UCRL-10780
1111111
University of California
Ernest 0. lawrence Radiation Laboratory
TWO-WEEK LOAN COPY
This is a Library Circulating Copy which may be borrowed for two weeks. For a personal retention copy, call Tech. Info. Dioision, Ext. 5545
ATOMIC BEAM MEASUREMENTS OF THE NUCLEAR SPINS OF COPPER-62 AND IRON-59 AND THE HYPERFINE-STRUCTURE SEPARATION OF COPPER-61 AND COPPER-64
Berkeley, California DISCLAIMER
This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. Research and Development UCRL-10780 UC-34 Physics TID -4500 (19th Ed. )
UNIVERSITY OF CALIFORNIA Lawrence Radiation Laboratory Berkeley, California Contract No. W -7405-eng-48
ATOMIC BEAM MEASUREMENTS OF THE NUCLEAR SPINS OF COPPER-62 AND IRON -59 AND THE HYPERFINE-STRUCTURE SEPARATION OF.COPP.ER-'6T AND COPPER-64 Barbara Marie Dodsworth (Ph. D. Thesis)
April 18, 1963 •
Printed in USA. Price $2.50. Available from the Office of Technical Services U. S. Department of Commerce Washington 25, D.C. iii
CONTENTS Abstract .•. v
I. Introduction .. 1 II. Atomic Theory . . . .
A. The Hamiltonian of an Atom . 3
1. Nuclear Hamiltonian .. 0 0 •. 3 2. Electrostatic Interactions in an Atom .• 3 3· Hyperfine Interaction Term 8
4. Interaction of an Atom with External Field.s . • . . . . 14
B. Nuclear Theory 21 III. Experiment 25 A. Description of the Apparatus . 25 B. lvlethod.s of Detection • 27 c. Experimental Procedure 36 61 IV. Cu Experiment 39 A. Isotope Production and. Chemistry • . . • . . . • • • • . . 39
B. Theory of the Cu Experiment • . . . • . • • , . • . . . • . 42
1. General Description of Theory •
2. Determination of the Sign of gi . 46
c. Experimental Procedure and Data Ana~sis 48 61 D. Results for Cu 50 v. Cu 62 Exper11nen. t 61
A. Isotope Production and Chemistry 61
B. Experimental Procedure and. Data Analysis 61 62 C. Theory of cu Experiment • . . • . . . • . . . . . • . • 63 62 D. Results for Cu . o • • • • • • • • o • • • • • • o • • • 67 iv
VI. Cu 64 Ex perJJllen. t 72
A. Isotope Production 72
B. Experimental Procedure and Data Analysis ...... 72 64 c. Theory of the cu Experiment ....•.... _...... 72
D. Results for Cu 64 ...... 75 VII. Fe59 Experiment 84 A. Beam Production 84
B. Isotope Production and Identification . 93 C . Experimental Procedure ...... 97
D. Multiple Quantum Transitions in Fe59 97
E. Theory of the Fe59 Experiment •...... 99
F. Results for Fe59 o o o o o o o n o o . o o o • e· o o o o o e . 99 ·VIII. Additional Isotopes 109 6-- A. Cu 1 Experiment . 109 223 B. Fr Experiment . 109 136 C. Cs Experiment 113
IX. Acknowledgements • 115
References . . . 0 • 0 116 v
ATOMIC BEAM MEASUREMENTS OF THE NUCLEAR SPINS
OF COPPER-62 .AND IRON-59 AND THE HYPER-
FINE-STRUCTURE SEPARP.TION OF
COPPER-61 .AND COPPER-64
Barbara Marie Dodsworth
Lawrence Radiation Laboratory and Department of Physics J University of California, Berkeley, California
. 1,· April 18, 1963
ABSTRACT
The atomic beam magnetic resonance method of the "flop-in" type using the technique of radioactive detection has been employed to measure the 62 nuclear spins of cu and Fe59 as well as the byperfine-structure separa 61 61 tion of cu , the sign of the moment of cu , and an improved value for the 64 61 6v of cu • The magnetic moment of cu was calculated from the . Fermi-Segr~6 formula, using previously measured values for the 6v and ~I of Cu 3 .- The results of the experimental work, together with calculated values of the nuclear magnetic dipole moments, are Isotope Half-life Spin hfs6v ~I (uncorr) (Mc[sec) {run) ' Cu61 3.3 hours 3/2a 11,400(300) + 2.16(6). Cu62 10 minutes 1 ------~ Cu64 12.8 hours la 1282.140(20) ± 0.216(2) Fe 59 45 days 3/2 ------
a Measured previously by other workers. 61 The cu isotope was produced on the Berkeley 60-inch cyclotron by the 61 62 reaction co59(a,2n)cu • The cu isotope was also produced on the cyclo- 62 . 62 tron by the decay of Zn formed by the reaction N~(a,2n)Zn • Beth the Cu 64 isotopes \vere chemically separated from the target materials. The Cu was formed by neutron bombardment of copper\ in the Livermore and_Val.lecitos.
"·. vi reactors; Fe59 was produced by irradiation with neutrons in~he-ETR reactor ;tn-I-d:a.he • Radioactivity in the beam 'vas measured by expos:i.ng collectors to the beam and counting these "buttons" in either sodium iodide--crystal scintil lation counters or continuous-flow methane counters, depending on the mode of decay of the particular isotope. The main boqy of the thesis contains theory of atomic structure, a description of the experimental apparatus and technig:ues employed.. , methods of data analysis, and results. The results are interpreted in terms of simple nuclear shell·-model theory. -· 1 -
I. INTRODUCTION
I In 1911 Dunoyer (mm 11) initiated the field of research with mole- cu.lar beams by producing a directed beam of neutral molecules at pressures low enough that the effect of molecular collisions could be neglected. The applicability of the beam method to studying properties of atoms and mole cules was first recognized by Stern in 1919. These studies later resulted in the Stern-Gerlach experiment (STE 21), w]lich, .for example, proved experimentally the space quantization of angular momentum. The new tech nique, utilizing a small oscillating magnetic field. to cause reorientation of the spin or magnetic moment with respect to a constant field, was de veloped by Rabi and others (RAB 38). In 191~2, Zacharias (ZAC 42) refined the technique by introducing the "flop.:..in" method. which, in conjunction with the radioactive detection scheme of K. F. Smith (SMI 51), enhanced the signal-to-noise ratio. This method was employed. to measure the nuclear properties of the Cu and·Fe isotopes presented in this thesis and is quantitatively as follOivs; The atoms are heated in a small container called an oven which emits the atoms through a slit on the front. Leaving the oven, the beam passes through a system of collimating slits and. finds itself in an excellent vacuum. Since the mean free path of the atoms is many times the length of the apparatus, very few atoms make collisions during the time of the experi ment, i.e., most of them are isolated from one another. Two inhomogeneous magnetic fields, called the A and B fields, are used to deflect the atoms by means of the interaction of the-magnetic moments of the atoms with the grad.ient of the applied magnetic field.. The C field region, betvreen the A and B field.s, consists of a very homogeneous magnetic field plus a small impressed radio-freq~ency field which is capable of inducing transitions between the energy levels of the atom. The rad.io frequency necessary to induce transitions is a function of the strength of the C field, which can be easily measured, and of the atomic and nuclear constants of the atom. If the atom undergoes no transition in the C field, it is deflected in the same d.irection in the B field as it was in the A field and. is "thrown out" away from the detector. If the atom undergoes a transition in.the C field and hence changes the sign of its effective magnetic moment~ its deflection in the B field is opposite to what it was in the A field and the atom is - 2 -
focussed. onto the detector, The detector is a sulfur-coated piece of brass which can be removed form the machine and counted in crystal or ~-counters depending on the mode of decay of the radioactive species. The resonance, which is observed as an increase in the counting rate versus frequency, can be used to determine various atomic and nuclear properties--,such as, for ex~ple, the nuclear spin and the hyperfine-structure separation, from which one can deduce the dipole and quadrupole interaction constants. It is also possible to measure the sign of the magnetic moment.
The bas~c design and construction of the flop-in atomic beam apparatus used in the following experiments is described in more detail in R. J, Sunderland's (SUN 56), Ph.D. thesis.
"' - 3 -
II . ATOMIC THEORY
A. The Hamiltonian of an Atom
One of the main features of atomic beam experiments it that the atoms '"' are isolated from one another because at-low pressures the mean free path for collisions is many times the length of the apparatus. Hence in the absence of external magnetic or electric fields, the interaction terms in the Hamiltonian are all internal to a single atom. According to the nuclear model, one may consider the atom as made up of a central massive positively charged nucleus surrounded by an electron syst·em arranged in the central Coulomb field produced by the nucleus. In accordance with this model, the total nonrelativistic Hamiltonian for a free atom may be divided into five parts:
1 + 1 t . +}! . :1-.. 't + }{ + '. - (1-} }{ ::: :u nuc eus :u e ec ron~c sp~n oru~ hfs J:r external '
Let us consider each part of this Hamiltonian in some detail.
1. Nuclear Hamiltonian
The nuclear part of the Hamiltonian represents the internal energy of the nucleus, which is dependent upon complex nuclear forces (BLA 52), Al though our knowledge of these forces is far from complete, it is possible to ignore any effect of excited states in using perturbation technique to solve for the eigenvalues of the remaining .terms in the Hamiltonian, since the energy difference between the nuclear ground state· and any excited state is much greater (keV or MeV) than any of the energy differences due to the remaining terms. That is to say,
6Enucleus >> (6Eelectronic' 6Espin o~bit) >> c~fs' 6Eexternal).
2. Electrostatic Interactions in an Atom
a. Electronic Hamiltonian
The second term in Eq.(l) has the form
2 e (2') }{electronic r .. ' ~J
in •.vhich the nucleus is regarded as a fixed center of force lvith :iilfihite: .mass. - 4 -
The first term in the brackets is the kinetic energy of the ith (p~/2m)l. electron. The next term represents the Coulomb attraction of the nucleus of · charge Ze on the ith electron at a distance r. from the nucleus. To a first l. a1)proximation the purely radial terms contribute quantities ,.,hich have the " same values for all levels belonging to a configuration. "Configuration" rcfc:!."s to specification of the enere:r of the electrons by their n,-t values 2 only. T'ne tel'T.l L. c /r .. gives the electrostatic repulsion bet,veen electrons i>j l.J i and j separated by a distance r. . . The Coulomb interaction of the electrons ~ . l.J (e~/r 1 j) is different for different states of the same configuration, and thus serves in a small degree to remove the degeneracy of the states be longing to the sa:rne configuration.
b. Spin-orbit Hamiltonian
The next term in Eq.(l) also helps to remove the degeneracy. This term is J{ .- b 't which treats the magnetic interactions of the electronic sp1n-or 1 , orbits with the spins. ·Although Dirac's relativistic theory for a single electron cannot be generalized to apply exactly to a system of several electrons, it is possible to approximate the spin-orbit interp.ction by a term of the form N I (3) ~==1
'-Ihcre 1 is the orbital angular momentum and s. the spin angular momentum i l. of an electron. The function s(ri) is given (THO 26) by
1 1 dV ~(r .) == 2 2 a-- 1 2m c ri ri
in terms of the central-field potential energy V(r). Even though hyperfine-structure terms and interactions with external fields have not been included, the Hamiltonian N 2 \,.; 2 2 Ze ~ e Jl [pi --- + 1. • s. (l+) ==?. ~(ri) l. l. + ~ 2m r. J l. I rij i=-=1 i>j is too complex to permit an exact solution. \·!hat can be done, however, is to separate the spherically symmetric term ~ and treat the rest as a per- ' 0 turbation, }~ • Thus, - 5 -
N 2 [pi (5) }!0 = -··2m +U(r i ) ] ' i=lI
,..,. N N 1J 2 2 e J:!' = ze s(ri) li· si - U(r.) rij - ri +I I ~ i>jI i=lI i=l i=l N (6) U(r ) = vij - 1 . i>jI i=lI
A detailed discussion of this method of solution as ,.,ell as a consideration of the problem of the best assumption for U(ri) and a discussiori of the quantities that depend on that choice may be found in Condon and Shortley (CON 57). In general terms, U(r.) is chosen so that the diffe:r (7)' or &:fow(~l' ... t ) = \ h(l. )q> c; ) = \ E: q> (t.) n L ~ E:i 1 L i €i ~ As discussed previously, U(r ) is then chosen so that 1 N 3 This expression for U(r.) can then be substituted. into M , from 1.rhich a nev l 0 improved set of vrave functions can be calculated. This self-consistent method. of successive approximations for solving the equations is known as the Hartree method, or, if the product wave function is properly antisym metrized, as the Hartree-Fock method. It is interesting to note that the U(r.) term incorporates the idea that l each electron finds itself in a potential which is "screened" from the at- tractive nuclear potential by the repulsive effect of all the other electrons, i.e.' z Ze e - -+ - e . (10) ui(r) = r. (i) Russell-Saunders coupling 2 -7 -7 In the lovr-Z region, vhere e /r ..>> ~ (r.) t. • s., the Coulomb inter- lJ l l J. action has the effect of coupling all the individual angular momenta to form ~ the total angular momentum t = and all the individual spins to form the Lt.J. - 7 - ~~ total spinS= L s. The eigenfUnctions are hence further indexed by the quantum numbers L and S and. are 28+1 degenerate. The degeneracy is lifted by the. spin-orbit term. The spin-orbit expression may now be regarded as a perturbation that splits a particular term into its various fine-structure levels, which are now indexed by 28+1 different J values where J = L + S. This is known as the Russell-Saunders coupling case, in which the good ~~ ~ ~~ ~ quantum numbers are J·, L and S. One can see this property of J, L and S by looking at the commutation relations of these vectors with the Hamiltonian J4 = }! + :U', where 0. N p~ 2 J. J:{ = 2m- Ze J ( :.:::(11) 0 [ lril i=lI and N N 2 1 e J:{' = 2 ::c:..{l2) I I 11. - ~.1 jfi=l i=l J. J Clearly~. commutes with${, since the Hamiltonian is independent of spin, and J. N hence S = L ~. connnutes with;}:{, However, it is not true that t. connnutes 0 1 J. J. J.= ~ ~ with J:{, and it is necessary to verify that L = L t. does commute with~. It ~ J. ~ ~ ~ ~ ~ is evident that L commutes with J:{ • The commutator of L ( L= Lt.= L r.x p,) 0 J. J. J. with ;}:{ is given by N N 1 1 1 m' 2 I I Jti=l i=l 1 ___.__I ) - t I I 1~.- ~.1 1~0- 1.! J. J J. J 1 1 I~rX'VI ~ I~r x ~\7 I = t m m =ti m m I I 11°- ~.1 I !"!7i - ~.1 J. J J N ~ ~ 1 ..... + I r X\7 (:.:: (13) 2 m m I II 1~. -1.1 m=l J. J The first two terms cancel, leaving only the third term, which is equal to Cr 0 - 1 0 ) c1 0 - ~. ) • J X J. J o +_.r X J. J ~ ,· .,.,. (-14) = \ ---- - 3 · m 14 --'~> 13 v jm f f f [~m !1. - :i. I J.m r 0 - r . m=l jfi=l i=l J. J J. J - 8 - N N ~ ~ (r.-~ ~)r. (r.- r.) ~ J. J J. J r. X - + -r. X =II J. 11.- 7.1 3 J j1.-"l.l 3 i=l jfi=l J. J J. J ?.x 1. = J. J + 0 . LL ( j?.-1.1 3 J. . J This, then, is the L-S or Russell-Saunders coupling case when L = L i., ~ ~ ~ J. = L and hence J = L + S are the good quantum numbers. S t.J. (ii) The J-J coupling scheme For high z, the spin-orbit term is dominant in forming the ener~r terms, and the Coulomb repulsion can be considered as a perturbation that splits each term into levels. In this scheme, where J:! . b"t>> }!C b , ~ ~ ~ spJ.n or J. ou 1 om rep 4 4 the good quantum numbers are j. = l. + s. and. J = L j. . This follovrs from J. J. J. J. + 1.' 1.] = o, (16) [l.J. J. 1J. .. J. since ~ ~ Hi 1. X s. : (17) J. J. and -) ~ -) ] -> ~ [ si, li• si ~in six li .(18) -> -) -) Therefore 1. and s of each electron couple tightly to form j .. This is J. i J. lD1ovrn as the J-J coupling scheme. 3· Hyperfine Interaction Term The hyperfine-interaction term represents the interaction of the atomic nucleus with the electric and magnetic fields of the surrounding electrons. a.Electrostatic interaction The general expression for the electrostatic interaction between the charged. nucleus and the charged. electrons is p (1 ) p (1 ) d 't" d 't" e e n n e n ( 19) ' 1-re --;I n 1-rhere pe is the electron charge density, Pn the nuclear charge density, and r and ~r the position vectors relative to the center of mass e n of the nucleus Fig. 1. Since idealizing the real charges as points not only permits greater mathematical simplicity but also gives rise to convenient physical - 9 - concepts for the description and representation of actual fields and potentials, this suggests an expansion for the electric (and also magnetic) potential in terms of Legendre polynomials, Besides giving the allowed electric (and also magnetic) 2.{. pole moments of the nuclear system, this expansion also furnishes the form of the Hamiltonian consistent with the concept of point charges, However, not all nuclear electrical multipole moments can exist. This can be seen by looking at the expression for the potential at a point r due to the nuclear charge density, ...' J p(rn)d'!:n ~(r) = . (20) · I~-~n I Expanding lJ'Jr-~1 in the usual way in terms of Legendre polynomials gives 00 ~(r) =) -:d:r! r: Pt,(cose)p(rn)d-rn. (21) i:o r It can no,., be shown by usint parity arguments that, (a) only terms of 2 electric multipole order 2 (where.{.= o, 1, 2, .. , implies monopole, quadrupole, etc,) can exist, and (b) that, depending on the nuclear spin or electronic angular momentum or both, the series will terminate for a definite value of .t. The general term of the series must first be put into quantum mechanical language, The charge density operator having p(r ) as n the expectation value of p p is 0 (22) Thus· * p(r ·) = 'It 0 (r': )p 'lt(r": )d-r 0 • (23) n J l l op l l Substituting this in the general expression gives r .t 'It * (ro~ ) I eoo(r-~ ~rJP .t (r.,r ~ ~ )'It (~rod-rod'!:, ) (24) ,J n l l n l l n l l n Integrating over d'!: gives the result n 'lt*(]t) \ e.r ..t P (!!,1.)'1r(1.)d-r. (25) J l ~ l l .t l l l .t * This can be written as Jri 1jtiP.{. '~trd-ri. Assuming that the nuclear spin is -10- Nucleus MU-24754 Fig. l. Schematic diagram defining quantities that describe the positions of electronic and nu~lear volume elements relative to the center of mass of an atom. - 11 - I·implies ~I must be an eigenfunction corresponding to an angular momentum I. The product r~~I must also be an eigenfunction of angular momentum I, since rt has no a~lar dependence. Because Pt is an eigenfunction of angular momentum corresponding to angular momentum t, the product of Pt and ¥ must correspond to a wave function in which the angular momenta.I and 1 t are combined. ~ the vector model, then, Pt~I describes a system with angular momentum between t + I and jt - Ij. Since eigenfunctions correspond ing to different eigenvalues are. orthogonal, the integral will vanish unless 1jri and Pt¥ correspond to the same anguJ.ar momentum eigenvalues. This r~ 1 implies that I must lie between + I and jt - Ij, or that I = I. Hence t t max - ~ 2I. t max It is also possible to show that all the integrals are zero if t is odd. This depends on_ the fact that for an isolated nucleus the Hamiltonian must be 2 unchanged upon reflection or that RH = HR, where RW = canst X 1jr, and R = 1. Thus the integral' can be written with nw(rl;r-2, ooo):;t' 1Jr(-rl,:.,.r2,-c) ~ •oo), giving 7<- ·~ ~ \ -e.. ~~ ~ (26) J~I (-r1,-r2 ···) ~ eiri ~~(r,ri) 1jr (-r1 , ···)dTi. Since ~I1jri* is even and Pt is even for t even and odd for todd' the integral vanishes if t is odd, or all 2t pole moments vanish for t odd. It is evident, then, that the electrostatic part of the interaction includes only 2 terms of multipole order 2 t for t = 0, 1, • • · -- i.e., monopole, quadrupole, etc. To see the form of Eq.(l9), which can be rewritten .7 ~ J---~- Pe (te)pn (rn)dTedTn 1~ , , I~ .,... I , (27) r e - r n in terms of multipole moments, it is necessary to expand the term 1j1:1-e r"" n I in Legendre polynomials. 'J:nis yields the expression for the multipole k ' moment of order 2 , ·--PePn ( --r~k Pk{cose )dT dT . (28) r r en e n e . "'' In order to evaluate the integral, it is necessary to separate it into two parts, one dependent on r only and one dependent on r only. This is ac- n e complished by using the .spherical harmonic addition theorem (CON 57), which gives - 12 - k 27T\ Pk(cose ) ( -l)q y(k) ( case ,~. ) y (k)( case ,~ ) ' (29) en 2k+l L -g n n +q e e q=-k ... where Y(k) is the normalized Tesseral harmonic. The 2k interaction energy q can be \ITi tten as (30) -vrhere Q(k) and.F(k) are irreducible tensors of degree k (RAC 1+2) and have the form Q(k)= .[ ~ p rk Yk (case ,cp )d-r. q 2k+l J n n q n n n .. n and F(k) = .J ~ J r -(k+l) y(k) (case cp )dt • q 2k+ 1 T p e e ' q e' e e e If we nov substitute the same quantum mechanical expression for pn as in the z preceding section ~~d ~~so let p = \ e ,1jr *1jr = q 1jr *1jr, ve find the same re- e ~ l e e e e i=l striction on k: i.e., the integrals exist only for odd values of k, and for a given I and J the highest electric pole interaction term (RN~ 56) is k ~ 2I for J >I 2J for I > J. The corresponding Hamiltonian may be written 2k (2k) 47T \ 11 2k__ ) ( -(2k+l) ) J{ = (-1) (or -7 k q r Y k · (31) electric 4k~l L ~ n 2 ,-11 e e 2 ,11 11=-2k b. Magnetic Interaction It has been shown (RAM 56) that, starting vith the equation for the magnetic interaction energy between an atomic nucleus of current density j and the orbital electrons represented by xhe electronic·vector potential n A , it is possible to \frite this energy as c d.- d-r (32) e n ·- 13 - for the electric currents external to the nucleus. Since this has the same form as the electrostatic interaction energy with p-- o and e ~ -9 e iiie ~ -> the magnetic interaction term can also be written as-a product Pn ~ -\1n. , mn ' of spherical tensors. There is one important modification, however, in that "fl ~ ~ ~ ~ \1 • m and \1 o m are pseudoscalars and. hence have odd parity, while the p e e n n e and p quantities in the electrostatic term have even parity. This implies n that, although the same type of argument holds for the existence of magnetic multipoles, the parity argument is just reversed. Hence only odd magnetic multipoles, i.e.~ k = 2~1, can exist. The q~antum states for the electrostatic and magnetic interaction of the nucleus with the surrounding electrons are indexed by the quantum numbers IJF, vThere I is the total angular momentum of the nucleus, J the total angular momentum of the electrons, and F the total angular momentum of the entire system, i.e,, :it = I + J. F is now a good quantum number, since de-=-dW Fe (t orque, ~n· the case of angu~r variables), W = a I J cose, ~ ~ ~ Fe = a I J sine = a( I x J ) = dJ/dt, di ~ ~ ~ ~ dt - a( J X I -a( I X J ); therefore ~ ~ d:i1 d(~ 7) di+dJ ~ ·~ ~ ~) dt = dt I + J = dt dt = -a( I X J ) + a( I X J = 0. (33) The system is indexed by the different F values corresponding to the dif ferent relative orientations of I and J, The number of different levels is 2J + l for I > J, and 2I + 1 for J > I. ~·he problem of finding the expectation value of the hyperfine-structure Hamiltonian WF =(IJF l~fs I IJF)= L(IJF IT~k) • ~~ IJF) (34) k has been thoroughly covered in a paper by Schwartz (SCH 55), and only the results are quoted here. The terms for k = 1 and k = 2 give the magnetic d.i pole and electric quadrupole interactions respectively. The eigenenergy of the :Uhfs for k = 1 to 2 is then - 14 - (35) >rhere a is the dipole interaction constant, b the quadrupole interaction con ... stant, and I·J = F(F+l) -I(I+l) -J(J+l) 2 (36) Since only dipole moment measurements are discussed in this thesis, only the relation of the dipole interaction constant, a , to the magnetic moment is given in any detail. 2 For the case of a single electron in a S state, the proportionality factor 1-ms d.erived by Fermi (FER 30) to be 2 8rr flo a=--gg- (37) 3 I J h w:ere gJ i! the electronic Lande g factor, gi the nuclear g factor (fli = gifl I ), flo the magnitude of the Bohr magneton, h . Planck's constant, 0 and ~r(O) the electronic ;rove function evaluated at the nuclear site, i.e., r = 0. In his derivation Fermi treated the nucleus as a point d.ipole and the electron as a relativistic Dirac particle. It is necessary to calculate factor a for each different configuration. However, a general result for a configuration of n equivalent electrons, each having an angular momentum -L, vras derived (HUJ3 58) in the limit of pure L-S coupling between the indi vidual electrons: a(J) = 2gifl2o (tl ....!It) { J(J+l)+L(L+l) -s(s+l) 3 2J(J+l) r 2 + 2(2L-n ) [L(L+l) [J J+l)+S(S+l) -L(L+l)] n2 (2L-l)(2t-l)(2~3) 2J J+l) _ 3 [J(J+l)-L(L+l)-S S+l)][J(J+l)+L(L+l)-S(S+l)] J} (8) 4 J(J+l 3 '0 ~ ~ ~ 1.rhere L = L--v., J = L + S. l l.;.. Interaction of an Atom 11i th External Field.s If octupole and higher-order magnetic moments are neglected, the Hamiltonian for an atom in an external field is of the form }{ mag - 15 - vhere H stands for the external magnetic field. The total Hamiltonian for the magnetic interaction is then given by (40) 1rhere Ji 0 a. LoT-r-Field or Zeeman Region In the lm.J"-field region the vectors I and J are still coupled tightly to form F, Hhich in turn precesses about the external magnetic field.. I I This is the region, then, for which~ >>J{ and. hence~ may be regarded as a perturbation through which the proximity of the adjacent F levels is felt. For very lmi field.s, first-order perturbation theory is adequate and the energy of a state varies linearly with H, the external magnetic field. This is the linear Zeeman region. The first-order perturbation result is (1) i w = (F,~I ~ IF,~) FJn}c = [ F(F+l)+J(J+l)-I(I+l) F(F+ 1)+ I(!f-1) -J( J+ 1) ][J.oHm -g J 2F(F+ 1) gi 2F(F+l) - F -gF[J. in H. (In) = ' o-"F If lie neglect terms in gi (since gi ~ 1/2000 gi), vre get ~ F(F+l)+J(J+l)-I(I+l) ( 4-2) gF ~ g,J 2F(F+l) ' As the Zeeman splitting becomes comparable to the difference betvreen F states, first-order perturbation theory breaks dmm. This is the region of inter mediate coupling I.J"here higher-order perturbation terms must be used to ac count for the splitting. The Zeeman result may also be obtained by using the vector model. T.Jith reference to Fig. 2, ~~ Ji' = -( ~ • ; ) F·H (43) . r-F 2' F Hhere the components of the electron and nuclear magnetic moments perpendicular to F time-average to zero. Hence, -16- ------I --- I I I I I I I I I MU-30246 Fig. 2. Vector diagram showing relative orientation of -F and -1-LF· - 17 - therefore I F2 + J-_2 I 2] [ F 2+I- 2 J~2] (44) J:t =~ 2F(F+l) ~-tgi 2F(F+l) ~ b. High-Field. or Paschen-Back Region In the high-field region, I and J are complete~ decoupled to v precess indep (45) = ( m~J~ a/2 (I+I- + I._I+) + I 2 J 2 !m:rnJ) =a m:rnJ' ! ~ ~ ~ where I+ = I + iJ and I X y Ix- iiY, andlt = (m~J!(-1-LJ- 1-LI)·H!m~J) = -1-L g Jllj1 - 1-L g....m_H . (46) 0 J z 0 ~ ~ z The quantum n~~ber mp = mi+ mJ is preserved for all values of the field, since it is on~ a different representation of the same quantity. This preservation, in conjunction ivith the 19 l'Jo mp Crossing Rule", which states that levels of the same ~ cannot cross, enables one to plot in a qualitative way the energy- .!:' level diagram from low fields t~~ough the intermediate region to high fields, as, for example, in Fig. 3· c. Breit-Rabi Equation For the case of J = 1/2, the secular equation for the Hamiltonian, (47) can be solved exact~v, since the largest submatrix is of order two and in volves solution of only a quadratic equation. The diagonalization of the quadratic results in the Breit-Rabi equation (BRE 31), which yields an ex- pression for the energy levels of the form 1 4 2 6W 6W [ wT!' 2] (48) wrnp = 2(2I+l) - gr1-Lorn_t1o ± 2 1 + 2I+l x + x .~ in vhich 6Td = h6v is the zero-field l1.yperfine separation between the states F = I + 1/2 and F = I - 1/2, and (gi - gJ)f.l.oHo x= ; ·.·•. ,, ', (49) 6W -18- 1.5 mJ mi J = 1/2 I= 3/2 3/2 1/2 1/2 1.0 1/2 2 I 0 -I -2 w 0 l::.W ~ .c -I 0 I -1/2 1/2 -1/2 1.5 0 0.5 1.0 1.5 2.0 X MU -17481 Fig. 3. Energy-level diagram for J = 1/2, I = 3/2. - 19 - 6.W ( and. hence 6.1/) is related to the dipole interaction constant a by the equation 6.W a ( ) 6v = ]1 = 2 2I+l • (50) The positive sign before the square root in the Breit-Rabi equation refers to the F = I + 1/2 state and the negative sign to the F = I ·- 1/2 state. An interesting geometrical interpretation of the Breit-Rabi equation may be found in the Ph.D. thesis of Y. l:l. Chan (CHA 62). For some cases of J>> l/2, perturbation theory starting from either the weak-field (F,m) representation or the strong-field (mi,mJ) representation may be used to approximate the energy levels at intermediate fields. For some cases of J > l/2, however, it is usually desirable to di~ agonalize the complete::.secular determinant of the Hamiltonian, 2 2 .,_r _ .... ~ [· 3( 1·1 ) +(3/2) 1·1- I ~ ]- ->.-t _ -t.-t <» - hai J+hb · · 2I(2I-l)J(2J'-l) 1-LogJJ H . 1-Logii H ' (512 The energy matrix will have the form shmm on the next page. The matrix elements may be calculated in either the (F,~) or (mi,mJ) representation, since the eigenvalues are independent of representation. In the F,.~ re presentation, neglecting off-diagonal terms in J, the only off-diagonal elements are the matrix elements of I and Jz coupling the states -:[F,~} 1vith 2 the states IF+l,~) and jF-:t~). Formulas for these matrix elements are ~.: given in Condon and Shortly, (CON 57), pp. 63, 64, and 67. Although the process of diagonalization consists of diagonalizing the indilVidual sub matrices corresponding to a particular value of ~' this still presents com putational problems in that it may involve solving polynomials of high order. In general, then, the calculation is tedious and a routine has been set up for both the IBH 650 and IB111 704, 709~ and 7090. The original method of solution was programmed for the IBI-·1 650 by Professor Hilliam A. Nierenberg. The outline of the solution, as w·ell as modifications of the program for other machines, is available in program. guides and also in the theses of Marino (HAR 59), Ehlers (EHL 60), and. Petersen (PET 60). In its simplest '... original form, the program would calculate the elements of a submatrix cor responding to a particular state (I,J,F_,~). It 1vould then solve for the root of the polynomial resulting from the diagonalization of the su.bmatrix for any particular state F. 1he most recent modification to the program was mad.e by Donald H. Zurlinden. This program, called BYPERFINE 4, can now be used to determine the best fit of observational data to any or all of th~. -20- ,..., >< 0 IJ...E >< >< 0 0 0 0 0 IJ...E I.LE 0 0 0 a >< .· 0 I --IJ...E . . . . 0 0 0 0 0 0 ,..., @ I>< lx 0 0 IJ...E IJ...E C\1 ~ ~ I>< C\1 --C\1 0 0 0 0 0 I>< I>< IL.E 0 0 IJ...E IL.E ~ ,..., ,....-- ,..., - C\1 >< I>< lx 0 0 0 C\1 IJ...E ~.~...e IL.E I>< - -- I>< ~ ~ ~ 0 -- 0 -- - - IJ...E 0 - I>< I>< 0 lx 0 IL.E 0 0 0 IL.E u.E IL.E ~ ~ ,..., -- ,..., - >< '>< 0 0 IL.E IL.E 0 >< ~ ~ 0 0 0 -- 0 X - >< ._e 0 0 IL.E IL.E ~ ,..., -- ,..., - >< lx 0 0 IL.E IL.E 0 - lB.. ~- 0 0 I>< - I>< 0 lx 0 IL.E 0 0 IJ...E IL.E ~ ..... -I ,..., >< 0 ->< I>< IL.E 0 0 IJ...E IL.E 0 0 0 >< ~ ~ 0 0 >< >< IL.E 0 0 IJ...E ~E ,...... >< 0 IL.E 0 0 0 0 ~ 0 >< >C >< 0 0 0 IL.E IL.E !:.E C\1 >C >C I >C 0 0 loc >C >C I>< . . . 0 IL.E IL.E 0 0 0 0 IL.E IL. IL.E IL.E IL.E IJ...E E lX C\1 >C >C loc loc . . . 0 IL 0 0 0 . . IL.E -E IL.E IL.E IL.E I - 21 - ~our parameters a, b, gJ' and gi. B. Nuclear TheOX"J The accumulation o~ experimental in~ormation on the properties o~ nuclear states has led. to an understanding o~ nuclear shell structure and the develop ment o~ shell-model theory proposed by Mayer (lvl.AY 55). 'l'his theory, based. on the indiiiTidual-particle model and the assumption o~ spin-orbit coupling, success~ully predicted the occurrence o~ the relatively large bind.ing energies ~or protons (or neutrons) at the so-called magic numbers o~ 2, 8, 20, 28, 50, 82, and 126, 1-rhich represent closed nucleon shells. The energy-level diagram sho-vm in Fig. 4 1.ras obtained by assuming a nuclear potential intermed.iatc bet1reen a harmonic oscillator and a sguare-i·rell potential, plus a strong spin orbit interaction. The ~ollovring empirical coupling rules were developed to correlate the observed nuclear spin with the shell model: (a) I1uclei -vlith even numbers of protons and. neutrons give rise to ground. states of zero angular momentum; ( \ (b) in odd-A nuclei, properties o~ the nucleus are determined. by those nucleons >vhich have the odd number; (c) ~or odd.-A nuclei, spins are coupled. in such a 1vay that the total angular nomentum is that of the last partially ~illed orbit. For odd-odd nuclei, Nordheim (NOR 51) _.has proposed empirical rules ~or coupling the odd proton to the odd neutron. The rules are as foliliovs: Nordheim's Strong Rule (Nl): J lj - j 1 for jl j = 1 2 = t 1 ±~and 2 = t 2 ~ ~; Nordheim's \Teak Rule In the veak rule, the resultant:;spin, J, tends tmvard the maximum value. In the above rules,·- j and-{_, represent the single-particle total and orbital angular momenta, obt-ained readily from the adjacent odd-A nuclei by using standard shell-model assignments. The distinction is made bet1veen the ob served total angular momentum of the odd-A nucleus, J (or J ), and the 1 2 single-particle momenta to account for cases o~ high seniority in -vrhich l_ 21+ j T J (or j J ) . An exanrple o~ this is Al The three neutrons in 1 1 2 f. 2 the d / subshell (j = 5/2) are coupled to a total angular momentum, J , of:'3/2. 5 2 2 2 -22- .. li------..... ------126 '-. 14--(126) li 137 2 2--(112) 3PI72 6--(110) 3p--<:>< -- 2£5/2 4--(104) 2£--< 3P37 2 8--(100) -- 2£772 lh972 I0--(92) / ------82 lh--< 3s---~ 3s 17 2 2---(82) 2d372 4--(80) 2d----<_ lhll7?. 12--(76). - 6--(64) -- 2ds7 2 8--(58) lg7 2 / lg----<: ------50 - lg97 2 10--(50) 2--(40) 2PI72 6--(38) 2p---<. lfs72 2 4--(32) /--- P372 If--< '-. ------28 8--(28) lf77 2 ------20 Zs-----.-< ld37 2 4--(20) ld--<_ 2s 17 2 b----(16) lds72 6--(14) ------8 lpl72 2---(8) lp---.=-::::... lp372 4---(6) ------2 Is---- Is 17 2 2--(2) MU-17154 Fig. 4. Schematic diagram of nuclear level systems with spin-orbit coupling. - 23 - There are, hmrever, frequent violations of the weak rule N2. Brennan and. Bernstein (BRE 60) have proposed revisions to the Nordheim rules that make it possible to obtain better agreement bet-vreen the observed and pre dicted spins. These rules, -vrhich 1-rere supported by consideration of the theoretical calculations by Schvrartz (SCH 54) and de Shalit (DES 53), are as follOI·TS: For levels that have configurations in which both the odd protons and odd neutrons are particles (or holes) in their respective unf~lled subshells, the coupling rules are: Rl: for ± 1 and 1 ! = I jl j21 jl =tl 2 j2 + 2 and R2: I + for ± ~ and j + .l = !•Jl - j21 jl = t 1 2 - 2 · For the special case of jl or j equal to the ambiguity of R2 is 2 ~' removed and the rule predicts J = jl + j . 2 · For configu2·ations in which there is a combination of particles and holes, the prediction makes no definite statement, although there is a tendency for the resultant spin to be given by The correlation of magnetic moments of nuclei to nuclear spin was first pointed out by Schmidt (SCH 37) and Schuler (SCH 37a). Although magnetic moments for a given nuclear spin ! vary appreciably, the odd-Z nuclei show the value of the moments increasing for increasing j . The odd-N nuclei do not p shm-r this variation. From this type of behavior, the assumption was made that both the angular momentum and spin of the nucleus are due to the last odd particle. Formulas for magnetic moments derived from this model are sho1m in Table I for the two cases of the angular momentum parallel or antiparallel to the intrinsic spin. Table I. Schmidt formulas for nuclear magnetic moments. .\· Type of nuclei Parallel (I = ~) Antiparallel (I = t -"lT" Odd proton ll = I + I l (-2L - ll ) lli = I - ~ + llP I I - p Odd neutron I 1-!r = I + l - 24 - In Table I, the symbol I replaces j or j , whichever is applicable. p n The s;ymbol 11 refers to the measured moment of the proton, 11 = 2. 793 nuclear p p magnetons (nm), and 11 to the measured moment of the neutron, 11 -1.913 11m. n n = On the basis of the Dirac equation, one would expect 11 = 1 nm and 11 = 0.0 n.-·n. p n The excess of the measured values is called the magnetic-moment anomaly, and. is usually attributed to mesonic fields that surround tbe elementary particles. Calculations of magnetic moments for different j's, using the Schmidt formulas and. both the measured value of 11 and the Dirac value, give, for odd-proton p nuclei, two limits for j = t + ! and j = t - -~. Host measured magnetic moments fall betvreen these Schmidt limits, although a few values fall on the limits. These intermediate values may be due to some sort of "quenching'1 of the anomalous magnetic moment of the proton and neutron 1v-hen they are bound to the nucleus (MAY 55). The same limits can be established in the odd-neutron cases, although the Dirac limits are the same for the parallel or antiparallel case. - 25 - III. EXPERTiv1ENT A. Description of the Apparatus Although the design is basically that described in an earlier thesis by Sunderland, modification have been made and are described in the theses of Shugart (SHU 57), Marino (MAR 59), Ehlers (EHL 6o), Chan (CHA 62), and Petersen (PET 6o). A schematic representation of the machine is shown in Fig. 5 and can be used to show the basic theory of the atomic-beam flop-in apparatus. The neutral atoms are thermally ejected from an oven situated at 0 and enter the inhomogeneous magnetic field in region A, where they experience a deflection due to the interaction of the gradient of the field with the magnetic moment of the atom. The atom then traverses the uniform C field, which corresponds to the external magnetic field quantity appearing in the Hamiltonian and determines the separation of the energy levels. This field does not deflect the atom, but there may be transitions induced between the energy levels by the superimposed rf field at certain frequencies (RAM 56). If there is no transition, the atom experiences a deflection in field B in the same direction as in region A, as shown in trajectoryQ). It therefore hits the wall of the machine and cannot reach the detector. If the atom undergoes a transition in the C field, the sign of its effective moment is changed and the atom is deflected in the opposite direction in the B field, following trajectory® and hitting the detector at D. The "stop wire" at "S" serves to prevent any undeflected atoms, such as those in the high-velocity tail of the Maxwellian distribution or zero moment atoms, from reaching the detector and contributing a high background. The conditions for refocusing can be obtained from the following equations. The force on an atom in an inhomogeneous field is dW dW dH F z = - d:Z = - dli dZ = 1-Leff '\1Hz ' where 1-Leff = - ~~ and W is the energy. The condition that the forces in A and B be equal and opposite for refocusing implies that, for equal gradients, (52) Since the magnitude of both the A and B fields is high enough so that the dW atoms are in the "high field" or Paschen-Back region, the 1-Leff or - dz is, from Eqo (46 ), -26- PUMP i I Ft I I --- :or---- I I I MU-13185 Fig. 5. Schematic component arrangement and atom trajectory in an atomic-beam magnetic -resonance (flop-in) machine. ·~ 27 - ~eff ~ gJ ~o mJ + gi ~o mi ' (53) or, since gJ ~ 2000 gi' the effective moment is given by (54) Therefore, the explicit refocusing condition is mJ(A) = - mJ(B) • (55) Thecactual apparatus used in the experiments described below is shown in Figs..6 and 7. Figure fu shows the oven end of the machine, which contains the horizontal radioactive oven loader and vertical calibration oven-loader. The radioactive oven loader is shown in Fjg. 8. The oven itself is heated by means of electron bombardment. Temperatures as high as 1500°C may be obtained with this arrangement. Figure 6b shows the detector end, which contains the vertical tube for taking sulfur-coated detector buttons in and out of the vacuum ,Fig. 9 1, and a hot wire used for detecting the stable alkalies used in calibrating. The brass plate shmm at the end of the machine was replaced by another plate with a Wilson vacuum seal. Radio-frequency power was fed through this seal into the hairpin, situated in the C field, by means of a rigid brass-walled coaxial line. The position of the hairpin can thus be moved to the region of maximum homogeneity to insure minimum line width. A detailed description of the electronics used to generate the rf frequencies is given in another section, although some of the equipment is shown in Fig. 10. A sketch of the hairpin is shown in Fig. ll. The hairpin could induce both ~(~ = ± 1) and cr(~ = 0) transitions, since there are components of the rf field both perpendicular and parallel to the direction of H , the 0 C field. For ~ transitions, the standard resonance curve is observed. For a transitions, the entrance and exit oscillating field components parallel to the C field are 180° out of phase and give rise to double-peaked resonance curves (RAM 56) with the resonance frequency at the central minimum. B. Methods of Detection The atomic beams of stable alkalies used for calibrating the C field were detected by letting the atoms impinge on a hot rhenium filament. Since the ionization potential of the Rb is less than the work function of the · rhenium, the atoms emerge as ions and are accelerated to a collector plate -2 8 - " Z N-2370 Fig. 6. (a). Oven end of atomic beam machine. (b). Detector end of atomic beam machine. -29- ZN-2362 Fig. 7. Oven end of machine after installation of lead shielding. -30- zI N r::: Q) > 0 Q) .>..... -+-> (.) ctl ...... 0 '"d ctl P:: ...... 00 ~ -31- ZN -17 33 Fig. 9. The button loader. -32- ZN -3659 Fig. 10. View of radio-frequency equipment. -33- I I I I ... I '·,.. ..' I I I ,, I II 1 .-·~· I 'lr-1 I I ''I I ... ~ l11 I .. I Ill I I Ill I I II I I Ill I Jll_ ...... J I I I ... I I I I I )- I •·· I .. I ,. I I I - < I~ I I I MU-19576 .. 7 ·.- Fig. 11. Sketch of the radio-frequency hairpin•. I w ~ ZN-2675 Fig. 12. Scalers, high-voltage supply, and shielded counting tubes used for detection of p-particle activity. -35- ZN-2363 Fig. 13. Counting equipment, showing f3 counters ~n foreground and crystal counters in background. - 36 - surrounding the filament. The resulting ion current is measured with a Cory vibrating-reed electrometer with a sensitivity of about lo-l3 A. Radioactive beams were collected on sulfur- or copper-coated brass "buttons" and were counted either in a crystal counter or a continuous flow ~ counter, depending on the mode of decay. Such ~ counters are shown in Fig. l2 and are described in detail in Petersen's thesis (PET 6o). The crystal counters as shown in Fig. l3 are discussed in the thesis of Ewbank (EWB 59). The radioactive buttons are counted in each of the four crystal (or ~) counters to improve the statistics on the counting rates. c. Experimental Procedure After the radioactive oven has been loaded into the machine, a fairly s~andard operating procedure is followed. The magD.i tude of the C field· is set at a particular value by varying the current thro~gh the magnet and calibrating the field with stable Rb. 8 8 Since the atomic and nuclear constants of Rb ~ and Rb 7. ,are accurately knoWn (RAM.. 56t tables ~r· frequency versus field were calculated for the focusable transitions. 'These calculations were done first on the IBM 650 and later on the 7o4, 709, and 7090, and the tables were printed for values ··or the field from 0 to 500 gauss in 5- gauss steps. Once the field is calibrated the oven is brought up to operating temperature, at which a suitable beam is obtained. There are now three types of exposures that can be made. For a "full-beam button, " all the magnetic fields are turned off and the stop wire is taken out of the way of the beam. This type of button, when counted, gives an indication of the amount of beam reaching the detector from the oven. An exposure for which the A and B fields are on, the-.rf is off, and the r stop wire is out of the beam is called a "half-beam exposure. 11 Counting activity on a button of this type indicates what percentage of the full beam is unaffected by the A and B fields and hence is unavailable for participating in a resonance. The percentage of beam available for a resonance is expressed by the throw-out ratio, R, defined by Full-beam counting rate) - half-beam counting rate) (56) R = Full-beam counting rate - 37 - The throw-out ratio may vary anywhere from 50 to 90% for the isotopes considered here. A "resonance" button is one for which the A and B fields are on, the stop wire intercepts the beam, and the rf is on. Since the beam intensity varies during an experiment, owing either to half-life decay or temperature fluctuations, the half-beam exposure is taken after every resonance exposure in order to normalize the counting rate of the resonance button. Hence, in order to sweep across a 1resonance, a resonance exposure is taken at a particular frequency and for a time long enough to collect a countable amount of material (varies from 2 to 15 minutes). A half-beam button :is exposed between each resonance button. The frequency is changed for each successive resonance button by an amount that is determined by the expected line width of the resonance. After each ecposure, the button is sent to the counting room (which is some five floors removed from the high-activity beam machine) by means of a pneumatic tube setup. A button and carrier are shown in Fig. 14. This procedure is repeated until the region of the resonance has been covered. At the end of the experiment, the C field is again calibrated to account for any drift that may have occurred during the run. This entire sequence was in general followed for the Cu and Fe experiments. -38- I i / 'I'JF J ~.J l lVII""' + ' .t' ry ""' ZN -2367 Fig. 14. Collector button and carrier used to transport buttons through pneumatic tube. - 39 - 61 IV. Cu EXPERIMENT A. Isotope Production and Chemistry 61 The Cu isotope with a half-life of 3·3 hours was produced on the Berkeley 61 60-inch Crocker cyclotron by the reaction Co59(a,2n)cu . An internal target (Fig. 15) was used so that the 47-MeV a particles could be degraded through 14 mils of aluminum foil to an energy of 34 MeV. This was inferred to be the 61 energy for the maximum cross section for the production of cu with 4-mil cobalt foil (GHO 50). Because of the radioactivity involved, the chemical separation of the copper from the cobalt was done inside the lead box or "cave" shown in Fig. 16. Because of the nature of the short 3·3-hour half-life, an effort was made to keep the chemistry simple and short enough to be completed in approximately 'l hour. The chemicals were contained in reservoir pipettes (approx l in. in diameter L the ends of which were terminated by a glass eye dropper. Pipetting was remotely controlled from outside the cave. Before the chemistry was begun, the chemicals were introduced into the cave and drawn up into the pipettes. During the chemistry; the required amount of a particular chemical could be obtained by pushing in the remote plungers (which can be seen in Fig. 16) above the lead glass window. The Variac controls for the hot plate and centrifuge can also be seen to the right of the window on the exterior of the cave. There are also inputs on the back of the cave for introducing various gases, such as H S, into the cave. 2 The chemistry 1>1a.s initiated as soon as the target came off the cyclotron. Since the cyc;Lotron beam pattern defined· the region of irradiation, the foil was trimmed of all extra cobalt. After trimming, the foil was dissolved in l2N HN0 , approximately 20 mg of Cu carrier was added, and the solution was 3 boiled to dryness, The residue was dissolved in water and a small amount of HCl to control the pH value for precipitation with H S. The copper was then 2 precipitated as CuS. The CuS was redissolved in water. Again a few drops of HCl .was added so as to assure a slightly acidic solution. The metallic form of copper was obtained by electroplating the metal out of the solution. The ) copper metal was placed in a tantalum oven of the type shown in Fig. 17. The slits on the front were opened to a width of about 3 to 4 mils for the emergence of the beam. A small amount of CsCl was added to be used for lining up the oven with the hot-wire detector and the oven was inserted into the machine. A picture of the oven used in this experiment is shown in Fig. 17. -40- I . I . lo I r . I . I )6 I rt . l9 ' ZN-3132 Fig. 15. Cyclotron internal target assembly. -41- ZN-3134 Fig. 16. Exterior view of lead cave in which chemical separations were performed. - 42 - B. Theory of the Cu Experiment 1. General description of theory 61 The electronic ground-state configuration of cu with 29 electrons is 2 2 6 2 6 10 l . . . . 2 ls 2s 2p 3s 3P 3d 4s whlch ln spectroscoplc notatlon is a 81 ground state" 2 1 1 This implies J =2, L = O, and S = 2· Hence the gJ value, defined by J(J+l) + S(S+l) - L(L+l) J(J+l) + L(L+l) - S(STl) 2J(J+l) ,_ gL 2J(J+l) (58) •. J • is equal to gJ = g1_ = g . The experimental value of gJ has been measured by 8 .· 2 Cu 61 Ting and Lew (TIN 57) to be gJ - 2"0026(10)" The nuclear spin of the cu isotope was measured by Nierenberg and others (NIE 57) to be. 'I = 3/2. Although the 3/2 nuclear spin implies that a magnetic dipole, electric · ·quadrupole, and magnetic octlipole may exist, the J = ~ electronic ground state ·makes only the magnetic dipole observable. The purpose of this experiment, then, 61 was to measure .the hyperfine-structure separation for Cu , from which we obtained 1 ·the magnitude and sign of the magnetic moment. Since J = 2, the Breit-Rabi equation, (59) 61 may be used to ~btain the energy-level diagram for Cu as shown in Fig. 18" This diagram shows in a qualitative ~ay the general relation between the energy levels characterized by mF = m + m and the uniform magnetic C field. The 1 J parameter x is given by (60) The hF = 0 transition that obeys the focusing condition mJ(A) = - mJ(B) is the m = - I + l/2, m = - I - l/2, as shown on the diagram, and is referred to Fl F2 as the standard transition, v . As is evident from the diagram, the frequency s difference between the two levels, v =W (61) s - w ~l ~2 goes to zero as H ~ 0 and does not depend directly on the hyperfine-structure separation as for a 6F = l transition. For x << 1, the energy difference varies -43- ZN-2195 F i g. 1 7. Tantahun oven. - 44 - linearly with H (Zeeman region) and shows a dependence on 8v only at fields for which x ~ lJ i.e.J fields strong enough for decoupling to begin. The explicit form of this·type of dependence is shown by taking the energy difference of the two levels as described by the Breit-Rabi equation) w - w mF mF . 4mF X 1 1 2 v + f:::Y { [l + _l + x2l2 - [1 + s h (~ - ~) 2 ; 2I+l . j 1 2 (62) Expanding the square roots and letting x.6.V (- gJ + gi) ~o H v (63) 0 2I+l 2I+l h gives the result: 4 v v flo H + 2I v 2 + 2I(2I-l) v 3 +B vo + ... (64) s 0 gi h b,V 0 ,6.V2 0 ,6.V3 Keeping terms to second order only gives v v - g flo~H + 2I v-2 (65) s 0 I h ,6.V 0 For ,6.V >> v and neglecting terms in giJ we have the Zeeman frequency 0 gJ flo v v J (66) s - 2I+l h H 0 which can be used to measure a spin) I. However, if the spin) and hence v , 0 is known) the shift from Zeeman frequency~ v - v = ov ::: 2I v 2 (67) s 0 ,6.V 0 is proportional to the hyperfine-structure separation) ,6.V. This was the pro- 61 cedure employed to measure the .6.V of Cu . The ,6.V was roughly estimated by using the previously measured fli values 6 63 of Cox and Williams (COX 57)) fli(cu 5) = 2.376(7) nmJ and fli(cu ) 2.226(7) nm. These values show fli decreasing with decreasing AJ and) if we assume a monotonic 61 65 63 decrease) predicts a value of fli = 2.085 for Cu The .6.V's of Cu and Cu 65 were determined by Ting and Lew (TIN 57) to be .6.V(Cu ) = 12,568.81(1) Me/sec) 63 and .6.v(cu ) = 11)733.83(1) Me/sec. If one compares the two isotopes) using the Fermi-Segre formula, Eq. (37)J one obtains the relation (68) -45- 1.5 mJ mi J = 1/2 I= 3/2 312 1/2 1/2 1/2 1/2 -l/2 2 -312 0.5 I 1/2 F=2 0 -I -2 w 0 D.W ~ .r: :..1/2 -3/2 0.5 -I F =I 0 I -1/2 -1/2 1.0 -1/2 112 -1/2 3/2 1.5 0 0.5 1.0 1.5 2.0 X MU- 17481 61 Fig. 18. Breit-Rabi energy diagram for Cu , showing observable L:J!' = 0 transition. - 46 - 63 6 With the values of gi and 6V for cu as the comparing isotope, for I(cu 3) 3/2, 61 the 6V of Cu was estimated to be 61 63 f.LI(cu )6v(cu ) 3 f.LI(Cu ) This approximate value could also have been obtained by assuming a monotonic decrease with A for the 6V's and using the measured 6V's of Ting and Lew (TIN 57). 2 With this estimate and using the formula ov ~ 2I/6v v J it was possible to 0 predict roughly the field for which an appreciable shift would occur. In practice, the 6V was calculated from the experimental data on the IBM 709 by using _the HYPERFINE 4 program mentioned earlier in this thesis. The approx imate value of 6V obtained from using Eq. (67) could be used to predict initial values of a for the computer routine. In brief, the required input for the routine is as follows: (a) a of a comparison isotope, (b) I, gi, gJ, and a of the calibration isQtope, (c) I, J, and a (some initial assigned value) of the experimental isotope, (d) resonance data: calibration isotope or magnetic field, resonance frequency fobs' and its corresponding quantum numbers F , mF , F , m 1 l 2 F2 The corresponding output is then: (a) calculated magnetic field, (b) best values of gJ' gi, and a with uncertainties, (c) calculated frequencies of two energy levels for each resonance, and the residual frequency, defined as (f b - f ). . o s ca1 c In the above description, b was assumed to be zero, since J = l/2. Since the program utilizes a least-squares fit routine, uncertainties on all the input data are also included. Uncertainties for all quantities are also included for all the output data. To determine the best fit for the parameters, the program finds the minimum of a function N(a,b,gJ,gi), which is commonly called the 2 "chi-square." This x , then, describes the "goodness of fit," and is also given in the output of the program. 2. Determination of the sign of gi A useful formula for the determination of the sign of gi can be obtained by inverting Eq. (62) for the standard transition and solving for 6V. The mathematics inv.olved in inverting the equation is straightforward, but tedious, and yields the result - 47 - . ~0 ~0 (v + gl h H) (- v - gJ h H) (69) gJ ~o + .2I ~o v + 2I+l h H 2I+l gi h H There is an ambiguity in this equation, since the sign of gi is unknown. How ever, there is a standard method for determining the sign of gi which utilizes the behavior of the equation at low fields. Let us assume that + g is the correct sign and define the quantities I v I ' and This/gives the results, for gi(+), (v+vJ)(v+vi) + !::::Y (70) 0: and for .g I (-) ' !::::Y (71) As H ---7 O, an approximate formula for the standard transition frequency is v J 2I 2I 2 v "' - v + !::::Y X (72) "' 2I+l ---2I+l 2 I (2I+l) Substituting this in the expression for f::,.V gives (v+v ) (v-v ) - J I f::,.V (73) 2I f::,.V 2 4I v 2 X 2I+l I (2I+l) 2 2 as H ---7 0. As H ---7 0, then, the terms in the denominator [2I/(2I+l) ]t:,.v X and [4I/(2I+l)]vi become comparable and give, for the incorrect value of gi' i a value of t:,.v- that will deyiate further from the correct value as H ---7 0. Sub- stituting in the value of v in the numerator of t:,.V gives v f::,.V 2I 2 v 2 J (4I+l) v + [::,.V X ] [v - +-- X J[- 2I+l (2I+l)2 J I 2I+l 2T+l I (74) !::::Y 2 [D.V X 2V ] 2I+l I - 48 - 2 t:Y X This expression has a pole at + 2VI; where the denominator becomes zero, 21 1 since, at this value 2V V - I J (4I+l) v + 2I v ] [vJ- vi+ 2I+l][- 2I+l 2 2I+l I (2I+l) I (75) '" 0 (v - v ) 2 I .· J and the numerator remains finite. The pole occurs at ~~~v~·~(--I~+-~) 2V or at 2 1 I I h(2I+l) gi -3 h(2I+lj H 2 bY ~ 10 tY gauss" (76) IJ.o (g - g )2 IJ.o I J 2 For very small H, the terms in X can be neglected, and (vJ- vi)(- vJ- (4I+l)vi) l (77) - 2VI 2I+l Hence LV ~ 0 as H ~ Oo The behavior of LV for which we have assumed the correct value of gi is as follows" As H ~ 0 1 2I l + [- 2I+l 2I+l] LV (78) (v - v ) 2 2I I J ----2 (2I+l) Therefore measurements of the frequency at low fields will indicate whether gi is + or - according to which value of !:::Y remains constant" The value of f:::Y calculated with the incorrect sign of gi ¥ill show large deviations; whereas the LV calculated with the correct sign will remain constant. At high fields; + the two values of LV--LV and LV---approach a constant (although different) value. This procedure is valid only for those isotopes whose moment is large in absolute value" Otherwise; the calculations give substantially the same + - result for LV and LV " Co Experimental Procedure and Data Analysis The experimental procedure follows the general description of Chapter III. Half-beam buttons were exposed between each resonance exposure for the purpose of normalization" All the buttons were counted in sodium i.odide crystal counters, since the pri.ncipal mode of decay was by electron· capture (see Fig. 19). These -49- 1.22 > Q) :E 0.655 >- (!) 0:: w z w 0.281 0.071 0 STABLE Ni61 MU-30247 61 Fig. 19. The Decay scheme for Cu • - 50 - buttons were counted repeatedly in each of the four crystal counters over a period of three or four half-lives. A decay curve was obtained from a plot of the counting rate versus time. This decay curve could be fitted by hand to the par-ticular half-live) or could be analyzed into its component parts with the aid of a computer program called OMNIBUS. This program was written by H. B. Silsbee (SIL 55) 7 and contains three distinct parts. The first part fits the decay curve by the method of least squares to a maximum of five half-lives. The decay curves serve to identify the isotope and also allow extrapolation of the counting rates of· each button to a common time. The "common time" resonance counting rates are then normalized by the corresponding half beams and the curves for counting rate versus frequency resonance are plotted. The second part also uses a least-squares method to fit a bell-shaped curve to the points of the resonance curve. The third part of the program calculates the hyperfine-structure separation) !:::Y 7 from a knowledge of its resonance frequency and the frequency of the cali brating isotope. The rf signal generator used to induce transitions between the F = 1 7 mF = 2) and F = l) mF = - l levels was a Hewlett-Packard VHF siggal generator model 6o8c with a frequency range of 10 to 480 Me/sec. For additional power; two "Instruments for Industry" wide-band amplifiers; Models 500 and 510) were used. Frequency-measuring equipment consisted of a Hewlett-Packar.d Electronic Counter, Model 524B, with Model 525A and 525B plug-in units. 61 D. Results for Cu 61 A typlcal· decay curve f or Cu lS· s h own ln . F"lg. 20 . Resonances were observed at fields of approx 57) 99; 111, 126J 152J 176) and 238 gauss for the standard transition. Figures 21 and 22 are representative resonance curves obtained from OMNIBUS bell fit. The values of 6V for g positive and negative I were calculated by OMNIBUS and are given in Table II. -51- cu61 ,3.3hours DECAY CURVE OF RESONANCE BUTTONS FROM RUN 2563 40 ! 20 T = 3. 3 hours 112 ~ ::> ·e<:: 10 .,~ Q. 8 !! <:: ::> 0 u 6 LLl ~ a: 4 (!) z i= z :::> 0 (.) 2 0 120 240 360 480 600 720 840 TIME (minutes) MU-30248 Fig. 20. The Decay curve for Cu61 • -52- 100 RUN 2563 cu61, 3,3h (2,-1-2,-2) H =176.116 gauss 80 !! ·;: f ,.,::0 _g~ .0 0 ILl 60 1- <( 0:· <.!) z 1- z :::> 0 u 0 ILl N ~ <( :::0 a: 0 z 20 0 126.6 127.0 127.4 127.8 128.2 FREQUENCY (Me/sec) MU-30249 61 Fig. 21. Cu resonance for the standard transition (2,-1 -2,-2). -53- RUN 2564 61 80 Cu , 3.3h (2,-1-2,-2) H = 238.763 gauss :0 ~60 w 1- a::~ (!) z 1- z 6 40 <..> 0 w N __J :;;~ ~ 20 z oL___ ~~--...l-----~~~----~~--~~--~=-~~--L- __u~ 174.2 174.6 175.0 175.4 175.8 FREQUENCY (Me/sec) MU-30250 Fig. 22. Cu61 resonance for the standard transition (2, -1~ 2, -2). -54- u w (/) ASSUMED fo POSITIVE ASSUMED fo u' NEGATIVE ~ z 0 ~ a:: 14000 ff. w (/) w a:: ::> 1- g 12000 a:: 1- CI) I wz u:: a:: w FIT~ POSITIVE -- g: 10000 :::c I ./" NEGATIVE----- I I I 0 50 100 150 200 0 50 100 150 200 FIELD (GAUSS) MU-18038 61 Fig. 23. l::.v sign determination for Cu • - 55 - 61 Table II Summary of D,V measurements on Cu Calibration Resonance + Run frequency frequency D,V D,V Rb85 Cu61 moment positive moment negative (Me/sec) (Me/sec) 2561 40.870(50) 40.636(30) 10)500(1200) 13,300(2300) 2861 72.055(50) 71.138(120) 11)850(1300) 13)860(2100) 2562 80.725(50) 79.694(60) 11,070(500) 12,440(700) 2610 91. 707 (30) 90.351(50) 11,200(250) 12,420(350) 2862 111. Boo ( 30 ) 109.749(60) 11,340(250) 12,350(300) 2563 130.150(150) 127.506(60) 11,030(400) 11,810(450) 2564 179·950(100) 174.779(80) 11,290(200} 11,870(200} Weighted average 11,240 12,090 Figure 23 is a plot of.D,V for + g and D,V for - g versus the magnetic 1 I + field at which the measurement was made. The curve for D,V gives a fit that is more within the statistics for a constant value of D.V, whereas the curve for D.V gives a statistically better fit to the predicted variation for the incorrect sign of g . The assumed positive value of g , then, gave the best 1 1 fit to the data and resulted in D,V = 11}240 ± 400 Me/sec. The value of D.V with g assumed positive and negative was also calculated by HYPERFINE 4. The data 1 are shown in Tables III, IV, V, and VI. The residual repr.esents the difference between the observed resonance frequency and the calculated "true" energy for each level, i.e., ) (79) where R represents the residual and X represents the true energy for a particular level. As can be seen from the tables, the residuals for the assumed positive 2 value of g are smaller in each case. The same is true for the x values. 1 Tables IV, V, and VI are the HYPERFINE 4 results for the upper and lower limits of gJ and for gJ variable. Because the calculated value of D,V depends on the value of gJ, through the shift from Zeeman frequency, the error in gJ gives rise to a large error in D,V. The change in gJ gives rise to a larger change in D,V because even at the highest field of 239 gauss, the shift was only about 7 Me/sec. The value of D,V was taken to be 11,400 ±.300 to include the maximum and minimum values of D,V calculated from the maximum ~nd minimum values of gJ. However, - 56 - 64 the cu data show that the result should probably be weighted toward the maximum value of gJ. When gJ is allowed to vary in the HYPERFINE 4 routine; the best- fit value appears to be 2.0034(15). 61 The absolute value of ~I(cu ) was calculated from the Fermi-Segre formula 6 (which holds to an accuracy of approx 1%) in conjunction with ~ (cu 3) = 2.226(7)nm 6 1 from Cox and Williams (COX 57)} and ~v(cu 3) = 11}733.83(1) Me/sec from Ting and Lew (TIN 57). Both isotopes have spin 3/2. The Fermi-Segre formula 61 ~v(cu ) (80) 6-=< L:,V(Cu -') . 61 results in a value for ~I(Cu ) = 2.16(6) nm. The nuclear spins} ~v and ~IJ of three of the odd isotopes of copper 61 6 6 (cu ) cl?- 3J cu 5) have nbw been measured. The nuclear spin I of all three isotopes is equal to 3/2. This value of the spin is accounted for by shell model theory -.;.rhich assigns the 29th proton to the p / shell. Since we have 2 63 3 ~ (cu65 ) = 2.376(7) nm and ~ (cu ) = 2.226(7) nm) the positive value of 1 61 1 ~I(Cu ) = 2.16(6) nm is consistent with the monotonic decrease of 11I with decreasing A. '.rhe res1.-ut of 2.16(6) nm also lies within the Schmidt limits of 3-793 nm and 2.000 nm predicted for those isotopes whose nuclear spin is 3/2" •· 61 Table III Summary of cu data for (2)-1) ~ (2)-2) transHion. Comparing isotope Calibrating isotopes 87 -2~ -- --- 85 2 63 2 I cu ) s ) = j~; Rb ) s ) I = 3/2 Rb ) s , I = 5/2 112 2 112 112 g = - 2.0026 g = - 2.00238 g = - 2.00238 J -4 J -4 J -4 gi = 8.07 X 10 gi = 9-95359 X 10 gi = 2.93704 X 10 a= 5866.900 Me/sec 6V = 6834.685 Me/sec 6V = 3035.735 Me/sec Run Resonance H Residual) Weight Residual) Weight number frequency (gauss) gi > 0 factor) gi < 0 factor) (Me/sec) (Me/sec) gi > o. (Me/sec) g < 0 I 2561 40.636(30) 57·389(70) 0.0336 293·0 - 0.0316 294.0 2861 71.138(120) 99.853(67) - 0.0731 59.6 - 0.1448 59·7 2562 79.694(60) lll. 464 ( 67) 0.0286 166.7 - 0.0385 167.2 2610 90.351(50) 126.053(40) 0.0109 297·3 - 0.0465 297·9 Vl 2862 109.749(60) 152.412(39) - 0.0261 225.4 - 0.0547 225.8 --J 2563 127.506(60) 176.116(192) 0.0894 41.2 0.0992 41.6 "2564 174-779(80) 238.763(124) - 0.0201 64.8 0.1497 65.4 g > 0 I gi < 0 a 5634·7515 6066.6315 oa 41.919 48.555 4 4 gi 7·7506 X 10- - 8.3447 X 10- IJ.I 2.1347 - 2.2983 - x2 l. 33 4.99 61 Table IV Summary of ~u data for (2}-1) ~ (2,-2) transition. Comparing isotope. Calibrating isotope Same as Table III Same as Table III except gJ = - 2.0016 Run. Resonance H Residual, Weight Residual, Weight number frequency (gauss) gi > 0 factor, gi < 0. factor, (Me/sec) (Me/ sec) (Me/sec) g < 0 gl > 0 I 2561 40.636 (30) 57·389(70) 0.0466 293.0 .:. 0.0175 294.0 2861 71. 138 ( 120) 99.853(67) - 0.0589 59.6 - 0.1293 57·7 2562. 79.694(60) 111.464(67) 0.0419 166.7 - 0.0239 167.2 2610 90.351(50) 126.053(40) 0.0222 297.2 - 0.0341 297·9 V1 2862 109.749(60) 152.412(39) - 0.0205 225.3 - 0.0485 225·7 (}) 2563 127.506(60) 176.116(192) 0.0873 41.2 0.0972 41.6 2564 174.779(80) 238.763(124) - 0.0543 64.8 0.1131 6§.3 g > 0 g < 0 I I a 5548.664 5959·754 oa 40.693 46.964 4 4 gi 7.6323 X 10- - 8.1977 X 10- 2.1021 - 2.2578 f-l. I - x2 1.88 3·29 61 Table V Summary of cu data for (2)-1) ~ (2,-2) transition. Comparing isotope Calibrating isotope Same as Table III Same as Table III except gJ = - 2.0036 Run Resonance H Residual, Weight Residual, Weight number frequency (gauss) gi > 0 factor) gi < 0 factor, (Me/sec) (Me/sec) g > 0 (Me/sec) g < 0 I I 2561 40.636(30) 57·389(70) 0.0206 292.9 - 0.0457 293·9 2861 71.138(120) 99.853(67) - 0.0874 59·6 - 0.1602 59·7 2562 79.694(60) 111. 464 (67) - 0.0152 166.8 - 0.0529 167·3 2610 90·351(50) 126.053(40) - o.ooo6 297· 3 - 0.0588 298.0 2862 109.749(60) 152.412(39) - 0.0317 225.4 - 0.0607 225.8 \Jl \0 2563 127.506(60) 176.116(192) 0.0915 41.3 0.1016 41.7 2564 174.779(80) 238.763(124) 0.0140 64.9 0.1868 65.4 g > 0 g < 0 I I a 5723.407 6177·970 Da 43.227 50.477 4 4 gi 7.873 X 10- - 8.498 X 10- f..I.I 2.168 - 2.341 - x2 1.20 7·19 61 Table VI Summary of c~ data for (2;-l) ~ (2;-2) transition. Comparing isotope Calibrating isotope Same as Table III Same as Table III except gJ variable Run Resonance H Residual, Weight Residual) Weight number frequency (gauss) gi > 0 factor, gi < 0 factor, g > 0 (Me/sec) g < 0 (Me/sec) (Me/sec) I I . 2561 40.636(30) 57-389(70) 0.0233 292.9 0.0231 294.2 2861 71. 138 ( 120) 99.853(67) - 0.0844 59.6 - 0.0848 59·7 2562 79.694(60) lll. 464 ( 67) 0.0181 166.8 0.0176 167.2 2610 90.351(50) 126.053(40) 0.0019 297.3 0.0014 297·8 0\ 2862 109-749(60) 152.412(39) - 0.0304 225.4 - 0.0310 225.6 0 2563 127.506(60) 176.116(192) 0.0913 41.2 0.0906 41.5 2564 174.779(80) 238. 763(124) 0.0074 64.9 0.0063 65.1 g > 0 < 0 I gi a 5705.004 5670-329 5a 142.489 141.818 gJ - 2.0034 - l. 9987 - 5g 0.0015 0.0015 J 4 4 gi 7.847 X 10- - 7.800 X 10- fl. I 2.161 - 2.148 x2 1.19 l. 20 ---...... _./ - 61 - 6 2 v. Cu EXPERIMENT A. Isotope Production and Chemistry 62 The cu isotope with a half-life of 9.9 minutes was produced by the decay 62 o f 9 . 3 - h our Zn 62) wh' lC 'h was formed by the reaction Ni(aJ2n)zn J with 40-MeV a particles on an internal target. The 10-mil nickel foil degraded the a 61 particles to 34 MeV) the maximum cross section for the reaction (GHO 50). cu J r 61 with a half-life of 3·3 hours and a spin of 3 I 2J formed by the decay of Zn ) is also present. The procedure for dissolving the metals and precipitating out 61 t rle~ c u as a sulf"d l e lS. Slml . '1 ar t o t h e Co-Cu chemistry with the exception that the nickel must be dissolved in hot aqua regia. The first Cu precipitation 61 contains mostly the 3·3-hour cu (since the short-lived activity decays away). The Cu precipitate is dissolved in nitric acid and water and saved to be added 62 to successive "chemistries" for the purpose of normalization. The Zn generates) 62 by its decay) a maximum amount of cu in 45 minutes) according to the formula (EVA 55) log ~ A.A (81) - A. A where A refers to the parent and B the daughter) and A. = 0.693(r / J where 1 2 'tl/ is the half-life. Approximately every 45 minutes the accumulated copper 2 was remove d b y a If c h emls• t ryII ( -l.e.J• an analytic procedure.· to separate the Cu 62 which had built up during that time from the nickel-zinc solution). The procedure 61 was as follows. An aliquot of Cu carrier and a measured amount of Cu were 62 added to the zinc- nickel-cu solution and the Cu was precipitated with H S. 2 The CuS was then dissolved) electroplated ontor.a platinum wire; and scraped into an atomic beam oven (see Fig. 17)J and inserted into the atomic beam machine. A small portion of the electroplate was dissolved and placed on a brass button suitable for insertion 1nto the beta counters. This particular sample is referred to as a "chem1stry button." A schematic diagram of the chemistry is shown in Fig. 24. B. Experimental Procedure and Data Analysis Because of the short half-11fe, the usual experimental procedure was some what modif1ed. 'rhe chemistry was designed to take not more than a half-life) i.e., about 10 to 15 minutes. ~~ile the chemistry was being performed, the C field of the atomic beam machine was calibrated so that the experiment could -62- C u 62 EXPERIMENT 62 BLOCK DIAGRAM Ni , Zn , Ct62 Cu 61 ,Cu ELECTRO- SPIN I OVEN CHEMISTRY r-- r--- BUTTON CARRIER - PLATE -- -· ! CHEMISTRY Ni , zn62 COUNTER BUTTON MU-19735 62 Fig. 24. Schematic representation of cu procedure. - 63 - begin immediately after insertion of the oven into the machine. The oven, loaded with cesium chloride as an indicator, was aligned with the hot wire, and then the entire oven load was blown out onto one button at a frequency corresponding to a particular spin. Hence each data point involved a 45-minute walt. for Cu 62 b Ul"ld -up from Zn and a chemistry to separate out the Cu 62 Normal- ization data were obtained by counting this spin button simultaneously with the 62 chemistry button in the beta counters (since Cu decays by positron emissi.on 62 to Ni ). The spin is experimentally verified when the ratio of 10-minute to 3-3-hour Cu is seen to be greater (through enrichment with 10-minute Cu) on the spin button than on the chemistry button. For spin values other than the correct 61 one, the two ratios should be approximately equal, since the Cu with a spin of 3/2 does not undergo transition and hence is not focused. To obtain decay curves, each button was counted in a beta counter for a period of approximately l hour. These data ~ere run through OMNIBUS, which fitted the curve to half-lives of 9-9 minutes and 3·3 hours. The program took all the counting rates from each decay curve back to a common time. This "t = 0" counting rate was used to compute all ratios. Usually a large error on the ratio reflects a lack of 10-minute component in the decay. The rf setup used for the experiment is shown in Fig. 25. 62 . c. Theory of Cu Experlment The electroni.c ground state and gJ of Cu was discussed in a preirious sec tion. Since the purpose of the experiment was a spin determination, all data 62 Here taken in the low-field region. Assuming a value of the spin of cu from the shell model and using the values for I (that is,. I = l) and t::Y (that is, 64 l::o:V = 1278(20) Me/sec) from Lemonick and Pipkin (LEM 54) for Cu , Qne roughly 62 estimates the 6V of cu from the Fermi-Segre formula to be of the order of 1000 Me/sec. Hence, setting the magnetic C field at a value of< 30 gauss should make it low enough to insure linear Zeeman region. The low-fi.eld expres si.on for the energy i.s gi.ven in Eq. (41). For the standard transi.tion, which, for the case of spin l, is indicated i.n Fig. 26, the equation gives, for the case of J = l/2J gJ !J.o v (82) s 2I + l h H 85 87 Since the calibrating isotopes Rb and Rb , also with J = l/2, obey the same expression, the relation between the calibration frequency and the resonance -64- HEWLETT- PACKARD ELECTRONIC COUNTER MODEL 524 8 TEKTRONIX SIGNAL GENERATOR TYPE 190 'VV'v w RF HAIRPIN MU-30251 Fig. 25. Radio-frequency equipment (0.35- 50 Me/ sec). -65- 1.5 mJ m 1 J = 1/2 I= I + lf2 +I 1.0 +1/2 0 mF .+3!2 + lf2 -1 0.5 +112 3 F= 12 -1/2 w ~ b.W 0 62 Fig. 26. Energy-level diagram for cu • - 66 - frequency for Cu can be obtained by taking the ratio of the two expressions. Since both elements have J = l/2, the g 's are approximately equal, and the J ratio gives (83) . 62 The,spin predictions for the odd-odd nucleus cu are ambiguous. The 29 33 odd 29th proton, which is ~ne more than the magic number 28, is assigned by the shell model to the 2p / level. The five neutrons beyond the closed shell 3 2 at 28 are divided by shell theory between the 2p / and lf / states, which 3 2 5 2 lie close together in energy (see Fig. 5). Occupation of these two levels depends on the magnitude of the difference of the pairing energies, P - P , relative to the level distance f5/2 p3/2 € - € f ; p / as follows (MAY 55): 5 2 3 2 (i) If the pairing energy of the two f / nucleons is greater than·~tltlat for 5 2 for the two p / nucleons by more than that needed to raise them from the p / 3 2 3 2 to the f / level, 5 2 there would be a gain in binding energy ifboth neutrons were raised into the f / level to pair in that level. The third neutron could go into the p / 5 2 3 2 level, since it has no particle with which to pair, but the fourth and fifth neutrons would pair in the f / level, giving the configuration 5 2 i.e., one neutron in the p / state, four neutrons in the f . 3 2 512 (ii) If the difference in pairing energy were greater than the level distance, but smaller than twice the level distance, ' the first two pairs would be formed in the p / level, completely filling that 3 2 level. Because of the Pauli exclusion principle, the fifth neutron would go into the f / level. However, energy is gained by greaking up one p / pair 5 2 3 2 - 67 - and bringing one neutron up into the f / level) where it can pair with the 5 2 odd neutron in that level. This gives a configuration (iii) If the pairing-energy difference were even smaller than the level distance) the levels would be filled in sequenceJ giving Cases (i) and (ii) give rise to jl = £ + l/2 = 3/2J whereas case (iii) gives jl = £ - 1/2 = 5/2. The Brennan and Bernstein coupling rules (Rl and R2) can be used to couple jl of the neutron to the p / J proton which has a 3 2 j2 = £ + 1/2 = 3/2. For j = £ + 1/2 and j = £ + l/2J rule R2 predicts a 1 2> total angular momentum J = /3/2 ± 3/2/ =OJ 3· For jl = £ 1/2 and j = £ + l/2J 2 rule Rl predicts a total angular momentum J = /5/2 - 3/2/ l. 62 D. Results for Cu A typical decay curve for spin l is shown in Fig. 27. Table VII is a collection of data taken from all the experimental runs. Figure 28 is a plot of the ratio of the spin ratio to the chemistry ratio versus spin value. In each caseJ spin 1 shows a significant enrichment well within statistics of the 10-minute isotope on the spin ratio above that on the chemistry ratio. With reference to the Brennan and Bernstein coupling rule RlJ spin 1 implies a 4 1 (p ; ) (f ; ) configuration for the five neutrons outside the magic-number 2 2 3 5 1 shell of 28 and a (p / ) configuration for the 29th proton. 3 2 An attempted resonance for spin 1 is shown in Fig. 29. The Zeeman predicted resonance frequency (for 6v assumed to be infinite) is 8.086(050) Me/sec. Since there were only three usable points on this resonance, it is difficult to pre- d.ict a peak frequency from the curve. However, that there appears to be even a slight shift at this low field indicates that the 6V is probably not much greater than 1000 Me/ sec. Owing to the scarcity of information) no definite limits to the value of 6V can be assigned. -68- 50 -!1 ·c: :::J ! >o 2 ~ 0 2 ~ :0 10 ~ ~ -~ 0 2 ·! 2 LLI ! £ 1- £ £ £ <( 2 2 £ ·CHEMISTRY 0:: ! DECAY 5 ! (!) ! z ! ! i 1- z ! ! :::> SPIN I 0 DECAY u ( Cu61) T1 =3.3 hr y2 QL---~----~--~--~----~--~----~------30 60 TIME (min) MU-19733 62 Fig. 27. Decay curves for a cu spin button and chemistry button. - 69 - 62 Table VII Summary of spin measurements on Cu . Ratio of ,counting r,ates Calibration freq_uency Exposure Run Rb85 Button freq_uency Spin (Me/sec) (Me/sec) 268 l. 595 IR l. 914 2 0.25 ± 0.3 l. 592 IS 3-190 1 21.78 ± 2.4 l. 592 IU 3-184 l 4.8 ± 0.3 l. 576 IV 1.910 2 0.098± o. 2 281 2.908 RX 5.816 l 9· 29 ± l. 5 2.892 UA 5.825 l 6.7 ± 4.0 296 4.042(025) YF 8.086 l 4. 28 ± o. 46 4 . 04 2 ( 0 25 )" YG 8.300 l 5· 65 ± 1.17 4.040(025) YH 8. 500 l 2.80 ± 0.80 304 l. 745 (100) 7G 3-690 l 3-32 ± 0.4 l. 816 (100) 7H 2.200 2 0-97 ± 0.3 l. 720 (100) 7I 3-672 l 5· 88 ± l. 8 312 3.202(025) Q.C 6.400 l 8.26 ± 0.8 3-211(025) Q.D 2.745 3 2.74 ± 0.5 3.209(025) Q.E 6.420 l 8.31 ± 0.6 4.946(020) Q.F 2-750 3 2.58 ± 0.3 4.942(025) Q.G 9-890 l 7-93 ± 0.7 4.936(030) Q.H 4.235 3 6.34 ± 4.5 4.936(030) Q.I 5·925 2 1.43 ± 0.4 320 8.oo6(o5o) lOC 15.650 l 1.59 ± 0.6 8.006(050) lOD 15.800 l 13.80 ± 6.0 7·972(050) lOE 15.900 l 20.0 ± 3·0 7·993(050) lOF 16.050 l 16.1 ±43.0 7·975(050) lOI 15.850 l 0.7 ± 0.3 400 5-031 31 9-\100 l 1.46 ± 0.3 5.044 32 10.088 l 4.04 ± 0.4 5.026 33 10.288 l 2.58 ± 0.2 -70- RUN 312 cu62 10 10 SPIN SEARCH E RUN 304 • 8 ~8.. Cu62 J::.., ..s SPIN SEARCH !~ ..... ·ec:: 2 ~6 6 ii. ~ J:: ~.., ..... c:: E g4 4 2 1- oct 0:: t7 2 2 Q 0 u SPIN I SPIN 2 FULL BEAM SPIN I SPIN 2 SPIN 3 MU -19734 62 Fig. 28. Spin search for cu • -71- RUN 296 Cu62 SPIN I RESONANCE f O~--~-----r----.-----.---~----~------8.000 8.200 8.400 8.600 FREQUENCY(MC/SEC) MU-19732 62 Fig. 29. Cu resonance for spin 1. - 72 - 64 VI. Cu EXPERIMENT A. Isotope Production 64 The Cu lsotope. Wl . th a half-1'lfe of 12. 8 h ours was plle-pro. d uce d ln . the LPTR reactor at Livermore) California) and the General Electric reactor at 6 64 Vallecitos;by the reaction cu 3(n,y)cu . The material used was ordinary number 8 Cu wire, which was cleaned and cut up into pieces small enough to fit into the standard tantalum oven shown in Fig. 17. The Cu wire was sealed in an evacuated quartz tubing 6 mm by 36 mm which was put into an aluminum capsule of the same type as used for the iron and shown in Fig. 44. The dura tion of the bombardment was usually about 12 hours. B. Experimental Procedure and Data Analysis The experimental procedure was the standard one described in Chapter III. The rf equipment used is shown diagramatically in Fig. 30. The counting rates +; were corrected for. decay by use of OMNIBUS. The final values of ~v and ~v were computed by use of the HYPERFINE 4 program. . 64 . c. Theory of the Cu Experlment 64 The spin and hyperfine structure of cu had been previously measured and found to be I = 1 and ~v = 1278(20) Me/sec by Lemonick and Pipkin (LEM 54). An + improved value for ~v was reported by Stroke et al. (STR 57) to be ~v = 1282.5(7) and ~v 1282.9(7). The.. purpose of this experiment was to further improve_ this value and to measure the sign of the moment. In order to facilitate the search for a resonance a program called F-TABLE was used to give tables of frequency versus field for various focusable transi- t lons. ln . Cu 64 ( see Fig. 31 ) . This program was written by Ewbank (EWB 61) to calculate frequency tables for ,J = 1/2 corresponding to a given range of magnetic field and for transitions between any-two~ levels. The input information required is ~v, gJ' gi' an initial and final value of the magnetic field and its increment, and the (F,~) values for the two energy levels involved. The output gives the transition frequency, frequency of each leve~, and dV/dH (the derivative of the frequency with respect to the field) corresponding to each value of the magnetic field. Tables were printed out for values of the magnetic field from 0 to 500 gauss in 1-gauss steps for the transitions (B/2) 1/2 ~ 1/2, - 1/2), (3/2, - 1/2 ~ 1/2, 1/2)) (3/2) - 1/2 ~ 1/2, - l/2)J and (3/2, - 1/2 ~ 3/2, -3/2), where the bracketed numbers represent (F ,m ~ F ,m ). 1 1 2 2 -73- FREQUENCY EQUIPMENT FOR L':.F =I TRANSITION (200-2500 Me/sec) HEWLETT- PACKARD ELECTRONIC COUNTER MODEL 524B AIRBORNE INSTRUMENTS POWER OSCILLATOR TYPE 124C 3~F HAIRPIN FREQUENCY EQUIPMENT FOR L':.F=O TRANSITION (10- 480Mc/sec) HEWLETT- PACKARD VHF SIGNAL ~MODEL 510 IFf WIDE- BAND AMPLIFIER GENERATOR MODEL 608C IMODEL 500 IFI WIDE- BAND AMPLIFIER HEWLETT- PACKARD ELECTRONIC II COUNTER E MODEL 524B RF HAIR p IN ~ MU-30252 64 Fig. 30. Radio-frequency equipment for Cu experiment~. -74- 1.5 mJ m 1 J = 1/2 I= I + 1/2 +I 1.0 + lf2 0 mF +3/2 + 1/2-1 +112 -1/2 -3/2 ~ -1/2 +I 1.5 0 0.5 1.0 1.5 2.0 X MU-13309 64 Fig. 31. Energy-level diagram for cu • - 75 - In experiments requiring accurate measurements} one method of eliminating broadening of the line width by inhomogeneities in the magnetic field is to measure transition frequencies at such a value of H that the frequency dependence on change of field is negligible, i.e., dV/dH = 0. A resonance of this type is called field-independent. The only transition predicted by F-TABLE to be field independent was the (3/2, - l/2 ~ l/2, - l/2) transition. Unfortunately this transition is independent of g , as can be seen from the expression for the 1 frequency difference between Brfid t-Rabi levels for the direct (N = ± l) transi tion. This expression is ± l) ( 8!!-) A g - independent transition may be used to improve the value of 6V. 1 The sign of the moment may be measured by using the transition-frequency difference between the (3/2, l/2 ~ l/2, - l/2) and (3/2, - l/2 ~ l/2, l/2) transitions. Transitions in which the roles of m and m can be interchanged 1 2 . are referred to as doublets. From Eq. (84)} the separation of any doublet is Measurements of this frequency difference depend on the magnitude .of g and on 1 the resolving power of the apparatus. 64 D. Results for cu Resonances for the &' = l doublet were taken at fields of approx 3·3 gauss and 4.9 gauss. A decay curve typical of all puttons exposed is shown in Fig. 32. The resonances are shown in Figs. 33 and 34. The peak frequencies of these resonances yielded an improved value of 6V = 1282.180(40) Mc/secJ which was, + however, still within the limits of error of Hamilton's values of 6V 1282.9(7). The improved value of 6V was used to recalculate the field tables by using the F-TABLE program; Successive resonances were observed at fields of.approx 152.7 gauss and approx 500 gauss. The value of 152.p gauss was predicted by F-1~LE to be the field-independent point for the g -independent 1 -76- 5oor-----~------. 64 Cu , 12.8 hours DECAY CURVE OF RESONANCE BUTTONS FROM RUN 494 100 50 .! T ; = 12.8 hours ::J 1 2 ·ec ~ Q) Q. !! c ::J 10 0 0 lJJ ~ 0:: 5 <.!> ~ I-z ::::> 0 (.) 1000 3000 5000 7000 TIME (minutes) MU-30253 64 Fig. 3 2. Decay curve for Cu • -17- RUN 494 64 Cu , 12.8 h (3/2,±1/2 -1/2, 'fl/2) H =3.23 gauss !! ·c; ::> >. ~400 :e 0 FREQUENCY (Me/sec) MU-30254 Fig. 33. cu64 resonance at 3.23 gauss. -78- RUN 494 6 Cu ~ 12.8h (3/2,±1/2- 112, 'fl/2) H = 4.89 gauss 0 ILl !::! ..J <( :::;;: 0: 0z 1282.35 1282.65 FREQUENCY (Me/sec) MU-30255 64 Fig. 34. Cu resonance at 4.89 gauss. -79- RUN 628 64 cu , 12.8h (31'2,-112 -1/2,-112) H= i52.5 gauss ·c:.:! :::0 > ~ ~ :0 ~600 LLJ !;i a: C)z FREQUENCY (Me/sec) MU-30256 64 Fig. 35. Cu resonance at 152.5 gauss. -80- RUN 628 cu64,12.ah (3/2,-1/2- 1/2,-1/2) H = 152·.5 gauss FREQUENCY (Me/sec) MU-30257 64 Fig. 36. Cu resonance at 152.5 gauss. - 81 - transition (3/2) - 1/2 ~ l/2) - l/2). Two resonances shown in Figs. 35 and 36 were observed at this field in an attempt to improve l6vl. These resonances exhibit the double-peaked structure typical of n(~ = l) transitions. As can be seen from Tables VIII and IX) these two/resonances have the narrowest line widths (20 kc), and hence have been most heavily weighted by HYPERFINE 4. The remaining two resonances are &' = 0 standard transitions (~F ,= - l/2 ~ - 3/2)) and were done at fields of about 152.5 gauss and 500 gauss. Although the resid uals for gi < 0 were slightly smaller than those for gi > 0 (approx 30 kc)J the difference is too small to give an indication of the sign. The final value from HYPERFINE 4) i~vi = 1282.140(20) Me/sec) falls slightly outside the limits of Hamilton's value for g < 0 (approx 50 kc outside the 6V lower limit for 1 6V- = 1282.200 Me/sec). However) this difference is again too small, and gives only a slight indication that the sign of gi may be positive. From the HYPERFINE output for gJ variab~e, the best fit to the observed resonances gives a value of gJ =- 2.0032(10) where the error quoted is twice that given by the routine. This value seems .to be sorriewhat higher than that of Ting and Lew who obtained g = - 2.0026(10). J 64 Table VIII Summary of Cu data for g > 0. I- Comparing isotope Calibrating isotopes 85 2 Cu 63 , 2 s , I - 3/2 Rb B7 , 2 s , I = 3I 2 Rb , s , I = 5/2 112 112 112 gJ variable gJ = - 2.00238 g =- 2.00238 -4 -4 J -4 gi = 8.07 X 10 gi = 9-95359 X 10 g = 2.93704 X lG I a= 5866.900 Me/sec 6V = 6834.685 Me/sec 6V = 3035-735 Me/sec Calibration Resonance Residual Residual: Residual Residual Run field, H frequency for for for for Weight number Fl ml F2 m2 (gauss) (Me/ sec) gJ=-2.0026 gJ=-2.0016 gJ=-2.0036 gJ variable factor (Me[ sec) (Me [sec) (Me[ sec) (Mc[sec) + l l - l 494 3/2 - 2 2 + 2 4.890(106) 1282.226(80) 0.0198 0.0200 0.0197 0.0198 156.1 + l l 494 3/2 - 2 2 +~ 3-225(107) 1282.223(75) 0.0534 0.0535 0.0533 0.0533 177-7 l l l 628I 3/2 - 2 2 - 2 152.666(50) 1208.810(20) - 0.0051 - 0.0049 - 0.0052 - 0.0051 2500.0 l l l 628II 3/2 - 2 2 - 2 152-757(50) 1208.810(30) - 0.0052 - 0.0050 - 0.0054 - 0.0053 2500.0 I 00 l 0.0161 N 628III 3/2 - 2 3/2 -3/2 152-728(67) 177-450(150) 0.0779 0.1849 - 0.0290 31.8 I l 628IV 3/2 - 2 3/2 -3/2 499-910(146) 836.000(250) 0.3135 0.8827 - 0.2559 - 0.0157 5.8 gJ = - 2.0016 g =- 2.0026 gJ = - 2.0036 gJ variable J a 854-7612 854-7612 854-7613 854-7613 oa o.oo66 o.oo66 o.oo66 o.oo66 4 4 4 4 gi 1.176 X 10- 1.176 X 10- 1.176 X 10- 1.176 X 10- f.! I 0.216 0.216 0.216 0.216 gJ - 2.0032 - ogJ 0.0005 x2 6.83 2.00 1.65 1. 25 64 Table IX Summary of Cu data for gi < 0. Comparing isotope Calibrating isotope Same as Table VIII Same as Table VIII Calibration Resonance Residual Residual Residual Residual Run field, H freq_uency for for for for Weight number Fl ml F2 m2 (gauss) (Me/sec) gJ=-2.0026 gJ=-2.0016 gJ=-2.0036 gJ variable factor (Me/sec) (Me/sec) (Me/sec) (Me/sec) + _l l "=Fl. 494 3/2 - 2 2 2 4.890(106) 1282.226(80) 0.0198 0.0200 0.0197 0.0198 156.1 + _l l 494 3/2 - 2 2 "=F~ 3.225(107) 1282.223(75) 0.0533 0.0534 0.0532 0.0533 177.7 l l l 628I 3/2 - 2 2 - 2 152.666(50) 1208.810(20) - 0.0051 - 0.0049 - 0.0052 - 0.0051 2500.0 l l l 628II 3/2 - 2 2 - 2 152.757(50) 1208.810(30) - 0.0052 - 0.0050 - 0.0054 - 0.0053 2500.0 l l 628III 3/2 - 2 2 -3/2 152.728(67) 177.450(150) 0.0528 0.1597 - 0.0542 - 0.0001 31.8 l l 628IV 3/2 - 2 2 -3/2 499.910(146) 836.000(250) 0.2828 0.8521 - 0.2865 0.0009 5.8 I 00 w I gJ = - 2.0016 gJ =- 2.0026 gJ = - 2.0036 gJ variable a 854-7612 854.7613 854.7613 854.7613 oa 0.0067 o.oo66 0.0066 o.oo66 4 -4 4 -4 gi - 1.176 X 10- - 1.176 X 10 - 1.176 X 10- - 1.176 X 10 IJ.I - 0.216 - 0.216 - 0.216 - 0.216 gJ - 2.0031 - og 0.0005 J - x2 6. 25 l. 79 1.81 l. 24 - 84 - VII. FE59 EXPERIMENT A. Beam Production One of the problems associated with the iron isotope was that of pro ducing a suitable beam. Since iron alloys quite readily with most metals, the oven could not be made of the standard matals. Various materials for containing iron were tested in the evaporator in Fig. 37· The evaporator is essentially a vacuum system which pumps the chanber seen on the top. The oven loader, which extends from the front part contains a platform for the ovens and an electron-bombardment heating arrangement. An optical pyrometer was used to.determine the temperature of the oven, which can be viewed through the side port. The various metal ovens tested were tantalum, molybdenum, carbon, and tantalloy. Iron alloyed with all these substances and usually sealed the caps on the ovens and closed the slits. The next materials tried were ceramics. Although ceramics are not good conductors and had .to be heated by being inside the hot tantalum oven, they are fairly unreactive, have high melting points, and--usually--low vapor pressures. The various ceramics tested were titanium carbide, zirconium carbide, alumina-87 (aluminum oxide), zirconium diboride, boron nitride, and zirconia (zirconium oxide). With the carbides, the carbon tended to come out of the compound and be replaced by the iron. Both the alumina and the boron nitride tend to outgas at high temperatures. The zirconium diboride and the zirconj:um oxide both held up fairly well at high temperatures. Since the iron does not wet the zirconium oxide at all, and also a.s it is somewhat more stable at high temperatures, this ceramic was the one used as a liner for the tantalum ovens • The tantalum oven and liner are shown in Fig o 38. The iron sample is entirely contained by the slotted zirconium oxide crucible and lid. To obtain uniform heating the zirconium liner is entirely surrounded by the tantalum oven and capo A tungsten rod through the bottom of the tantalum oven matches the groove in the bottom of the crucible and hence lines up the slit of the oven with the slit of the crucible. Although this arrangement worked fairly well, it was still necessary to exercise caution in heating the iron. If the pmver for the electron-bombardment heating went nmch over 160 watts, the half-beam counting rates and pressure fluctuated quite markedly -85- ZN -3661 Fig. 3 7. Evaporator used in testing ovens for producing an iron beam. -86-, I ZN-3656 Fig. 38. Tantalum oven and zirconium oxide liner. - 87 -·· and a small crystalline growth of iron tended to grow up near any openings, i.e., around the cap or the slit •. The electron-bombardment emission current also fluctuated and hence the temperature changed, also contributing to an erratic half beam. Although the temperature of the oven was measured with an optical pyrometer and found to be approx 2000°F, this reading lvas probably somewhat low, since the window had been plated with various metals in the course of time. Figure 39 shows tantalum ovens with zirconium liners of various designs which were "overheated." Figure 4o shows two more "overheated" ovens whose design is the one finally adopted. It was also noted that the beam tended to be less erratic if the iron wire had been melted prior to bombardment in the reactor. Hence all the iron samples were melted in a zirconium-tantalum oven in the evaporator before irradiation. Also, various materials were tested to determine which had the greatest collection efficiency for iron. Collecting surfaces were made of sulfur, carbon, tantalum, aluminum, copper (cleaned and uncleaned), platinum, lead, and brass. Sulfur buttons were exposed between each exposure to check beam level. It was found that a freshly cleaned copper surface had almost twice the collecting efficiency of sulfur. All other substances had either the same or a lower efficiency. Figure 41 represents the counting rate on various surfaces. Copper surfaces were then used for collection surfaces. A typical button is shmm in Fig. 42. The brass button has a small magnet in the center which holds a small iron slab. The copper surface is electroplated onto the iron slab. Immediately before the button was inserted into the machine, each slab was cleaned by dipping it into a weak solution of nitric acid, then water, and finally acetone. The slab was quickly dried on soft tissue, put onto the brass button, and inserted into the machine. Unfortunately the half beams seemed to fluctuate quite badly even when the oven power was steady. A subsequent check of the beam level for copper and sulfur collectors at various temperatures showed that although the copper exposures counted consistently higher, the sulfur exposures gave a steadier indication. Although~;the ·results ·as shown in Fig. 43 show a fairly steady beam level for a power of 151 watts, the counting rates are too low at this temperature. A reasonable power is usually 160 to 170 watts. -88- ZN - 3654 Fig. 39. Used tantalum ovens with zirconium liners. -89- ZN -3655 Fig. 40. Used tantalum ovens with zirconium oxide liners. -90- 100~------r------. cleaned copper 59 801- NORMALIZED COUNTING RATES OF Fe ON VARIOUS COLLECTING SURFACES f- uncleaned copper ~ 60 I- :::J ....>- f'"'''" ~ :;; bro" 2 f- ['"" 1 UJ !;( t. 0: (!) 40 I- ~ lead 1 1-z ::::l 0 aluminum (.) f- tantalum c UJ J N :::::i I platinum ~ 20 1- I 0: z0 f- I 0 MU-30258 Fig. 41. Counting rate of Fe 59 on various collecting surfaces (arbitrary horizontal arrangement). -91- ZN -3657 Fig. 42. Button with copper slab collecting surface. -92- RUN 763 o points- copper- coated buttons Efficiency of Cu and S as collecting 6 paints- sulfur- coated buttons surfaces for Fe power 180 watts LLI 1- <( a: zC> lk_ • / ·z' 1- /.~o~~! "=> · · . 180 watts.. 0 u 0 LLI N ::J <( :::;: 0 a: 0z TIME (minutes) MU-30259 59 Fig. 43. Plot of beam level of Fe for copper and sulfur collecting surfaces for various oven temperatures. - 93 - B. Isotope Production and Identification The radioactive Fe59 isotope with a half-life of 45 days was pile produced by bombarding 99.6% pure stable iron with neutrons. Iron of this purity was available only in wire form. The wire was cut into pieces small enough to fit into an atomic beam oven and then put into a quartz tube 8 mm by 1 and 5/8 inches, which was flushed out with helium and sealed off. The quartz was then inserted into an aluminum capsule. The entire arrangement is shown in Fig. 44. For long-term bombardments at ETR, the aluminum capsules were opened by Health Chemistry at the Radiation Laboratory before being sent to the researcher. Only the qu.artz capsules were sent to campus. These were opened in a standard lead cave by the device sbo"Wln in· Fig. 45. The quartz is placed on the indentation in the wedge-shaped block at one end of the brick. The similarly shaped hinged block swings over and holds the capsule in place. The quartz is long enough to project out over the edge o:f the vedge. This end may be :filed off or broken by the bar, 1-rhich is :free to slide back and forth as vell as rotate. Since the radioactive iron is fairly hot, this device vras designed so that the entire procedure could be done by remote control vith tongs. The reaction Fe54,58 (n,r)Fe55,59 also produced the 2.6-year Fe55 isotope. Since the cross section for the (n,y) reaction for both isotopes is 0.7 barn, 54 the number of atoms of Fe55 produced from the 5·9% abundant Fe isotope is greater by a :factor of about 10 than the number of Fe59 atoms produced from 8 the 0.33% abundant Fe5 • However, since the counting rate is proportional to the product of the number of atoms times the inverse of the halfli:fe, the ratio of the counting rates (CR) CR(Fe 59 ) = (85) . CR(Fe55) In order to identify the isotopes positively, decay curves were taken over a period of a :few months. It was found that the beta counters were more efficient for counting Fe59 (the decay shceme is shown in Fig. 46) than the crystal counters. Unfortunately, the beta counters are unstable over periods of more than a few days. To compensate for any change in efficiency of the counters, the buttons were decayed along vith a Ni63 sample, which has a half-life o:f 125 years. (All half-lives and decay schemes presented are taken from the Table of Isotopes (STR 58) ). All Fe59 counting rates were -94- ZN-3658 Fig. 44. Containers for reactor bombardments. - 95- ZN -3660 Fig. 45. Devic e for opening quartz capsules. "' ., 1.289 ··,) 1.09~ > CD ::E 43% >- (!) a:: til .Z, -. L1J 0 STABLE co 59 MU-30260 Fig. 46. Decay scheme for Fe 5 9• - 97 - normalized to the initial Ni63 counting rate. Although optimum irradiation time would be of the order of 6 months, both the ETR and Vallecitos reactors have much shorter cycles. Since ETR has a flux approximately 10 tim5that of the Vallecitos reactor, most of the bombardments were done at ETR, which has a theoretical cycle of 6 weeks. In practice, however, these cycles are subject to the whims of the reactor and usually ran anywhere from 12 to 28 days. C. Experimental Procedure Although the experimental procedure was for the most part the standard one for a spin search, there were some differences due to the long half life and the low activity level. In order to accumulate a countable amount of activity on a button, the spin button exposure times were about 10 to 15 minutes, whereas the half beam exposures were from 2 to 5 minutes. The counting rates were not corrected for decay, since all the counting was done in a time short compared with the half-life. D. Multiple-Quantum Transitions in Fe 5 Because Fe59 has a ground state n4 and hence even J states, the transition that obeyed the refocusing condition mJ(A) = -mJ(B) was a multiple-~uantum transition. The theory of multiple-quantum transitions has been treated extensively in several references--(BES 54), (SAL 55), (HAC 55), and (HAC 56)--and only results are quoted here. For an N-quantum transition, the resonant frequency is given by the generalized Bohr condition E(F,m+N) - E(F,m) (86). hN and with an uncertainty width ~ill= 2n/Nt. According to Hack (HAC 56), the maximum transition probability for an N-quantum transition is equal to 2 sin (to), where t is the time spent in an oscillating rf magnetic field of amplitude IHrfl. The quantity· 5 is the product of N matrix elements of the rf perturbation between the adjacent states divided by the product of (N-1) resonance (frequency difference) terms. The explicit· form of 5 - 98 - is given by (87) where and A'ij = < wi!J+ + J wj ) for J = J ± i J ± X y The maximum transition probability occurs for to = ~/2, a~d hence it is possible to obtain an expression for the optimum rf power. The value of t is taken as the inverse of the natural line width, ovv, of a single quantum transition. The value of JH fl t is also proportional to the value r op of the homogeneous C field H through the quantity The expression for c ov. the optimum rf field { ( (N-1) ~ )2 2N-2 } (-A:--7'-. -~-'-v----:--:---- ) 1/N ~,~-1 A'f+l,f X (ov) (N-1) /N (88) was verified experimentally by Christensen and others (CHR 61). No effort was made to optimize rf power, since only a spin value wa~ being me~~u~~d, and resolution and observation of the various multiple-quantum transitions would not contribute to the measurement. In measuring a ~v, however, resolution and observation of multiple-quantum transitions of order greater than 2 would be advantageous, since the separation of the various N-quantum transitions is proportional to ~v. In this case there would be a problem in choosing an optimum value of the rf field, since different orders of multiple quantum transitions require different values of the rf field to saturate the transition. In the spin measurement, some of the resonances. were redone at higher rf power levels. In each case higher counting rates were obtained, implying that the rf power was not enough to saturate the transition. Since 0 is proportional to (JH fl )N, for small values of IH fl or for 2 2 small values of sin (to), the trans~tion probability varies as (lHrfl ) N. Hence as the quantum multiplicity increases, the rf field required to produce the transition increases also. To obtain the maximum rf power, the circuit shown diagramatically in Fig. 47 was used. The L network acted as an impedance-matching device to maintain the rf - 99 - current through the rf ammeter at a constant high value. The rf level was maintained at a value of approx 4oo mA. Although this is not a measure of the actual rf power into the hairpin, it provides a means of monitoring the rf power level. E. Theory of Fe 59 Experiment 5 The electronic ground-state configuration of 26Fe 9 is 2 2 6 2 2 6 2 33 ls 2s 2p 3s 3P 3d 4s • Hund' s rule couples the six equivalent 3d electrons to a 5D ground state. For the temperatures necessary to produce 4 the iron beam, the J = l, 2, and 3 states were also present. Figure 48 shows the relative energy differences of the various J states (MOO 52) and the relative population of the J states and the magnetic substates. The 6 gJ of iron was measured for the 5D state of Fe5 by Kamlak (KAM 62) and 4 was found to be gJ(5D ) = -1.50020(3)· The gJ's of the other J states were 4 taken from optical spectroscopic data (MOO 52) to be approximately -1.5 5 ( gJ( D ) = -1.497, gJ(5D ) = -1.494, gJ(5D ) = -1.498 ). Since only the 3 2 1 nuclear spin of iron was to be measured, all resonances were done at low fields of a few gauss. The Zeeman frequency is given by VF = gF(Il /h) H , ,mF o ~ where F(F+l) + J(J+l) - I(I+l) gF ~ gJ 2F(F+l) Observable transitions are indicated on the energy-level diagram of Fig. 49. Nuclear spin values of I = 3/2, 5/2, 1/2, and 9/2 are allowed by the shell model. However, the value of 3/2 was the most probable, since coinci dence experiments by Metzger (~lliT 52), using a lens spectrometer and scintillation counter techniques, predicted a spin of 3/2 from the beta-ray spectrum of Fe59. F. Results for Fe59 The decay of a button taken at the peak frequency of a resonance is shown in Fig. 50. Also shown on the same figure are the decays of a half beam and a chemistry. All curves exhibit, within statistical limits, the decay "' · · · characteristic of the 45-day Fe59. Figure 51 is a plot of the linear Zeeman frequency for Fe59 versus the 8 frequency of the calibrating isotope Rb 5 for the various values of F, I, and J. The points plotted on the Zeeman lines indicate resonance peak -100- HEWLETT· PACKARD ELECTRONIC COUNTER MODEL 524 B TEKTRONIX SIGNAL GENERATOR TYPE 190 I Fl WIDE- IFI WIDE- L BAND HRF BAND L AMMETER NETWORK AMPLIFIER AMPLIFIER MODEL 500 MODEL 510 HAIRPIN L NETWORK] RF HAIRPIN MU-30261 Fig. 47. Radio-frequency equipment (0.35 to 50 Me/sec). -101- RELATIVE POPULATION OF ;J RELATIVE POPULATION PER ENERGY (CM-I l STATES ACCORDING MAGNETIC SUBS TATE FOR I= 3/2 TO THE BOLTZMAN DISTRIBUTION 50 978.1 0.03 0.0075 0 5 888.1 0.07 0.0060 01 50 . ----- 704.0 0.16 0.0080 2 5 o ----- 415.9 0.27 0.0096 3 0.45 0. 0125 MU-30262 5 59 Fig. 48. Approximate D leyel structure in Fe from optical spectroscopy data. The relative population per magnetic substrate is calculated for zooo•c, the approximate temperature of the iron beam. -102- m mi ;r 3/2 112 4 -1/2 -3/2 3/2 f:ll/2 1/2 -1/2 3 -3/2. 3/2 1/2 2 -1!2 -3/2 3/2 112 F=9/2 -112 -3/2 1 3/2 >- 1/2 0 (!) -1/2 a:: -3/2 zUJ F=7/2 UJ 3/2 1/2 -I - 1/2 -312 3/2 F =5/2 l/2 -2 -1/2 -3/2 3/2 1/2 -3 -1/2 -3/2 3/2 1/2 -4 -112 -3/2 ZEEMAN PASCHEN- BACK - H MU-30263 Fig. 49. Energy-level diagram for the system J = 4, I = 3/2 in a magnetic field (not to scale). - 103 - frequencies of the various runs. The errors indicate the half-,vlidths of the resonances. In some cases, the resonances were broad enough to include ... several possible values of the spin. This was especially true at the lov1er field values. The higher-field spin-search experiments (Runs 761, 765, and 766) indic~te a strong signal at a frequency corresponding to spin I = 3/2. These three resonances are shown in Figs.52, 53, and 54. The measured value of I = 3/2 is consistent with the shell-model prediction for the five neutrons outside the closed shell of 28. The 2 configuration of the partially filled level is (2p ; )3(lf ; ) • 3 2 5 2 -104- IOOr------, 59 45dFe .... Q) Q. !! c :::s 0 u • "Half Beam" RUN 768 !::. Chemistry (x 0.1) o Spin BUTTON RUN 768 TIME (days) MU-30264 Fig. SO. Fe 59 decay curves for a spin button, a half-beam button, and a chemistry button. -105- W2 7'/27/2 7/2 11/2.,9/2. 3/2,9/ZI/2 5/213/l 7/l lk 1/21/2 1/2 1/2 Yl J/2 1/2 3/Z 3/2,5/2 1/.!,3/25/2 3125/2 5/2 Numbers next to each resonance indicate run number. 9/2.17/2,15/2 ''""'512:9/2.,7/2 >- 30 u z "'::> 0 9/.! 13/2 "'0: "- I 5/2:7/'i! u "'z <( z 29/211/2 0 0:"' "' i9!2.111'l .,'" 4 5 6 8 9 10 II 12 13 14 15 85 Rb FREQUENCY (Me/sec) MUB-1780 59 Fig. 51. ['lot of linear Zeeman frequency for Fe versus Rb8 frequency for all observable double-quantum transitions. -106- RUN 766 12r- 45d Fe 59 1- 2 SPIN SEARCH f- H= 19.4 gauss .1!! ·;:: 2: ::s f- ~ 2: :e~ 8 f- 2: ~ r- LIJ ~ a:: 1- 2: (.!) ~ 2: ~ 1- § ~ £ 2 2 1-z .2: 54f- ~ u £ i 0 r- LIJ N £ :J 1- MU-30265 Fig. 52. Spin search for Fe59. -107- RUN 765 45 d Fe 59 SPIN SEARCH ·c:!!2or H= 16.9 gauss ::> >. ~ ~ f 16r- o UJ ~ a: l2f-' I 8 81- I I f 0 I UJ I I I I N I ~4f- i J=4 I ~ I I= 3/2 0z 0 I I I I I I I I I I I I I I I I I I I 29,0 29.4 29.8 30.2 30,6 EXPOSURE FREQUENCY (Me/sec) MU-30266 Fig. 53. Spin search for Fe 5 9. -108- RUN 761 6f- 45 d Fe 59 ..-. ~ SPIN SEARCH r::: H= 23.2 gauss ,.," f- ~ ~ I :0 6 IJJ 4f- I 1- I <[ I a: f T zC> II f= f- f 1 z ::l If 0 i u fyfff 2r- ~ I 0 IJJ £ N £ I t ::::i ~ <[ ~ i ::;; ~ a: '-- 0z J"=4 J=3 1=3/2, 5/2 1=3/2 0 I I I I I I I I I I I 35.0 35.8 36.6 37.4 38.2 EXPOSURE FREQUENCY(Mc~ec) MU-30267 Fig. 54. Spin search for Fe 59• -) - 109 - VIII, ADDITIONAL ISOTOPES This section describes experiments which were undertaken for the measurement of a particular quantity, but which yielded no experimental data, usually because of lack of activity. The experiments are described only, in enough detail to indicate the procedure and the possible reason for failure, 6 A, Cu 7 Experiment This experiment was undertaken to measure the spin of the 58-hour cu67, Initially Zn was bombarded in the Livermore reactor in the hope that a 6 6 67 Zn 7(ri,p)eu 7 reaction would give enough eu • The Cu was chemically separated from the Zn and both samples counted in the beta counters, Unfortunately, the chemical separation was poor, and both buttons had considerable amounts of 6 14-hour metastable zn 9, However, the decay curves indicated less than 1% . 6 of the material was Cu 7, Equivalent results were obtained with the fast neutrons (approx 14 MeV) from the 60-inch cyclotron. Because of the low cu67 6 67 yield from Zn67 (n,p)cu 7, an attempt was made to produce the cu isotope from 6 6 64 the Ni \a,p)cu 7 reaction. Because of the low abundance of Ni (Ll6%), a 20-mg ball of >95% enriched Ni was obtained from Oak Ridge National Laboratory at a cost of $320. The ball was flattened, put onto an external jumbo target as shown in Fig. 55, and bombarded for about 12 hours in the 60-inch cyclotron. 62 After bombardment; a chemical separation similiar to the Cu chemistry was done, The Cu was loaded into the oven and·:tten into the atomic beam machine, Decay curves of a subsequent spin 3/2 exposure and half beam indicated almost 67 pure eu . Unfortunately, the activity level was too low to per.mit an experiment. The Ni was recovered and the experiment redone several times with longer bombardment periods and less carrier. In each case the activity level was too low to permit a spin measurement, B. Fr223 Experiment The francium experiment was designed to measure the nuclear spin of 22 22 22 21-minute Fr 3. Fr 3 is a decay product of Ac 7 (actinium) although only 1.2% of the disintegrations produced the francium isotope. The decay chain is shown in Fig. 56, Three curies of 22-year Ac 227 was available, Since 22 223 l curie of Ac 7 produces an equilibrium quantity of 12 millicuries of Fr , 22 36 millicuries of Fr 3 was available for the experiment, The chemical procedure for separating the francium was developed by Howard A. Shugart from standard reference:sources (HYD 6o) and (KAT 57), and7 in general, is as -110- 6l s'l ZN-3133 Fig. 55. Cyclotron external target. - 111 - follows. The actinium was dissolved in 10 ml of concentrated HCl. Some 10 chemical separations were performed on the sample. Each consisted of the following sequence or a slight variation of it: 1. A 20-ml solution of Ac227 is saturated with HCl gas. The solution is kept cool with an ice bath. 2. Two drops of 0.4 M silicotungstic acid are added. 22 3· The silicotungsti~ acid precipitate and Fr 3 are centrifuged down. 4. Supernatant is removed by decantation. 5· The precipitate is redissolved in 10 ml of H 2o. 6. Steps 2, 3, 4, and 5 are repeated twice more. 7• The last precipitate is dissolved in 0.5 ! HCl and passed through an ion exchange column containing Dowex-50· 8. The column is washed with 2 ml of H20 to wash through the silico tungstic acid. 22 9· The adsorbed Fr 3 is eluted with several drops of concentrated HCl containing Cs carrier. 10. The eluate is evaporated to dryness in the atomic beam oven. After insertion into the atomic beam machine, the oven was aligned by using the Cs carrier and the hot wire detector. Because of the short 21-minute halflife, no half beams were taken. The field was calibrated after each spin exposure by use of the Cs beam and the hot wire detector. The output of the vibrating-reed electrometer was fed into a recorder and the cesium resonance displayed by sweeping the frequency. Since both cesium and francium are alkalies and hence have similar physical properties, it was assumed that the beam level was proportional to the cesium peak resonance height. The first experiment was the most successful as far as the efficiency of the chemistry was concerned, although the beam lasted only long enough to take a full beam. The decay curve of the full beam showed the 21-minute 22 halflife characteristic of Fr 3. The second chemistry was done 3 days later. The cesium beam lasted long enough for spin exposures to be taken at frequencies corresponding to nuclear spins of 13/2, 11/2, 9/2, 7/2, 5/2, 3/2, and 1/2. Out of all the spin exposures, only the spin 3/2 button had a countable amount of activity, and decayed with an approximate 21 minute halflife. While this was indicative of a possible spin resonance, it was the only time a countable amount of activity was accumulated on a button. After nine unsuccessful runs, during which very little francium activity was seen, -112- AcX(Ra223) 223 11.68d FRANCIUM DECAY SCHEME a The main path of the decay is 219 shown in bo I d arrows. An(Rn ) 3, 92 Sec a 215 AcA(Po ) 211 Ace' (Po ) 1.83XIo-3sec 0.52Sec a 211 AcC (Bi ) a 2.16 Min 211 AcB (Pb ) 36Min 207 STABLE AcC"(TI ) 4.79 Min MU-30268 Fig. 56. Decay chain for francium. - 113 - it •ras decided that this series of experiments should be concluded. c. cs136 Experiment The Cs experiment was undertaken to measure the nuclear spin of 13-day 136 . 136 136 1?6 Cs by the react1on Xe (p,n)Cs • Although the production of Cs ~ is 136 marginal, possible cs resonances had been observed by Shugart (SHU 57). Cesium was produced by bombarding xenon gas, in a bell jar assembly shown in Fig. 57, with protons of approx 12 MeV from the 60-inch cyclotron. The procedure for extracting the Cs from the bell jar is described in detail in Shugart's thesis (SHU 57). Approximately 45 mg of Cs carrier was added to the Cs taken from the bell jar. After each spin exposure, data for spin button normalization and C-field calibration were obtained from the level of the Cs beam current from the hot wire detector; as measured by the Cory vibrating-reed electrometer at resonance. Spin exposures were done at frequencies corresponding to spins of 4, 5, and 6. In order to obtain a countable amount of activity and to average out beam level fluctuations, these three buttons were each given four 5-minute re-exposures, in rotation, in order of decreasing spin. These buttons were then counted in the beta counters. It was hoped that the higher efficiency of the beta counters (as compared with the crystal counters used for the previous Cs experiments) would provide countable buttons. However, the activity level on the three buttons was extremely small (about 2 counts per minute), and hence the buttons could not be decayed to identify the isotope. Also the activity was so low, that, to within statistics, the counting rates on the three buttons were the same. -114- ZN-1730 Fig. 57. Bell jar assembly. \...: - 115 - ACKNOWLEDGMENTS I would like to take this opportunity to thank those people without whose help this thesis could never have been written. First, my parents, for their love, patience, and confidence in me. Professor William A. Nierenberg, for his help and encouragement. Professor Howard A. Shugart, whose constant and unfailing good humor combined with his professional expertise saw me through many an experimental crisis. Dr. F. Russell Petersen, Dr. w. Bruce Ewbank, Dr. Vernon J. Ehlers, Dr. y, w. Irving Chan, Mr. Murray Steinberg, and Mr. Richard Worley for their assistance during runs and for helpful discussions. Mr. Gerald Sims, Mr. Michael Devito, Mr. Ralph Stein, and Mr. Michael Fallon for their help with various laboratory problems. Mr. Loran Cadre, Mr. Morley Corbett, and 1~. Douglas MacDonald for their concern and aid in matters of apparatus and design. The Health Chemists, Mrs. Ruth Mary Larimer, Mrs. Patricia Shaw, Mr. John E. Bowen, and Mr. Robert E~ McCracken for their always ready and efficient assistance. This work was supported in part by the u.s. Office of Naval Research, the u.s. Air Force Office of Scientific Research, and the u.s. Atomic Energy Commission. .. - 116 - REFERENCES . BEL 53 E. H. Bellamy and K. F. Smith, Phil. Mag. 44, 33 (1953) . BES 54 c. Besset, J. Horowitz, A. Messiah, and J. \'linter, J, Phys. Radium 15, 251 (1954). BLA. 52 J, M. Blatt and V. F. Heisskopf', Theoretical Nuclear Physics ( Joh:p. _Hiley & Son~,~Inc !_,_ ~]~Iew Yo:r]i, __ 1952). BRE 31 G. Breit and I. I. Rabi, Phys. Rev. 38, 2082 (1931). ERE 60 M. H. Brennan and A. M. Bernstein, PJ:zy·s. Rev. 120, 927 (1960). 112 CHA 62 Y. W. Chan, The Nuclear Spins and Magnetic Moments of' A.g , 11 4 Ag 3, Au19 , Aul95, and Au196m (Ph.D. Thesis), Lawrence Radiation Laboratory Report UCRL-10334, June 1962 (unpublished). CHR 61 R. L. Christensen, D. R. Hamilton, H. G. Bennevitz, J. B. Reynolds, and H. H. Stroke, Pbys. Rev. 122, 1302 (1961). CON 57 E. U. Cond.on and G. H. Short ley, Theory of' Atomic Spectra (Cambridge University Press, Cambridge, England, 1957). cox 57 H. L. Cox and_D. \1/illiams, Bull. 4m· Phys. Soc. g_, 30 (1957). :CES 53 A. de Shalit, Phys. Rev. 91, 1497 (1953). DUN 11 L. Dunoyer, Compt. Rend. 152, 591~ (1911). EliL 60 Vernon J. Ehlers, The Nuclear Spins and Moments of' Several Rad.ioactive Gallium Isotopes (Ph.D. Thesis), Lavrrence Radiation Laboratory Report UCRL-9123, March 1960 (unpublished). EVA 55 R. D. Evans, The Atomic Nucleus (McGraw-Hill Book Company, Inc., New York, 1955). EHB 59 lv. B. Ewbanl';:, The Nuclear Spins and Magnetic Moments of' Certain Gold and Silver Isotopes (Ph.D. Thesis), Lawrence Radiation Laboratory Report UCRL-8756, June 1959 (unpublished) . \.-!. B. E'·rbank ( University of' California, Berkeley), private communication, 1961. FER 30 E. Fermi, z. Physik 60, 320 (1930). GHO 50 S. N. Ghoshal, Phys. Rev. 8o, 939 (1959). HAC 55 M. N. Hack, Phys. Rev. 100, 975 (A) (1955). HAC 56 M. N. Hack, Phys. Rev. 104, 84 (1956). HUB 58 J, C. Hubbs, H. A. Nierenberg, R. l·1arrus, and J. L. \1/orcester, Phys. Rev. 109, 390 (1958). - 1:17 - IIYD 60 Earl K. lJ;yd.e, The Radiochemistry of Francium, (Subconuni ttee on Radiochemistry, National Academy of Sciences, National Research Council, ~!ashington,. 1960, IIAS-NS-3003). Jmdros Ka;·nlah (University of Heidelberg, Germany), private communication, 1962. Ki\-'r 57 Jose·ph Katz and Glenn T. Ses.borg, Chemistry of the Actinide Elements, (Methuen and Company, London, 1957). A. Lemonick and F. M. Pil;kin, Phys. Rev. 95, 1356 (1954). 206 200 2(") HAR 59 Lavrrence L. Marino, Some Nuclear Properties of Bi , T1 , Tl_uc. 10 11 111 ' In 9, In 0m, and In (Ph.D. Thesis), Lawrence Radiation Laboratory Report UCRL-8721, fq)ril 1959 (unpublished). MP.Y 55 H. G. Mayer and J.IL D. Jensen, Elementary Theory of Nuclear Shell Structure (JohnPiley &Sons, Inc., Ne1,rYork, 1955). ~··. R. 1-ietzger, Phys. Rev. 88, 1360 ( 1952) . MOO 52 C. E. Moore, Atomic Energy Levels, :Natl. Bur. Std. (U.S.) Circulnr Ho. 467, 1952. IUE 57 :;. li. ITierenberg, H. A. Shugart, and H. B. Silsbee, Bull. Am. Phys. Soc.~' 200 (1957). NOH 51 L.A. Nordheim, Hev. l1Iodern Phys. 23, 322 (1951). PET 60 F. Russell Petersen, Atomic Beecm Research on the Spins, Hyperfine 43 90 140 177 ( Structures, and I1Ioments of K , Y , La , and Lu Ph.D. 'I'hesis), Lavrrence Rad.iation Laboratory Report UCRL-9L:-8o, November 1960 (unpublished). EAB 38 I. I. Rabi, J, R. Zacharias, S. l'lillman, and P. Kusch, Phys. Rev. 53, 3~L8 (1938) • RAC 2J.2 G. Racah, Phys. Rev. 62, ~-38 (19lt2). Hf'J,1 56 :I. F. Ramsey, Holecular Beems (Oxford University Press, London, 1956). S/~L 55 II. SB-hren, Phy s . Rev. 99, 127 l.~ ( 195 5 ) . ·~ sen 37 T. Scrunidt, Z. Physik lOG, 358 (1937). sen 37a H. Schuler, z. Physik 107, 12 (1937). sen 52t- Charles Sch>vartz, Phys. Rev. 91+_, 95 (1954). sen 55 Charles Schvrartz, Phys. Rev. ~~' 380 (1955). SHU 57 IImmrd. A. Shugart, The Nuclear Spins, Hyperfine Structure Separation, 12 12 1 1 2 and l-'lagnetic Homents of cs 7, cs 9, cs 3°, and cs 3 (Ph.D. Thesis), University of California Radiation Laboratory Report UCRL- 3T{O, Hay 1957 (unpublished). - 118 - SIL 55 H. B. Silsbee (University of California, Berkeley), private communication, 1955. SMI 51 K. F. Smith, Nature 167, 942 (1951). STE 21 0. Stern, Z. Physik 1, 249 ( 1921) . STR 59 H. H. Strol\:e, R. L. Christensen, D. R. Hamilton, and J. }J; Reynolds (Princeton University, New Jersey), private communication, 1959. STR 58 D. Strominger, J. M. Hollander, and G. T. Seaborg, Rev. Modern Phys. 30, 585 (1958). - . 82 83 81} sun 56 Robert J. Sunderland, The Nuclear SpJ.ns of Rb , Rb , and Rb (Ph.D. Thesis), University of California, Berkeley, June 1956 (unpublished) . THO 26 ...... T n . Thomas, Nature 117, 514 (1926). v TIN 57 .L. Tins and. H. Lew, Phys. Rev. 105, 581 (1957). ZAG 42 J. R. Zacharias, Phys. Rev. 61, 2'(0 (191~2). This report was prepared as an account of Government sponsored work. Neither the United States, nor the Com~ mission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, appa ratus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any infor mation, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Com mission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor . • 11~11 .,