'fB' the general wave functions for the degenerate .level are given by 'f, = Q. I 'Yl Cl z Y;; +- b2 Y& 1ft. + h, 'fs 1 QZ/2 +-1 bz.t-=-, ct:-a.2 +- b~b2.. =0 • At higher t emperatures, we mat consider the tact that the electron spin-lattice relaxation is so fast that all the electronic . states are poJUlated during the time of the nuclear deee,y and so we JllUat a verage ove~ the );X)pUlation~ Since 'f'1 and 'fa are degenerate, the Boltumm :factor Yill be the same 1'01" each, and the average ag ~ netic field at the nucleus ~ this degenerate level le l.<~jJl./f,)+ ~<'Iz/J~/'iz>= z =I [/4,!'"{ 'fA I J~IYA) +-/b./1.< tslJaJ +1~2./2.(t J J~ J ~) +l bz./ (,t8/Jl-1 ta~ ts> .:: f[(lo} I tjCl.,J'<'IA I Jz.1 'fA) + (jb./2. ~ /p,/2.) <tal J~ I 'fa>] = ~[ ('f.q 1Jl:/~) +- (V'B/J~I 'f8)] • Since the 8ubmatrices of the-cryatal field perturbation (aee ~ble ~I) 1':roIII which If'A and ~ vere :found are Herraitian conjugates, -28- -'In then fa =L (1- rn )j with flLm/:: ICl m I ~ -ltl (DO ~ appee:rs 1n both Then ~ and 'fB) . <t Url ~) =-l /<Xmlm .<'fBIJr I ~) ~ ~ 1~_ml2. (-m) '1. ,." so that aM thus nO doublet state gi ves any hyperf'ine interaction . i f the elec - -10 t ronic spin-lattice relaxation t 1ml!l is short compared to '" 10 seeonds. Since only t he degenerate state. contribute to the magnetic interaction, the a veraging by the spin-lattice re1axatlonproce •• 1• . leS8 , critical with respect to the re1.&xation t1llle than that 01' the . quadrupole interact ion. -29- 6. The Nucle&l' ~pole Ibmeot of rna169 }bclel in the range A. : 150 - 190 are ~ly vell described by the unified lIIIOdel of Bohr, Jobttelaon, aDd BUs80ll (12, 13). In this model, an odd A nucleu.~. coa8t4ered as. core containing all the nucleons but the last (odd) nueleon, vldch then lIIOVee in the field . . of the core. Tba core 18 defonaed into an axially 8~trlc ellipsoid. Blcleer .tates can be aade 1"rom COIIIblnatlons of rotational states o-f the core and intrinsic states of the last nucleon, Vith the angular momenta of the core and the odd particle eoabining to give I, the net nuclear spin. The predictions of t he above lIIIOdel ( . . 13) lire in good . agreement vith the spectrum of et al (14). The rrrJ.69 studied expe:ro1Jlenta1ly by lloehll I : ! ground state of er.l69 1s the lowest state of .. 1/2, 3/2, 5/2, 1/2, 9/2rotattonal baDd, and the 8:4 kev (I : 3/2) excited state studied in the present expert.ent eorreepom. to the second state of t hat band. SollIe ucited states eorrespondlng to intrinsic exe1tations of t he odd proton are alao Observed 1n thedeclliY s cheme of TJztl69 (fig. l)~ '!'be unified lIIOdel allova us to aka eetblates of the nualear JIIOIIIent8~ We can calculate the qualdrupole -..mt 1"or the 8:4 ,lutv · state by aaeum1ng that the a1nglA particle contribution vill be small in comparison to that t'rom the detoxmed. core~ Tben the NU.1IOn lIIIOde1 (13) gives _ (3KZ-Z(HI}J.i 'lR2( I + ~/z.+ .. . ) Q - (I-rl) (2I+3) J 5 0 . 0 -30where K " ~ is the project ion of I on the axie of sysetry of' the core, ~ i~ tbe detol"llBtion of the core , and Z and. Ro are the charge and the ~ : 0.28 &Ddilo:l.4xlO-13;./3 eJI, mean radius of tbe nucleus. Using (13) we find Q : 2.1 x 10- 24 crtf?~ We will use thie value Of Q in evaluating the quadrupole interaction. Since no magnetic byperfine interaction ls observed, the magnetic moment will not be calculated. - 31 ~ III. Experimental Procedures The technique used in measuring the hypert"1ne structure was to measure the transmi seion o f gamma rays froa the source through a thin foil or resonantly absorbing aterial. Using the linear Doppler effect , the absorption lines are moved relative to the emission Unes by moving the absorber toward and away from the souree. When, at a certain speed, an absorption line coincides nth an emission line, . absorption peak results. an ~ 32 - A. Exper1lllental Equipaent 1. VelocIty Spectrometer The velocity spectrometer vhich provided t he ao'~nt of the absor ber consisted of a prec ision ground ea vhich converted - rotary motion to linear to -and-fro motion. The dIfferent velocities required vere obtained by changing the angular velocity of' the c_ vtt h a gearbox~ The velocity range covered vas O.066am/s to 10~O am/s i n a t otal o f 69 steps. Th1a type of' velocIty drive har; the ed'fantagea of being accurate, simple, and reliable. The mechanical arrangement used is shoWn in f1g. 4. The Calli vas made of hardened s t Ml, bearIng against nat hardened steel fol l overs. The ampl1t ude of t he stroke vas 1.9 em, 1.7 em of wh1ch represent ed t he region o f constant velocity. To reduoe vibrations, t he motors and gearboxes vere JIIOWlted on ,a seperate ebas81. 1'l"CIIII the cam mechani8'lll. The following tests have been perfol1Ded to cheek on the accturacy 8lId constancy Of t he velocity apectl'Olleterc a. Stroboseopleal;ly observing the rotation of the motor shaft, no dependence of the .,tor 'a~ on t he load vas detected. b. A static check o f' gear and cam linearity vas made by measuring the carriage dIsplacement as a f'unction of motor ahatt rotat ion, usIng a dial Ind1cator. '!'hie indicated that the carriage vas alv&ysvtthin 't 0.001 CJ/1 ot the correct poeition. -33c. To cheek the proper behavior of the · velocity spectrometer at high speeds, a velocity tranadueer vaa used. This measurement showed no variation greater than :t O~l em/s at velocities up to 2 emf. and no variations greater than :!: 0~25 ca/s at velocities up to 10 em/.~ These checks shoved that any inaccuracies in the cam drive d1d not influence the experimental results. Photoelectric gates restricted the meaeurement to those regions of the motion vhere the speed vas constant. A l1ght beam focused on a photomultiplier vaa interrupted by a sector attached to the cam. The photqDa1ltlpl1er output vaa used to gate the sa&lera. Two separate photoelectric gates vere used to enable positive aDd negative velocities to be studied separately. '!tie gate. operated alternately, each gate va. open 34i· of the time, and closed the remainder of the time. FIGURE 4; CAM DRIVE MECHANISM USED IN VELOCITY SPECTROMETER ~ ABSORBER 1 C~1 ~ SOURCE , -i:" , IN -352. Pl'O'portional Counters Beeause ·ot the extremely low energy of the transi Uon being studied (8.4 kev), p!."OP)rttODal counters vere used to detect the gu:aa r~s. The. . vere bullt using en aluminum tube (40 ell long and 10 em tnside diameter) tor the cathode, and a stainles8 steel wire (0.06 _ diameter) tor the anode (see i'ig. 5)~ 'l!le enda of' the aluminum cylinder yere sealed: off rl th Pryrex end plates Vhtch &leo auPJlC):l'1;ed the anode rlr.~ . The counter vas filledrlth a mixture of' _ l~ methane to a pres8Ul'e of just under one atmosphere~ argon ~ The counter rlndOY vas a 1 lEI thick (200 mg/~) beryllium dise 4 em indlameter~ Counters vere assembled: using an epoxy ree1n 1'01" rastening the end plates and the ylndov, and then evacuated to a pressure of 10- 5 _ be1'ore filling. Arter f'illIng, the anode wire vas electrically heated: to 1mprove the resolution. Thereeolutton attained Y&8 about 171> at 6 key, Vhlch 1s close to the theoretical l1lD1t~ Unrortunately, this resolution vas not good enough to resolve the 8~4 key gamma-ray Une hom the thulium and erbiua L X·ray COIIPlex present .. a strong back- ground.~ The spectrum abovn in fig. 6 re8U1ts froID the composition of the e~4 kev gIUJIIIl& ray end the L X-ray COIIIplex~ Dle to the very high counting rates obtained (ae high as Txl03 counts/second in the channel, and·a total counting rate twice that), .0.& precautions vere necessary to prevent tnstability in the gas amplification and avoid rapi4 decomposition of the counttDg ~. The counters vere run at a relat1vely low ga8 amplIfication ot about 5x103 (high voltage about 2~2 kv), lind then would count i'or about 1010 PYREX END PLATES STEEL ANODE \"lIRE ~ , FIGURE 5: CROSS SECTION VIEW OF PROPORTIONAL COU NTERS USED ~ ""EPOXY \ ALUM It-lUM CATHODE I, fERYLLI UM WI NDOW ~ I I 0" - W ...I u 0 ::::> Z III I- Q.. I.LJ a! ::I: <z: u z z UJ 1,000 2,000 3,000 4,000 • • 10 0- • 20 .- • • •• • •• •• •• • o· •• I • ...1...1 40 q(~ ...I" 1 • I I 00 • .:t ~ > I.LJ • II • • 1 ...I • 30 • • o • • • • ., • • • •• • 70 •••••••• • •• • •••• 60 •••••••••• 50 • o •• CHANNEL NUMBER FIGURE 6: PULSE HEIGHT SPECTRUM OF OUT PUT FROM PROPORTIONAL COUNTER SHOWING THE COMPLEX SHAPE RESULTING FROM THE X·RAY BACKGROUND. THE POSIT IONS CORRESPOND ING TO THE ENERGIES OF THE STRONG ERBIUM L X·RAYS HAVE BEEN IND ICATED • . t- "" I I ....., · counta before the HIIIOlut1orl deteriorated serioualy. At this point, heating the anode Y1re generally reatored the original re801ution; thia process could be repeated several times before it vas neeeatNLl"Y to refill the eounter~ The output pUlse was abOut 5 mv for an e key 3. Electronics A block diagram o r the electron1c equipment used 1s shown 1n f 1g . 7 . The signal 1'l'OIIIIthe countere vu ted 1Dto a cathode follower preampl1tier tollowed by a delay. line-c11pped pulse -.plitt.r and -- di fferential discr1m:lnatol". The v1n4ov of' the -differential dbcrim- inator vas set appreciably wider thaD the actual width of' the line - being measured to min1m:lse counting rate drift: due to ga1n changes. 'l'he pulses f'roIII the d1:ft erential dbcr1ll1nator were counted by 8. tranaistoriaed mult1- channel scaler with autoaat1c print out. The scalera were controlled by the photoelectric gates. The 81gnal :t'roIIl a 10 kc quarts-crystal-controlled oacl1lato%r vua1Jmltaneously gated end CQUllted to detena1ne the actual JDeUU1'ing tt.. The measuring technique employed w.a to alternate runs of' about 10 minutes with the absorber IIIOving at 12 <:m/_ (a standardbing velocity hi gh enough to el1m1nate resonance absorption) v1th runs o f - t he s.., length at t he meuuring velocity v. in the f igures vas def'ined as (Count rate at 12 m' - CCiWi£ ra 'Ibe "E1'tect- &8 . plotted count rate at v) at 12 Ci/s . • The equip.ent vu autoat1cally controlled by 8. dev10e which alternated atandardising erId 1IIeUuring runs and printed out the scaler. - at the end of the run. PROPORTI ONAL COUNTER PREAMPLIFIER GATE AMPLIFIERS TO CLUTCH ANP CAM ORIVE MOTORS . 931A PHOTOMUlTt- \. ' PLIERTUBES ---- - I- AMPLI F I ER ANC . SI NGLE CHANN EL to KC CLOCK CONTROL CIRCUIT FIGURE 7: BLOCK OIAGRAMOF ELECTRON ICS ,,. GATES : . I SCALER' PR1NTCOMMANO · I' PRI NTER ~ i .-, o, -414. source Oven and Cryostat The source temperature vas varied. rrc. about 6tfJ K to 'l2.«P K during the present exper1ments~ The temperatures below 3«P K were attained by the use of a s1Jlrple cryostat with 4l-y ice or liquid nl trogen as a refrigerant. tranaml t the g&mII8. rays. BerylllUJ1 Y1ndova vere used to Temperatures below the boiling point of nitrogen (7.,0 K) were attained by pumping on the 'nitrogen; in thb range the temperature vas controlled by a pressure activated switch that measured. the vapor pressure of the nitrogen and actuated & solenoid valve in the pumping line. The source heater used 18 shown in fig . 8~ It had the advantage of baving the heating element isolated. from the source, 80 tllat the atmosphere on each could be controlled separately to minimise chemical reactIons. By using both b11'1lar and ordinary winding of the Kanthal heating coil, it vas shown that the magnetic field due to ' the heating current, a lII&Xilllllll of 50 gauss, had no influence on the pattern of source lines. The oven temperature "... controlled to a fw d.egrees and monitored by a thermocouple. - 42 \BERYLL IUM WI NDO\,J · ..\r/ATER COOLED BRASS SHELL ~ ~ • • • A li03 BO T • • .. • • • • • • • • • • • • • • : : _ -_ SOURCE ~ ........ ..... ....... . ";::- • • • • • • • • • • • • !o !o I" ...., STAiltJLESS I . STEE L ALUNDUM' CORE KANTHAL "~ IRE , .... .... , .1 1 ) 1 FI GUJE 8: SOURCE OVE N USED AT TEMPERATURES TO 1300 K B. Preparation of Sources and Absorbers 1. Source Preparation Sources were produced by irradiating natural erbium metal and oxide for three veeu 1n a flux of 5xlol4 N/es?/s 10 the *terllUs Testing Reactor at Idaho Falla, Idabo. '!'be specific act1vIty obtained vas usually on the order ot 10 C/g~ Sources Of about 20 me. were used, result.1 og in a counting rate ot about 3 , 000 ( gamma rays plus L X-raya)/secOnd 1n the channel, attertbeattenuat iOD by windows and the absorber photoab8orption. The strong internal conversion of the 6.4 key transition required relatively high source - activity to get useful. gaIIIID& counting rates. Since ·the experiment is primarily a study of the interaction of the nuclear quadrupole moment vith the electric fIeld gradient depending on the crystal lattice symmetr1es, the ettects ot the radiat10n damage to the lattice from the reactor irrad1ation had to be taken lnto account. To eliminate these ettect., the oxide aoIU'ces were chemically proce88ed atter lrradiation. They vera dissolved 1n acid, precipltat ed as erbIum oxalate, and :then heated 1n oxYgen to form the oxide. Metal sources were mad.e1ther by vacuum evaporation at a pressure ot 10. 5 l1li1 Hg or better, or 1'l'OII lmd1ated metal filIngs with no post.irradiation treatment • . This procedure vas justifIed because the types o .f radiation ~ caused by theral DeUtron irradiation and subsequent gaIIIII& radiation YOUl:d be expected to be annealed out a t room temperature 1n the metal. -44. sources were usually mounted on beryllium discs about 1 _ thick and 4 em in diameter. Powder sources (_tal and oxide) had to be apread very uniformly to minimise the effeeta of self.absorption; they vere held in place vith a coating of paraffin or by clamping vith a beryllium cover disc. Berylliua vas particularly useful tor source holders because the low Z all<Ned the transmise10n of the 8;4 key with only small attenuation and gave little bremstrahlung in stopping the electrons resulting from the beta decay. sources of III1xed (Tm-Y)2~ were made by dissolving the acti ve material and the yttriW11 together in acid, p-ec:lpi tattng the 1II1xed oxalate, and heating in the ssae we:y as the pure Er~· IIOUl'ces. -45 2. Absorber Preparation The resonance absorption cross section vas approxlMtely 7xlO- 19 cmf!/atom (8ee eq. 1). Taking into account 11ne broadening effects ani photoe.bsorption, the sst useful absorber thickness vas in t he range of 2-5 mg/crJ!: It vas possible to make uniform layer. ot thulium oxide and garnet in this thickness range by allOWing a 8uspen- don ot the powdered compound in an organic solvent to settle onto a beryllium disc. The same · di8C then served as the suPlJOJ't tor the ebsorber, since i t was rigid and transparent to the gaaa rays. The powder vas covered vi th a thin layer ot paramn for mechanical - stability and protection against atmospheric bua1dity. The eo&ting made no noticeable difference in the observed a~rptlonspectJ'\DI. Metal absorbers were made by evapOrating thulium _tal fl'cm a tantalum or tungsten f ilament onto a beryllium backing disc. It V88 necessary to etch t ho beryllium slightly to make the thulium layer adhere. P.t'eeeures from 10- 5 to 10-7 l1li vere . .lntained during the evaporatIon, and a shutter Y&8 used to prevent depodtion during the outgassing procedure and the first part of the evaporation. Since the e vaporation was done by 8ubl1JD1ng the thul1W1 f'rGa the 110114 stat., contamination by the boat aterial vas not a problem. There V88 a noticeable improvement in the !Sharpness ot the absorption Un.s when thepreS8Ul'e during evaporation vas lowered troa 10- 5 _ Kg to 10- 6 , but further improvement to 10-7 a4e no ob.ervable d1f't.renc.~ Attempts to anneal the metal absorbers to imprOve the crystal structure of the t huliwa layer :reeulted in very bad _.aring ot the absorpt1on apeetrum,probably due to d1ff\1eion ot the berylliWll - backing into the thul1Wl1. Absorbers o f thul1Wl1 d1ftuaed 1nto copper (.11111lar to those used by oter (3» were made by vacuWll evaporat1on of thu.l.1Wl1 onto a clean copper tOil, heating the combination for prelim1nary annealing vi thout breaking the vacuum, and then annealing in a pure hydrogen atlllOsphere for 12 houl's at 96d' C. This IiIIOUnt Of heating vas POt sufficient to distribute the -thulium through the copper with perfect unif'ol'Jlli ty, but at least some bad d1t1'uaed eOlllpletely through the copper. ~47- IV. Results The ground. state of Erl69 produced by neutron ir:radiation decays to the 8~4 key state in Tm169 : Thus the source consiat. of r .e .dioe.cti ve thuliilm ions in a surrounding of erbium ions. The local surrounding of the thulium ion8 in eouree and. abeorber 18 theref'ore diff erent. This dIfference can be neglected in interpreting the results of the present exper1lDent because of tbe chemical e1m1larity of these two element.. No experillental evidence vas found. tor & different byperfine structure in source and absorber under equivalent - cond.i tions. A. Mea8uremel'lts at Room Telllperature 1. Oxide SOurce and Absorber Figure 9 shovs the trlUl811iSaion observed . . a function o~ velocity between an Er2<>:3 eource aDd ~ absorbel". .According to For ione Part II, the pattern can be explained in t he ~ollov1ng Yayl In physically equivalent lattice sites, the nuclear aId.sston line is symmetrically spl1 t into t w components 0-[ equal intensity. The split is produced by the quadrupole interaction only, stnce the magnetic interaction Is cancelled by the spin- lattice relaxation phenomenon. The nuclear absorption Une is s1m1larly split into two components. The relative position· of ellis8ion and absorption 11ne8 is illustrated in 1'ig. 10 assWlling identical spUttlngs in source and .. absorber. The resonance absorption should be the strongest at ae1"O relative Yelocity between source and absorber,.tnce each em1.e1on line coincides wit h an absorption line. It the 8plitting between the lines 18 A E, and. i1' we move the absorber toward or a".y f'rcIe. the source with velocit y v = c ~ I we obtain ai4e peak. o~ one-hal1' the intensity of the central peak which result from a coincidence between one emission line and one absorption liDe. In this Yay, we obtain the three peak pattern 01' rig. 9. The eXplanation above neglects the 1'act that in 'l'III2O.3 the 'lD ions appear in two physically inequiva1ent aites, in the ratio of three TIll ions in aites With C2 8yaaetry for each 'lD 100 in a alte V1th C31 symmetry. We obtain two quadrupole doublets in the intensity ratio c::: Vl W 0 z < z • I • • • • • • • • • - • -- - - - - - -- - _ .. _- - -- • • • P 0 N. ABSORBER VELOC ITY (CM/S) -- - - - - - • • • • • • • •• • • • • • • • • P. ABSORBER TOWARD SOURCE • • • • • • • • • I \0 I ~ FIGURE 9: PATT ERN OF RESONANCE ABSORPTION OBSERVED WITH OXIDE SOURCE AT 300 K AND OX IDE ABSORBER AT 300 K. RESONANCE EFFECT IS DEF INED AS COUNTING RATE AT 12 CMIS - COU NT ING RATE AT V COUNTI NG RATE AT 12 CMIS w w u • u... u... w U ... 1% l- 2% - 50- . LEVELS IN SOURCE · ± 3/2 ±1/ 2 RESULTI NG EMISSION SPECTRUM ""/2 Eo RESULT ING ABSORPTION SPECTRUM LEVELS IN ABSORBER ± 3/ 2 I- ~Ed + 1/:: E. + 1/ 2 bAEd i Eo v=0 OBSERVED ABSORPT ION PATT ERN RE SULTING FROM ' H 11SS ION AND ABSORPT ION SPECTRA SHOWN FIGURE 10 : EXPLA NATION OF 3 PEAK PATT ERN SHOWN IN FIG. 9 3:1 f'rOIII these tvo lattice sites. In the presence or the st.rong peak., the veak peaks resulting from the lea8 populated sites have not been observed, and. we rill neglect their exietence in the 1nter-. pretati01l of' the experimental reaul t •• 2. Metal Souree and Absorber If the source and absorber are erbium and thul.ium metal, respectively, the resultant l~rfine pattern ie ~letely dif~erent from that of the oxide source IUld absorber. The observed pattern (see fig ~ 11) shows that in both souree and absorber, any byperfine splitting is eall compared to the 11ne width observed. Thia abovs that the field gradient at the nuclei in the metal (.YJIIII8try ~h) 1. lIl1eh Weaker than that in the oxide. a:: « z 0 II) ...., :z u « ...., co II) 0 a:: t- 1°' Q. 0 :z 2% • • • • 2 • • • • • • • • • • ~P 0 N'" 2 ABSORBER VELOCITY (CM/S) FIGURE 11: RESONANCE ABSORPTION CURVE FOR METAL SOURCE AT 300 K ABSORBER: METAL AT 300 K • • I I • • • • • • I I W Vl -54. 3. Metal SOUrce and Oldde Ab1lOrber CorrespoDdlngly, 1:r a _tal eouree is used with aD oxide . absorber (or vice versa), the moving of the single liDe of the metal over the two lines of the oxide . result. in an ahsorption pattern of two peaks (8ee tlg : 12), vlth the s . . energy separation ail tn :fllJ: 9, representing thequedrupole splitting in the oxide absorber. ~ : o 3.... ~~ w " W ~ ~ W .... U • 2 • • • • P • 0 • til • • • ABSORBER VELOCITY (CM/S) • • • • • • 2 • • • • FIGURE l2:RESONANCE ABSORPTION PATTERN OBSERVED USING OXIDE SOURCE AT 300 K AND METAL ABSORBER AT 300 K • • I I I \;" Vl 4. StudIes of Other Absorbing Mat(!rial. In the same fashIon, the absorption spectra 01' .various other materials were studied using metal .and oxide scur~a. For example, an absorber of thulium dlffuaed into copper in the ratio 1:30 (atomic) vas stu4ied~ The absorption spectrum of thta absorber taken V1th 8. source emitting an unspUt line b fig. 13. shown in Though the pattern !'esesables that 01' an oxide absorber, it 1s beHeved to result ::f'roIII the quadrupole interaction ot thulium ione - in copper. It is not yet known whether the thuliUll ion appears aa 8. replaceJIent for & copper ion, an interstitial, or in a binary alloy V1th the copper. In another experiment, a prel1m1nary run ueing an absorbeJ" of thulium ethyl sulfate shoved no resonaJice abaorptiQl\. The reason for this 18 not yet known, but the JlBterial mer! ts further study since it would be useful in tying together the :oeaults of' MIlssb4wer expedmenta, paruagnetic resonance, and optical spect~eopy. In an · effort to detfn'llline the magnetic moment of the exei ted state of orm169, several runs were lIIIlde using thulium iron garnet, which 18 ferrtagnetic at room temperatures. A strong resonance composed of several lines vas obtained (fig. 14), but the resolution , - vaa not good enough to deCOlllPOl!le the pattern. Iia ~ ... eIght 11nee were expected under the Inf'luence of the nuclear zen -. quadrupole shifts. n spUtting and Il: t11% 0 z <t z u <t w ~ 2% Il: 0 e.. l- 0 z w 3% W lL. lL. IU 4% • 2 • • • • .. p • 0 •• N· • • • • • • ABSORBER VELOCITY IN CMIS FI GURE 13: ABSORPTION SPECTRUM OF THULIUM OlFFUS EO INTO COPPER SOURCE : UN SPLIT LI NE FROM ERBIUM OXIDE AT 700 K 4 - • I • • • I I \T1 ..... 4 z.p .. .. . • • •• 0 N· 2 ABSORBER VELOCITY (CM/S) FI GURE 14: ABSORPTION PATTERN RESULTING FROM THU LIUM IRON GARNET AB SORBER AT 300 K SOURCE METAL AT 300 K . I ..• . I I co \J'1 -59- Figures 15. 16 and 17 ehov a " _leetton of exper1mental results with an absorber of ~~ at 3r:x:P K .and a eource of Er2~ at teJiPeratures from no K to 123(0)C. The figure. dftonstrate the strong temperature dependence of the quadrupole splitting. Figure 1e shows the temperature d.ependence of the qua4rupole splitting obtained b:y the an&lysie of all th« _aeurement8 Vi th oxide source. and oxIde - and metlll absorbers. Veing _tal sources, no spl1t ting vas re80lved at room temperature or above~ but a splitting vas observed at 770 K (tIg~ 19). Below 170 K, the resonance absorption disappeared almost completely ~ • • o .,. • o • o • • o • • o o 000 o • • o o o o o 0 • 2 0 o • 0 o 0 o. . . p .o...- •••• 0 • 0 o • o o o 0 o 0 : .0 • N" • : o 0 o o 0 o • 2 - •• • • •• ..... ... o 0 o o 0 ... • o 00 • .00 • • ABSORBER VELOC ITY (CHIS) ...: .. . o • o o o • • • • • • •• • • .:. • •• • • •• • 188j ' K • • • • • . 0 • , •• • 77K • FIGURE ~5:AB SORPTION PATTERN aESULTI NG FROM OXIDE ABSORaER AT 300 K AND OX ID~ SOURCE AT·TEMPERATURES SHO\1N 8 O~b' 1% o I 0% ' I • 1% o • • • • • • • oI I (1\ - 61- • • •• 2% • • I • • • • • •• ••• 0/ • • • 1/0 • • 2% • I .. • • • 1% 557 K • • • • 4~ 9 K ... •• • • • • • • • • • • • • • 2% • I • • •• •• 1% • ••• •• .. •• • • •• • • 300 K • • •• •• • • • • - p • ,. •• •• • •• • •• • • • • N 2 0 4 FI GURE 16 : ABSORPT IO N PATTERNS RESULTI NG FROM OXI.D E AB SORBERS AT 300 K AND OX IDE SOURCES AT TEMPERATURES SHOWN IN F IG URE 4 2 • - 62•:\• . • • ••• 2% I • 1% • • •• • I .. · .. • • • • •• •••• • 2% . • , • • • • • •• • • •• •• • • •• • 727K '. • • 2 .. , 858 K • ·0 4 • • •• •• • • • •• ". • , •• I 1% •• • • • 1230 K • • • •: • , • 4 P 0 N- 2 4 ABSORBER VELOCITY (C M/S) FIGURE 17:ABSORPT IO N PATTERNS RESULTING FROM OXI DE ABSORBERS AT 300 K AND OXI DE SOURCES AT TEMP ERATURES SHOWN IN F IGURE - 63 - I Q 0 ~ 1 VI =:J I.!.. N ...J -' ..:t N ::I 0 . ~ I 0 0 .... <IN x I- -~ U u ::.:~ 0 0 ~ L1J 0 I- ~, - ? ,.;.." -, . ::-:- I-U 1.1- , 0 ....... N lLJ VI - 1 - 11 <! - 0 0 0 O...JO' VI « <to w <.!J ...0 ~>I.!J U oc 0- 0=J :z -4 0 ...Jo ::;, - UJ - V ) VI VI 1.1- 1I<t w c 0 0 Co 0 x 0 ~ ",-, - -~ 0 !.tJ c:: I..'J::I ;:-;:1- 0 -<t 1-0:: I-I.!.! -0.. ...J::: Q..w IIlI- -~ 0 0 .. CO 0 '-!.J fZ :::' ~ - 0 I.!.. 0 0 N 0 I '--" I J J. N - I I I O. N ..:T (SIW~) 9NIHlldS 0 • • • ....c • • • -,-, • • • • • • ~ C'-l i' • _i' •• VI • • • ...... 1- ...c•,& w;::: « ........w u >"'" C! !-, - • -' 0 u V) 0 ...J - l l!J<C • > t- ~ • W • C!!! ZO •• c: lk. ri', w 0 c:: 0 0 f-(.,.'1 ::.: <t ID =:, • « c:: -J • t-<J: • u I~ Q, := Ww • -, Ii) .....J • ...:.;, C~ • OL!J - [:.c:: • C} IJI C"J • • • ~ - - Cf) W <t ~D '" • W r.;;: ::; t;; :".J c'·? N " 0 c' l:)3~I :EI ~ J:; : ~\';:OS :J i:1 -65V. Diacussion A. . The Magnitude . and Temperature Dependence of' the Hyperfine Structure The analysis of the hypert1ne inte:netion in Part nahmred that the quadrupole interaction 1a the only 1Japortant source of h,vperfine splitting in est of th& present exper1lllent. It Was also shown that the field gradient Which produces the quadrupole splitting l'vi', the antiahield1ng of the cryatal has two significant sourcesl --=n field gradient by the closed she11s, aM V E ' . the fi.14 greient generated by the 41' electrons, ~ that vi : v1:" + tV'E· ~ V -" E eannot be calculated &8 a function of taperature aDd Cl"Yl'ta1 syasaetry with the present I1m1 ted kDovle4ge of particular crystal field and electronic spl1tttngll. However, the . .,..,.,. poae1ble value of v1:" can be euUy calculated~ Tbe 4f' elect.roDlc wave function giving the largest field gradient at the nucleus is the ·one containing only Dlj : ±6. Using the set of equationa on pages 22 and 23, and the notation of page 8, we obtain: ~ :: e Q ;: 2 e <r- 3 >......f... l~" and 3·5 "l ~O . From equations 5a and Sb, 1).£= [3+3) e 'tQ (1+ ~)~ 12 ' 2 (r-3)= 7 ~1 • 1025 em- 3 (15, 16) and Wling Q : 2.1 • 10,:,,24 J end A E :: 5 • 10",6 ev :: 18 ca/a. Tbi8 eati_te of the .u:1aua quadrupole interaction resulting f'rom the 41' electrons only fa entirely ind~.nt of the crystal ayumetry. The aceuracy should be 1rl.th1n :t.2&I>. Yith the -3or pert o~ the uncertainty coming troa the eet1aate o~ Q 1"roa the Nils.on .o4e1. ..... 4 ___ r VE , the temperature ......epelldent c-<l8IlODent ot the Neld gradient, producee the seeond eontribution to the quadl'upole splitting . It depende pr!Jla.rily on the crJstal syaaetry. estimate of We can .uea crude ...... ¥ VE tor ~ :trom a model that eona1.ts of a thuliUll ion halfway between two rP~ ione 4.6 1 ap!U't. Uaing an ant1ehie141ng rector ~ : -100, the resultant splitting 1e 1O~5 ev : 36 ea/.~ The curve of tig. 18 sbon that the splitting varies troa 6.6 f!fA/s at 770 K to -2.8 em/sat 13300 IC. At 68fP IC the etfective gradient passes through aero vi thin the e%per1mental &t!curacy, shoving that "0 r7-' -::;; • vE :::: - VE The total variation of' the 8plitting with temperature 18 9.4 cm/s, well within the 1IWx11!1tua predicted fl"OIl the 4t electronic wave function8~ '!he temperature independent part of' the splitting ie about an order or magnitude emaller thaD the result or the crude calculation above. In the metal source, the total quadrupole splitting appears to be small compared to the oxide ease. Thls eaD probably be aeoounted for by the higher s~try o~ the metal crystal, which makes vEt very small and decreases Ei , the spUtting of' the eleetronic levels. The relatively..all splitting of the electronic levels in the .-tal allova the spin-l.ettice relaxatiOn avenging process (aee page 17) to cancel the fie14 gradient rr.. the 41' electrons even at 3000 K, resulting in an unaplit 11ne at roo. temperatures. .67The dlH:pJIearanee of resonance absorption below 710 K can be attributed to the fact that erbiUJII metal is ant1f'erraagnetic below 780 K, resulting in very complex patterns: This distributes the intend ty of' the 11nes over 80 any peaks that the l"NOnanee ab sorption beeomes undetectable. B. Slze ot the Resonance EN'ect The relatively weak strength Of the resonance effect, only a few percent for all source and absorber C!OJIIblnationa, ia due to a strong background of X-rays 'lihich have approxilllately the energy of the gaIIIIa l ine. The mat important contribution to the X-ra.v bacltground come. hom t he ionbation of erbium L shell electrcma by the 300 key electrons resul tins from the beta decay of the Erl.69 ~ Since there are about 200 betas produced for each 8.4 kev gaDIIB ray and each beta can produce lleveral L ahell ioniaationa, a strong X-ray background ariaea. In addition, the 8:4 kev sa.- ray line 18 energetic eDOUgh to be cr1 t1eal.ly absorbed. in the LyII shell of erbiua in the source, with L X-rays resulting. The use of thin and uniform sources".. effective 1n reducing the X-ray background, thereby enhancing the resonance effect. c. Line tl1dtha '!be natural 11ne width, r , calculated meuured halt- Hte ot 6~9 JlS (17), 18 0.2 cals. experiment, a. aourcf! 11ne having Width 11ne o"t width r 18 f'rcIIa the recently In the present IIOved over an abllOrption r re8ulting 1n a total Width ot 2 r in 1 the absorption pattern 18euured as a function of relative velocity betw~ source and absorber. However, the actually ob.erved line widths have been at lea8t six times thi8 value. There are three likely cauaes for 11ne broadening in the present experimental a. exeessive abllOrber th1cm.s8 b. lattiee imperfectione and chemical l~ritie. c. in tbe source and imperfect averaging over the electronic states by the spinlattice process . Theee etfects will be discussed 1n the abOve order. a. Figure 20 ah0w8 curve. ot peak reeonance absorption and measured 11ne width as afunct10n of absorber thickness. The resulta of a theoretieal calculation ot 11ne brotlden1ng .a a . fun ct 10n of absorber thickness are plotted 01'1 the . . . . .eale. Z 2.0 ~ :5 > ;:1,0 W ~ :z L1J :J;L5 e:::. l- :c "- <[ L! ' ~~ ~ U'I W (5 2 4 6 8 10 0 12 h 0 METAL ABSORBER TH IC KNESS (MG/CM 2) FIGURE 20: PEAK RESONANCE ABSORPT ION AND RELATIVE LINE WIDTH AS A FUNCT ION OF ABSORBER THla~NESS . SOURCE: MC TAl ~ 2°1 7 h ..." W ILl « a:l U'I o a:: '"\./, 0 .. 1.,,1 I- (:l l) I o I ...., -71From these curves .it is apparent that absorber thicknesses in the range 2-5 -S/~ do not appreciably broaden the observed pattern. b. Lattice imperfections,. however, were definitely established to be aignifieant &8 a cause of line broadening since the line widths observed shoved. a dependence on the preparation techniQUe of sources and absorbers. In _tal. eourees 8D/l abeOJ'bers l118de by vacuum evaporation, the l1ne width decreased noticeably vben the pressure during the evaporation vas reduced, but there vaa DO further improvement in using pressures belov 10. 6 . . JJg~ Atte.pts to anneal. the e vaporated films to improve the crystal structure have fahed to date because of the di ffuaion of the thul1ua _tal into the backing IIl&teri&!. ExperiMnts to produce unsupported . .tal filme are nov in progre.l. In oxide 8OUl'ce and abaorber materials, the ulti_te line width ach10ved by various phy81cal &D5. chemical treatMnt.s vas 2.4 em/a, corresponding to a broadening by a factor of 6~ eon.iderable care va. taken to prevent deecapoa1tion and difi'u8ion of the Er O:3 2 sources at elevated temperatures. a~re The u . . of boats of ~03 in an of pure nitrogen resulted in stable eDIl reproducible - spectra. No line broadening trom radiation ~ vas expeoted afier chemical treat.ent of the oxide 8OUrCes. e. The raaining cause of' the observed 11ne broadening 18 then that the spin-lattice relaxation t1ae :1a not fast enough to avere.ge the .apetic and quadrupole splitting -72.. perfectly. A broadening from thll cause 18 very dltf'lcul.t to estimate, 12 8 In the metal at since the relaxatlon ttmes, supposedly about 10. o 300 X, are not prec1sely known. ('!be spin-lattice relaxation t1Jaes in thulium ethyl sulfate are knovn to be 10· 6 at 4 0 K (18):) The spin-1Attlce relaxation tiM increases sharply' vi th dec:-eaatng temperature, and the line broadeDing obeerved at low temperatures (8'ee figs: 15 and 19) may be due to a bretLkdown of - the avet"&ging process at thea. teJllp(traturea. -73VI. SWIIaary The recoilless reeonance absorption of the 8:4 key ga:BII& re;y ellitted from Tal69 bas been observed: Using thi~ resonance, the bypertine spUtting of the nuclear. energy 18,",18 in Tal69 bas been studied in source and absorber I118teria1s of varioua chemical compo81tions in a temperature range f'rom 650 K to 13 300 K~ Arguments based on the fundamental properties of the Hamiltoni an of the rare earth ion in the ery'stal electric 1'1e1d and on the electron spin-lattice relaxation phenolllenon have been presented to shov that there is no JlagDetlc hyper1'ine interaction under .,at .. conditione. The quadrupole contribution to the hyperfine interaetton vas s t udied both t heOretically and expert.entally., vi th particular emphas1a on the variaUon of the qu.&drupole eplitting vith tempera- - t ure. It ¥as shovrl that at certain temperatures the quadrupole spUtting could be el1m1nated, 80 that an UD.pUt lin. resulted: This procedure makes it possible to produce sources of rare earth ions emitting an UDsplit line Without the use of 8. cubic eurrounding, which is difficult to obtain vi th the 3+ rare· earth leme. 'l'he use of • 8CUrce emitting an unapl1t line greatly sblpl11'l. . the inter- pretation of the absorption patterns by allO¥1ng the direct observation of the absorber spectrtUII alone. Unfortunately, the line vidthe attUne4 he,", net been adequate to fully resolve the by"perflne spectra detected. It is hoped that vtth the background of these exper1l1l1!tnts, better sources - and absorbers can be made. These should eventually make it poaaible to study the very interesting magnetic properties of the rare earth metals at lev temperatures. -75- R. L~ • •bauer, BaturY1. .enschaften!it 1. 538 (1958h z. Pb;ra1k 151, l25 (1959)~ .- L. )fieabauer, F. W~ Stanek, W. H. wtecl.eann, Z. Phyatk Z. Naturtorsch 14&, 2ll. (1959)) .2. R. 3. s. Ofe:r, P. Av1y1, R. Ball'm1ngert J. 1ILr1nOv, S. G. Cohen, 161, 388 (196l). - .. - Pbys. Rev. R. Ba.um1nger, s. Lettera .2, r.. - 406 (196OJ. . Cohen, A. Ma.r1nov, S. oter, Pbya. Rev. 481 (1961) • . 4. M. K'alvlU8. P. Kienle, 1:. lloclmann, H. Etcher, Z. Pbye1k 163. 5. R. v~ Powld, G~ ~ Rebka, 6. S. l)eBenedet~1, G: Lang, R. IJ2gaUa, J.'bys. Rev: Letters .2, 60 8T (1961). Jr., Pby.; Rev. te:ttera!, 274 (1960). (1961). 7. F. H. Spedd1n€:L 1md A: H. Daane (m.),. The Ran Elu"tha, 1961, Nev York. 8. J. B'. G~ber, .J. G. Couvay, J: Fby•• ~ 1531! (1960») J. Chela. Phyw. l!; 1178 (1960). '. 9. w. IDv, ~,..§'?'tlc Reaooance in 80110. 1960, New York. 10. Cbem: - - R. M. 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