Table Of ContentSpringer stcarT ni Modern Physics 96
Editor: .G HOhler
Associate Editor: E.A. Niekisch
Editorial Board: S.Fl(~gge H.Haken J.Hamilton
.H Lehmann W.Paul
Springer Tracts ni Modern Physics
37 Excitons at High Density Edited by .H Haken, .S Nikitine. With contributions by
.V .S Bagaev, J. Biellmann, A. Bivas, J. Goll, M. Grosmann, J. .B Grun, .H Haken,
.E Hanamura, .R Levy, .H Mahr, .S Nikitine, .B .V Novikov, .E I. Rashba, T. M. Rice,
A. A. Rogachev, A. Schenzle, .K .L Shaklee
47 Solid.State Physics With contributions by .G Bauer, .G Borstel, .H J. Falge, A. Otto
75 Light Scattering by Phonon-Polaritons By .R Claus, .L Merten, .J re110mdnarB
67 Irreversible Properties of Type II Superconductors By H. UIImaier
77 Surface Physics With contributions by .K ,re110M .P WiBmann
87 Solid.State Physics With contributions by .R Dornhaus, .G Nimtz, .W Richter
97 Elementary Particle Physics With contributions by .E Paul, .H Rollnick, .P Stichel
80* Neutron Physics With contributions by .L Koester, A. Steyerl
18 Point Defects in Metals h Introductions to the Theory (2nd Printing)
By .G Leibfried, .N Breuer
28 Electronic Structure of Noble Metals' and Polariton-Mediated Light Scattering
With contributions by B. Bendow, .B re~egneL
83 Electroproduction at Low Energy and Hadron Form Factors
By .E Amaldi, .S .P Fubini, .G Furlan
84 Collective Ion Acceleration With contributions by .C .L Olson, .U Schumacher
85 Solid Surface Physics With contributions by J. ,lz16H .F K. Schulte, .H Wagner
68 Electron-Positron interactions By .B H. Wiik, .G Wolf
87 Point Defects in Metals :1I Dynamical Properties and Diffusion Controlled Reactions
With contributions by .P .H Dederichs, .K Schroeder, .R Zeller
88 Excitation of Plasmons and Interband Transitions by Electrons By H. Raether
89 Giant Resonance Phenomena in Intermediate-Energy Nuclear Reactions
By .F Cannata, .H 0berall
90* Jets of Hadrons By .W Hofmann
19 Structural Studies of Surfaces
With contributions by .K Heinz, .K ,re110M .T Engel, and .K .H Rieder
92 Single-Particle Rotations in Molecular Crystals By .W Press
93 Coherent Inelastic Neutron Scattering in Lattice Dynamics By .B Dorner
94 Exciton Dynamics in Molecular Crystals and Aggregates With contributions by
.V M. Kenkre and .P Reineker
59 Projection Operator Techniques in Nonequilibrium Statistical Mechanics
By H. Grabert
69 Hyperfine Structure in 4d. and 5d.Shell Atoms By .S B0ttgenbach
97 Elements of Flow and Diffusion Processes in Separation Nozzles By .W Ehrfeld
89 Narrow-Gap Semiconductors With contributions by .G Nimtz and .B Schlicht
99 Property of iV--V! Compounds With contributions by .H Bilz, A. Bussmann-Holder
and .W Jantsch
100" Quarks and Nuclear Forces Edited by D.C. Fries and B. Zeitnitz
* denotes a volume which contains a Classified Index starting from Volume .63
.S hcabnegtteB
Hyperfine Structure ni
4d- and 5d-Shell Atoms
With 41 Figures
galreV-regnirpS
Berlin Heidelberg New York 2891
Dr. Stephanus Bettgenbach
tutitsnI rof Angewandte Physik red t&tisrevnU Bonn, eBartsrelegeW 8,
D-5300 Bonn, Fed. Rep. fo ynamreG
Manuscripts for publication should be addressed to:
Gerhard HOhler
Institut f0r Theoretische Kernphysik der tStisrevinU ehurslraK
Posffach 6380, D-7500 Karlsruhe ,1 Fed. Rep. of Germany
Proofs and all correspondence concerning papers in the process of publication
shouM be addressed to:
Ernst A. Niekisch
Haubourdinstrasse 6, D-5170 hcilOJ ,1 Fed. Rep. of Germany
ISBN 3-540-11740-7 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-11740-7 Springer-Verlag New York Heidelberg Berlin
Library of Congress Cataloging in Publication Data . BQttgenbach, Stephanus, 1945 -- Hyperfine structure in 4d- and
5d-shell atoms. (Springer tracts in modern physics; 96) Bibliography: .p Includes index. .1 Hyperfine structure. .I Title.
.1I Series. QCLS797 vol. 96 QC173.4H95 539s 539'.14 82-10808
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Preface
tneceR secnavda in experimental techniques have denepo pu wen fields of applications
for the atomic maeb magnetic resonance dohtem dna provided a broad spectrum of wen
information no the hyperfine structure of free atoms. This is particularly true for
the transition elements with unfilled d4 or d5 electron shells. Their study using
atomic maeb magnetic resonance saw edam possible yb the development of a universal
dohtem of producing intense atomic smaeb of these highly refractory elements.
ehT hyperfine structure of the -d4 dna 5d-shell atoms is of particular interest,
both from the standpoint of atomic physics, since most of these elements have ynam
metastable atomic states, which are sufficiently populated at the evaporation tem-
perature to permit atomic maeb magnetic resonance studies, dna from the standpoint
of nuclear physics, since especially the d5 elements lie in a demrofed region of the
nuclear chart. In this book recent experimental results no the hyperfine structure
of metastable states of d4 dna d5 elements are described. At the emas time, the -om
dern theory of hyperfine structure desab no the effective operator approach is re-
viewed. morF na analysis of the data with respect to this formalism a considerable
tnuoma of wen information is obtained concerning the nuclear ground-state properties
sa well sa the atomic structure of the transition elements. Special sisahpme is laid
no discussing in detail the influences of relativistic dna configuration interaction
effects no the hyperfine interaction.
ehT mia of this hpargonom is to demonstrate - no the basis of a detailed analysis
of hyperfine structure stnemerusaem in -d4 dna 5d-shell smota - that atomic maeb
magnetic resonance is a powerful technique for getting valuable information no both
nuclear dna atomic structure.
,nnoB July 2891 .S B~ttgenbaeh
Contents
I. Introduction ........................................................... I
2. Theoretical Considerations ............................................. 5
2.1 Traditional Hamiltonian for the Hyperfine Structure of Free Atoms ,. 5
2.2 Effective Operators ............................................... 6
2.3 Relativistic Effects .............................................. 8
2.4 Effects of Configuration Interaction .............................. 13
2.5 Eigenvectors in Intermediate Coupling for Complex Atoms ........... 20
2.6 Hyperfine Structure in an External Magnetic Field ................. 25
2.7 0ff-Diagonal Hyperfine and Zeeman Interactions .................... 28
2.8 Hyperfine Anomaly ................................................. 29
3. Experimental Methods .................................................. 33
3.1 Atomic Beam Magnetic Resonance .................................... 33
3.2 Production of Atomic Beams ........................................ 37
3.3 High-Resolution Laser Spectroscopy and State-Selective Detection of
Metastable Atoms .................................................. 40
4. Experimental Hyperfine Interaction Constants for 4d- and 5d-Shell Atoms .. 44
5. Intermediate Coupling Wavefunctions, Atomic gj Values and Parametric
Interpretation of Level Isotope Shifts ................................... 53
6. Effective Radial Parameters of the Magnetic Dipole and Electric
Quadrupole Interaction ................................................. 62
6.1 Determination of Effective Radial Parameters from Experiments ....... 62
6.2 Comparison Between Experimental and Theoretical Radial Integrals .... 69
7. Nuclear Moments and Hyperfine Anomalies ............................... 78
7.1 Direct Measurement of Magnetic Dipole Moments ....................... 78
7.2 Electric Quadrupole Moments ......................................... 18
7.3 Hyperfine Anomalies ................................................. 85
Vlll
8. Concluding Remarks .................................................... 87
References ................................................................ 89
Abbreviations in this Work ................................................ 94
Subject Index ............................................................. 95
1. Introduction
In recent years investigations of hyperfine structure (hfs) dna isotope shift (IS)
in cimota spectra evah dedivorp a daorb murtceps of wen information gninrecnoc eht
electronic structure of free smota dna eht properties of nuclei. This ssergorp is
detcennoc with eht application of wen latnemirepxe seuqinhcet sa well sa with -mi
stnemevorp in eht theory of cimota fine dna hyperfine structure.
ehT hyperfine interaction neewteb eht suelcun dna eht electrons of na mota nac
eb represented, in general form, yb na noisnapxe in multipoles of order k,
fhH s = Z Tk(n)'Tk(e)
k
erehw Tk(n) dna Tk(e) era spherical tensor operators of knar k in eht nuclear dna
electronic ,ecaps respectively.
ehT spherically lacirtemmys O=k term is just eht bmoluoC interaction neewteb eht
electrons dna a point nucleus. Since eht suelcun sah a finite extension this mret
requires modification for electrons with a finite egrahc density within eht nuclear
.emulov ehT ygrene shift of eht fine structure levels eud to this modification yam
eb different for different isotopes of eht emas tnemele esuaceb of eht variation in
eht nuclear egrahc distribution with nortuen .rebmun This part of eht IS, eht -os
called field (or )emulov shift, is proportional to eht egnahc of eht erauqs-naem
nuclear egrahc radius. ehT dnoces contribution to eht experimentally devresbo SI is
eht ssam shift hcihw originates from eht recoil of eht electron noitom no eht -un
cleus. It sniatnoc a trivial correction eud to eht egnahc of eht decuder electron
ssam lamron( ssam shift) dna a contribution gnidneped no correlations in eht noitom
of eht electrons (specific ssam shift).
ehT 1=k term stnuocca for eht interaction of eht nuclear citengam dipole tnemom
with eht citengam field created at eht suelcun yb eht cimota electrons. ehT 2=k
mret stnuocca for eht interaction of eht nuclear electric elopurdauq tnemom with
eht suoenegomohni electric field decudorp yb eht electrons. ehT citengam eloputco
)3=k( dna electric elopacedaxeh (k=4) terms era nearly syawla hcum smaller than eht
magnetic dipole dna electric quadrupole terms, dna so far these effects have been
observed in some favorable cases only.
Since hfs and IS depend no properties both of the nucleus dna of the electrons
their investigation can give information on nuclear properties (spins, moments,
charge radii) sa well as on atomic structure. In order to evaluate nuclear quanti-
ties from hfs dna IS measurements the electronic part of the interaction has either
to eb calculated by means of semiempirical or ba initio methods, or to eb determined
from an independent measurement of the nuclear quantity for at least eno isotope or
isotope pair of the same element. Magnetic moments are available for most stable
isotopes /I/ from atomic maeb magnetic resonance )RMBA( or from nuclear magnetic
resonance (NMR). In contrast, most quadrupole moments are based no theoretical cal-
culations of the average electric field gradient at the nucleus. However, nowadays
an increasing number of quadrupole moments are being determined nearly model in-
dependently from the hfs of mesonic atoms /2/. In order to extract the change of
the mean-square charge radius from IS measurements the optical data yam eb cali-
brated with respect to those obtained by measurements of muonic /3/ or electronic
X-ray shifts /4/ or by electron scattering /5/.
nO the other hand, independent measurements of the hfs and the nuclear stnemom
allow a detailed study of the electronic structure of free atoms. ehT experimental
results yam eb compared to theoretical calculations, thus providing a rigorous test
of atomic hfs theory. ehT main difficulties in analyzing experimental hfs data arise
from the influence of relativistic dna configuration interaction (CI) effects on the
hyperfine interaction. In order to take into account these effects the effective
operator formalism is frequently used. In 1965 it saw found by YEVRAH /6/ in his
analysis of the magnetic dipole hfs of oxygen dna fluorine that a considerably im-
proved fit to the experimental data could eb obtained by use of a three-parameter
Hamiltonian. In order to make the inclusion of relativistic effects in the hfs of
many-electron atoms more convenient, SRADNAS dna KCEB /7/ in 1965 introduced na
effective Hamiltonian that, when interacting between nonrelativistic atomic states,
produces the same result sa the true Hamiltonian between relativistic states. This
operator contains three effective radial parameters for each open electron shell
dna for each order k of the hyperfine interaction. It sah been shown by DDUJ /8,9/
dna SRADNAS /10/ that CI effects can eb included in na effective Hamiltonian of
the same form. Therefore, in a modern analysis of hfs data the effective radial
parameters are treated as free parameters which are fitted to the experimental re-
sults in order to take into account relativistic dna CI effects.
This parametric method can eb applied if the hfs has been measured in a suffi-
ciently large number of fine structure levels. For example, the hfs sah to eb known
in at least three levels for na electron configuration of type nl N (ImO). In 1974
NERGDNIL dna NESOR /11/ dezylana a large rebmun of experimental sfh data mainly in
cimota dnuorg configurations using the effective operator formalism. Their -irapmoc
nos of the experimental radial sretemarap with theoretical results obtained morf
relativistic Hartree-Fock calculations sah detartsnomed that there is appreciable
influence of IC no the hyperfine interaction. ,revewoH the accurate ba initio cal-
culation of the radial sretemarap is still a challenging .melborp oS far theoreti-
cal studies of IC using the multiconfiguration Hartree-Fock dohtem or ydob-ynam
perturbation theory evah neeb demrofrep for simple smota only /12-14/.
latnemirepxE investigations of the sfh require high ypocsortceps resolution -eb
esuac the energy splitting of eht fine structure levels desuac yb the hyperfine in-
teraction is in general very small. ehT ycarucca of classical optical ypocsortceps
yb snaem of high-resolution interferometers is limited yb the Doppler width of the
spectral lines. A elbakramer ecnavda in experimental technique over that of optical
ypocsortceps saw the tnempoleved of the RMBA dohtem yb IBAR dna co-workers /15,16/.
gnisU this ,dohtem precise values evah neeb obtained for the sfh constants in dnuorg
dna in low-lying metastable states of free smota esuaceb eht Doppler width is -neg
erally quite negligible in radio-frequency (rf) spectroscopy. In addition, a rebmun
of experimental techniques have neeb depoleved to ecnahne the population of -atem
stable states dna to increase the detection efficiency for metastable atoms, thus
allowing RMBA investigations of high-lying metastable levels sa well. In particular,
the esu of tunable eyd lasers sah led to a variety of modifications of the classi-
cal RMBA dohtem opening wen fields of application of radio-frequency .ypocsortceps
latnemirepxE details dna results of RMBA evah neeb described in several review
articles /17-22/. A large rebmun of stable dna long-lived radioactive isotopes evah
neeb investigated yielding nuclear spins, citengam dipole dna electric elopurdauq
stnemom sa well sa electronic gj factors dna sfh interaction constants of elbatsatem
fine structure states /23,24/. Moreover, during recent years considerable ssergorp
sah neeb edam in the tnemerusaem of spins dna stnemom of short-lived nuclei far morf
stability. roF these stnemerusaem na RMBA sutarappa sah neeb detcennoc on-line to
the isotope separator EDLOSI at NREC /25/. Extensive investigations of short-lived
excited atomic levels evah neeb demrofrep mainly yb eht optical ecnanoser-elbuod
,dohtem level crossing experiments, dna optical gnipmup techniques /26-28/.
nA ideal field for a detailed study of the influence of relativistic dna IC ef-
fects in the sfh era the transition stnemele with na unfilled ,d3 ,d4 or d5 elec-
tron shell. esehT stnemele evah ynam metastable states belonging to the configura-
tions dn ,N ,s)1+n(1-Ndn dna s)1+n(2-Ndn .2 Therefore, in d-shell smota the sfh nac
eb derusaem in a rebmun of different states providing a rigorous test of fine -ed
tails of hfs-theory. First extensive stnemerusaem of the sfh in ynam elbatsatem
states of the emas mota evah neeb demrofrep for the 3d-shell smota /29,30/. erehT
