effects of relativity and correlation on l - mm ...
TRANSCRIPT
PHYSICAL REVIEWS A VOLUME 31, NUMBER 1 JANUARY 1985
Effects of relativity and correlation on L-MM Auger spectra
Mau Hsiung ChenLawrence Liuermore National Laboratory, P.O. Box 808, Liuermore, California 94550
(Received 14 June 1984)
Relativistic computations of Ll-MM, L2-MM, and L3-MM Auger spectra have been carried outin the intermediate coupling with configuration interaction for a final two-hole state and j-j cou-
pling for an initial state. Results for ten elements with 18 &Z & 92 are listed and compared with ex-perimental data. Good agreement with the scarce experimental data is attained. The effect ofcorrelation is shown to shift some of the Auger energies by as much as —15 eV. The effect offirial-ionic-state configuration interaction is found to increase the L3-MlMl rate by a factor of -2for Z &45. Intermediate coupling is necessary to analyze the L-MM Auger spectra for 30 & Z & 80.As in the case of K-MlM45 transition calculated Ll-M3M3( P2) and L3-MlM45 intensities asfunctions of Z are found to peak sharply in the neighborhood of Z=63 due to the strong level-
crossing interaction. This interaction is found to increase the L l-M3M3( P2) intensity at Z =60 bya factor of 50.
I. INTRODUCTION
The effects of relativity, spin-orbit mixing, and final-ionic-state configuration interaction have been found to bevery important in analyzing the X-I.I. and E-MM Augerspectra. ' For very light elements (Z & 15), the electro-static interaction dominates and Russell-Saunders cou-pling applies. The effects of electron-electron Coulombcorrelation are much more important than the effects ofrelativity for these light elements. To predict relativeintensities accurately, one should include not only final-ionic-state interaction but also final-state interchannel in-teraction. ' For medium and heavy elements, relativisticeffects become quite important, and the E Auger spec-trum must be calculated relativistically in intermediatecoupling with configuration interaction. The good agree-ment between theory and experiment for K Auger spec-trum of medium and heavy elements' seems to indicatethat the effects of final-state interchannel interaction be-come much less important for high-energy transitions.
Although there exist some nonrelativistic intermediatecoupling calculations for L-MM Auger spectra for a fewselected elements, *' there is no systematic relativistic in-termediate coupling calculations. Furthermore, the exist-ing theoretical Auger energies are mostly obtained fromthe semi-empirical approach. "' There are very fewab initio calculations of Auger energies. Here we reporton theoretical L-MM Auger energies and transition ratesfrom Dirac-Hartree-Slater (DHS) calculations in inter-mediate coupling with configuration interaction for tenelements with atomic number 18 & Z & 92. The effects ofcorrelation on Auger energies and the effect of stronglevel-crossing interaction on I.-MM Auger intensities arealso discussed.
II. THEORY
A. Relativistic intermediate coupling theoryof Auger transitions
From perturbation theory, the Auger transition proba-bility is
where g; and Pf are the antisymmetrized many-electronwave functions for initial and final states, respectively. Inthe frozen-orbital approximation and in j-j coupling, Eq.(1) reduces to the two-hole-coupled Auger matrix elementinvolving only active electrons,
T(aJM a'J'M')-
Here (j&jzJ'M'~
represents the initial antisymmetrizedtwo-hole-coupled state, including the initial bound state j'~(n
&a.&) and the hole j2 (eaz) in the continuum that is filled
by the emitted Auger electron. The final antisymmetrizedtwo-hole-coupled state is denoted by
~ j&j2JM }.The con-tinuum wave function is normalized so as to represent oneelectron ejected per unit time. Atomic units are used un-less indicated otherwise. Coupling between an outermostopen shell and inner-shell vacancies is neglected in Eq. (1).This approximation is justified because the relatively weakcoupling does not introduce any appreciable Auger-electron energy shift in transitions discussed in this paper.In the present relativistic calculations, the two-electronoperator V~2 is chosen according to the original M@llerformula' which is, in the Lorentz gauge,
V)2 ——(1—a ) az)exp(icor)z)/r(2,
where the a; are Dirac matrices, and m is the wave num-ber of the exchanged virtual photon.
In the present calculations, the initial state is represent-ed by a single j-j configuration. The final-ionic-state con-figuration interaction among all the possible final double-MM-hole states (i.e., [M,MJ. ]; i &j=1—5) is taken intoaccount. For these calculations, j-j-coupled basis statesare used. In j-j coupling, intermediate coupling can betreated as configuration interaction. Coulomb as well asBreit interactions are included in the energy matrix. Thej-j configuration average energies were calculated fromDHS wave functions' with the appropriate final-hole-
31 177 1985 The American Physical Society
17& MAU HSIUNG CHEN 31
state configurations, including quantum-electrodynamic(QED) corrections. The energy splittings of the specifictotal J states of the two-hole-coupled configurations andoff-diagonal matrix elements of the energy matrix werecalculated by using a slightly modified general relativisticAuger program. ' Eigenvalues and eigenfunctions wereobtained by diagonalizing the energy matrix. The eigen-functions with total angular momentum J can then bewritten as
a=1
where C p(J) are the mixing coefficients and P are thej-j-coupled basis states.
The Auger matrix element for the Pth state is
J)= g c.p(J) &0(jij2J~)I
I'i214' (j ji2J~) & .
The total radiationless transition rate from n&aI to thePth eigenstate of the final two-hole-coupled states witheigenfunction gp( J) is
The relativistic Auger matrix elements in j-j couplingwere calculated from DHS wave functions that corre-sponding to the initial-hole-state configuration. " The de-tailed treatment of relativistic intermediate coupling withconfiguration interaction is described in Ref. 1.
B. Relativistic Auger transition energies
The earliest method to estimate Auger energies is basedon a semiempirical approach. However, Auger transitionenergies are nowadays calculated by the ASCF method. '
In terms of the relativistic model, a separated relativisticself-consistent-field (SCF) calculation is performed for in-itial single-hole and final double-hole states. The Augerenergy is then determined by taking the energy difference.In our present DHS calculations, a first-order correctionto the local potential approximation is made by comput-ing the expectation value of the full Hamiltonian. Thiscorrection is essential in accurate calculations of transi-tion energies.
The natural coupling scheme for the Dirac-Fock orDirac-Hartree-Slater approach is j-j coupling. Intermedi-ate coupling is, however, more appropriate for the finaltwo-hole states in most cases. For the relativistic SCF ap-proach, intermediate coupling can be implemented eitherby diagonalizing the energy matrix of Coulomb and Breitinteractions with respect to fixed j-j coupled basis statesor by using the multiconfiguration Dirac-Pock approachin which the radial wave functions are optimized simul-
taneously with the diagonalization of the Hamiltonianmatrix. ' In our present calculations, fixed j-j-coupledbasis states are employed. The QED corrections: vacuumpolarization for all levels and self-energy for L levels arealso included in the calculations.
The effect of electron-electmn Coulomb correlation onAuger energies is largely ignored in most existing calcula-tions. In principle, one should find the correlation contri-bution to the Auger energies by calculating the totalcorrelation energies for initial and final states and takingthe difference. This, however, is a very expensive proposi-tion, and a more tractable procedure needs to be chosen.In first approximation, the correlation energies of the pas-sive electrons from initial and final states can be assumedto cancel each other completely. We further assume thatthe correlation contribution to the binding energies of thefinal double-hole states can be estimated by summing thecorrelation contribution to the binding energies for thesingle-hole states. Hence, we only concern ourselves herewith three important correlation contributions to the tran-sition energy, namely, the ground-state correlation correc-tion, the energy shift due to the Coster-Kronig or super-Coster-Kronig fluctuation of the hole states, and thefinal-ionic-state configuration interaction. In our presentwork, the first two corrections are equivalent to the corre-sponding corrections for the binding energies.
The ground-state correlation correction arises becauseof the broken pairs in the hole states. This correction canbe evaluated froin nonrelativistic theory as a sum of sur-viving pair energies after cance11ation between ground andhole states, '
where E„, (a,b) is the total pair energy between two closedshe1ls,
E„„(a,b)= g(2S+1)(2L+1)E(n, l„ni, li„SL), (8)L,S
with e(n, l„nh li„SL) being the symmetry-adapted pairenergy.
Another important correlation contribution to the bind-ing energy is caused by dynamic relaxation processes inwhich the core hole fluctuates to intermediate levels of theCoster-Kronig or super-Coster-Kronig type, in addition tocreating electron-hole pair excitations. ' ' If the transi-tions are energetically impossible, these effects alwaysreduce the binding energies: they can be estimated byfinite configuration-interaction or multiconfigurationHartree-Fock (MCHF) methods.
When the hole state is embedded in the (super-) Coster-Kronig continua, we can use Fano's' approach of config-uration interaction with the continuum to calculate theenergy shift. Neglecting the effect of channel couplingand using the fixed-energy approximation, the energyshift due to the interaction with the continua can be ob-tained by calculating the principal-value integrals,
31 EFFECTS OF RELATIVITY AND CORRELATION ON L-MM. . . 179
TABLE I. Theoretical L.3-MM Auger energies (in eV).
Final state
M)M i('So)MiM2('PI )
MiM2( Pp)M)M3{ P))MiM3( Pp)M,M, ('S, )
M2Mp('D2)M2M3( P) )
M3M3( Po)M3M3( P2 )M )M4('D2)M, M, ('D, )
M, M, ('D, )
MiM5( D3)MpM5{ 'F3)M2M4{ 'P) )
M,-M.('D, )
M3Mg{ Di)M,M, ('P, )
M,M, ('D, )
M,M,('P. )
M,M, ('P&)M3M4( F2)M,M, ('F, )
M3M5{ F4)M,M, ('D, )
MyM4( Sp)M,M, ('G, )
M,M, {'P,)M,M, ('P, )
M,M, ('P, )
M,M, ('D, )
M,M, ('F, )
M4M5{ F3)M,M, ('F, )
)8Ar
164.7181.9189.6189.6189.7203.2204.9206.8206.8207.0
30Zn
704.2749.2764.3765.5767.4803.8806.2813.3813.2815.5844.0846.1
846.3846.5886.8889.4894.9895.5897.2896.4897.9897.8900.5902.4903.8902.6974.5978.8979.8979.9979.8980.6982.3982.5982.8
1055.41121.71139.11142.61147.31197.91204.71212.81214.91219.31261.91265.31265.91266.61325.71327.81335.61338.51340.11340.51342.51342.51344.01348.01351.41349.41456.31463.71465.01465.11465.11466.61468.91469.41470.4
4gRh
1695.41800.01818.81832.81844.51909.91933.31943.41958.21965.52018.72202.22025.52027.72121.02117.62131.52146.32135.32149.121S1.52152.22153.221S8.82167.62163.62323.32336.82339.32336.62338.42341.32345.82345.22350.0
54Xe
2430.32579.32597.1
2640.82660.22725.22786.02797.32845.32853.72899.02902.22911.72915.13050.03036.53056.53103.53058.43104.43107;53112.13110.53119.43133.73128.13343.83365.63372.63359.73367.53370.73382.23376.13387.7
2989.13168.03186.73269.23293.93340.13444.43457.03546.23551.63578.33577.33598.83602.23764.43736.83761.73850.63773.03851.53853.63866.83858.13875.43894.33886.94131.24166.34181.54149.84167.54171.44194.54178.14201.2
6,Ho
3738.13955.73977.44127.84157.44161.94341.54493.94516.64544.44484.24355.24520.04534.74733.34688.04716.1
4878.34741.24878.54880.84907.64886.44917.04939.54930.85211.45263.65291.95232.35264.45268.85307.65276.75315.2
70Yb
4072.84308.34328.04521.74553.44530.84753.44767.54790.54994.64905.64914.24950.64962.75178.35124.45154.35358.2S186.15358.35360.75394.1
5366.85404.05428.0S418.85715.3S776.05810.65737.45776.65781.35827.65789.75835.7
80Hg
5047.85347.55369.45766.35805.05629.26061.66077.56486.76510.76241.56249.36329.06341.46617.86517.76553.86963.9662S.66964.06966.1
7039.76974.07051.27080.67069.27403.67510.57584.1
7429.87510.27516.07605.47526.37615.1
5920.56309.76334.67175.87222.96674.87561.17579.28434.38462.07767.27775.27938.97954.38315.78125.58170.39027.28323.89027.49029.09185.29039.39199.19234.69220.8-9574.09771.39925.79605.69769.69776.99952.39789.49964.1
Here E~ and E~ are the threshold energies of the single-hole state and doubly ionized Auger continuum, respec-tively. The Auger matrix element (P~, ~ g, r;~
'~N)
for channel A, is evaluated with the aid of a general rela-tivistic program. ' In our present work, the level shift b,F.is approximately energy independent.
III. RESULTS AND DISCUSSION
TABLE II. Level-energy shift (in eV) produced by, configura-tion interaction with (super-) Coster-Kronig continua.
Atomicnumber
Z 2$Level
3s 3p
The QED corrections including self-energy and vacuumpolarization on L-shell binding energies for heavy ele-ments are quite significant. The L&, L2, and L3 bindingenergies for 92U are reduced by -39, 6, and 7 eV respec-tively. ' The more detailed information on the QED
The calculated 1.3-MM Auger energies are listed inTable I. The contributions from the effects of relaxation,Breit interaction, QED, and limited final-ionic-state con-figuration interaction are included in the calculations.However, the ground-state correlation and energy shiftdue to the interaction with the Coster-Kronig or Super-Coster-. Kronig continua are not taken into account be-cause these corrections are only considered for binding en-ergies.
18303645S4708092
'From Ref. 20.
—2.2—3.3—5.0—3.7—S.O
—4.2—1.7
—6.3—4.5—4.5
—3.5—7.9—8.4—6.9
—3.247
—2.7—3.0—4.7—5.8
180 MAU HSIUNCx CHEN 31
TABLE III. Theoretical and experimental Auger energies (in eV) for argon and gas-phase zinc.
Element
&sAr
3pZn
'From Ref. 10.From Ref. 23.
'From Ref. 22.
Transition
L3-MI M)L3-M23M23( SP)
L3-Mz3M23('»L3 MP 3M4 5( F3)L,-M4, M4, ('G4)
DHS-ICCI
164.7203.2204.9206.9886.8978.8
Auger energyDHS-CORR
176.8201.7203.4205.4886.7973.8
Expt.
177.79'201.10b
203.48b
205.21b
886.7'973.3'
corrections can be found in Ref. 14.The ground-state correlation effect is the dominant
correlation contribution to the binding energy for anoutermost she11, and for inner shells with orbital angularmomentum l =n —1, where n is the principal quantumnumber (e.g., 2p and 3d in our present calculations). Thiseffect always increases the binding energy since all pairenergies are negative and there are more pairs in theground state than in the hole state. The ground-statecorrelation contributions to the binding energies were es-timated to be —1 eV for 2s and 3s levels and —1.5 eV for2p and 3p levels, ' and -3.3 eV for 3d level of 30Zn. '
The energy shifts of the single-hole states due to the in-teraction with the (super-) Coster-Kronig continua werecalculated from Eq. (9) using DHS wave functions. Theresults for 2s, 3s, and 3p levels are listed in Table II.These effects are important for hole states that can decayby Coster-Kronig or super-Coster-Kronig transitions (e.g.,2s, 3s, and 3p). However, they are quite negligible for 2pand 3d hole states. In our present calculations, these en-
ergy shifts reduce the binding energies by 2—8 eV.The correlation effect on the final two-hole state of an
Auger transition is approximated by the sum of the con-tributions from individual hole states. The net effect ofthese correlation corrections on Auger transition energiesdepends on specific transition. The effects from three dif-ferent levels could almost cancel completely (e.g., L3M2 3M4 5 of 30Zn). They can also add up and yield alarge correction (e.g. , 12 eV for L3-M~M~ of ~sAr). In-cluding these correlation corrections (DHS-CORR) leadsto improved agreement between theoretical Auger energiesand experimental results from gas-phase measure-ments' ' ' (Table III).
The calculated relativistic I.-MM Auger transitionrates in intermediate coupling with configuration interac-tion (DHS-ICCI) are listed in Tables IV—VI. The intensi-ty ratios from Dirac-Hartree-Slater and Hartree-Slatercalculations and experiment are compared in Figs.1—5. The effect of relativity on the individual Augerrates has been thoroughly studied. In our present calcula-tions, the relativistic effect on some of the relative intensi-ties [e.g., I (L 3 M3M 5 ) /I (L 3
—M2—M3) and I (L 3—M3M3 ) /I (L 3—M2M3 ) j is quite significant (- 15
—25%%uo). In Fig. 1, the relative intensity I(L 3
M/M3 ( P, ) )/I(I. , —M, M, ('P, ) ) as a function of
2.0—
1.6—
DHS —IGCI---- DHS —JJ
~ ~ ~ ~ HS —JJLS
I [L3 —Mllvl3 (3P1)]
I [L3 IVlg IVI3 ( Pg )]
0.8
0.6
0.4
0.2
0 I I I I I I I I
20 3Q 40 60 60 10 80 9QZ
FICx. 1. Ratio of calculated L3-M~M3( P~) Auger rate toL3-MlM3( P2) Auger rate, as a function of atomic number.The solid curve represents Dirac-Hartree-Slater results in inter-mediate coupling with configuration interaction, the dashedcurve indicates Dirac-Hartree-Slater results in j-j coupling, andthe dotted curve represents the nonrelativistic Hartree-Slater re-sults in mixed coupling scheme, all from the present work. Theexperimental results are from Ref. 24.
atomic number Z from Hartree-Slater in mixed coupling(i.e., j-j for the initial state and LS for the final state),Dirac-Hartree-Slater in j-j coupling, and Dirac-Hartree-Slater in intermediate coupling are compared with experi-ment. ~ The transition from LS coupling for low-Zatoms (Z &20) to intermediate coupling for medium andmedium-heavy (20&Z&75) and from intermediate cou-pling to j-j coupling for heavy elements (Z & 75) are clear-ly demonstrated. As in the cases of IC LL and -K-MMAuger spectra, the effects of configuration interactionamong M&M, (J =0), M2Mz(J =0), and M3M3(J =0)states are very important. These correlation effects in-
EFFECTS OF RELATIVITY AND CORRELATION ON I-MM. . .
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184 MAU HSIUNG CHEN 31
I j~ I
/ + I(L3 - M3Ms) X 3/
40— DHS —ICCI—JJJJ
3.2
XI 5
4
I
3
p 2.4~«
CACEQ
C
1.6
0.8—
4)g)
2
——HS- J
30 40I
60z
I
70 80I
90
2&2
2.0—
1.8—
I I I I I I
DHS —ICCI-——DHS- JJ—-HS- JJ
0 Expt. It L3 —M3IVI3)Expt. I-(L3 —M&IVI3)
el
I I I I I I I I
25 35 ' 45 56 65 75 85 95Z
FIG. 2. Ratio of calculated L3-M~M~ and L3-M3M5 Augerrates to L3-M2M3 Auger rates, as functions of atomic number.The solid curves represent Dirac-Hartree-Slater results in inter-mediate coupling with configuration interaction, the dashedcurves indicate the Dirac-Hartree-Slater results in j-j coupling,and the dotted-dashed curve represents the nonrelativisticHartree-Slater results in j-j coupling, all from the present work.The experimental results are from Ref. 24—32.
FIG. 4. Ratio of calculated L3-M3M4 Auger rate to L3-M3M5 Auger rate as a function of atomic number. The legendis the same as in Fig. 2.
1.0I I
DHS —ICCI
crease the L3-M, M& rate by a factor 1.5—2 for Z(45.For all the relative intensities studied in the present work,good agreement is found between theory from relativisticintermediate coupling with configuration interaction andexperiment, considering the scarcity and uncertainty ofexperim. ental data.
For Z & 60, the M3M3 (J=2) level lies above theM&M4(J =2) and M, M5(J=2) levels. As Z increases,M3M3 (J=2) first comes down to cross M&M4( J=2) atZ=62, then crosses M&Mz(J =2) at Z=65. Similar to
1.6—
~ 'l.4
1e2
~- 1.0
0.8
0.6 —I
I( L3 M3IVI3 )
~sagy«
II&r--.
«~~~ ~~~~~~~ ~ 0~aaee w ~
0.8—
.o 06—CO
CfD
C 0.4—
———DHS- JJ—-—HS- JJ
I( L3 —MgM5)
i(L, -M,M, )
~ -41
I(L, —M, M4)eW
I(L3 —M4M~)
0 I I I I l w I
15 25 35 45 55 65 75Z
I I.85 95
0 I
30I
40I I i
50 60 70 80I
90
0el
FIG. 3. Ratio of calculated L3-M&M3 and L3-M3M3 Augerrates to L3-M2M3 Auger rate; see caption of Fig. 2 for details.The dip in I(L3-M3M3)/I(L3-M2M3) ratio near Z=63 iscaused by level crossing (see text).
FIG. 5. Ratio of calculated L3-MSMg Auger rate to L3-M4M5 Auger rate; see caption of Fig. 2 for details.
18531 EFFECTS OF RELATIVITY AND CORRELATION ON L-MM. . .
t eoretical L2-MiM23 and L2-M23M4~ Auger energiesTABLE VII. Comparison between selected theoretica 2 ] 23
(in eV) and transition rates (in a.u.) for 36Kr.
Final state
MiM2('Pi )M, M3('P) )
M2M4( P& )' M3M4( Di )
M3M5( P) )
MiM3( Pp)M2M4( Dp)M2M5( P2)M,M, ('F, )
M3M5('Dg)M3Mg( F3)M2M5{ 'F3)M3M4( D3)
DHS-ICCI
1174.61195.51380.61391.41395.31200.21388.41392.91396.91402.31400.91378.61393.4
Energy
1174.61195.41380.41391.31395.31200.11388.31392.91396.91402.21400.91378.41393.4
DHS-ICCI
1.20( —3)3.43( —4)2.74{—3)2.17(—4)2.03( —4)9.0( —6)1.86( —3)2.47( —4)2.6( —5) .
2.6( —5)1.16(—4)5.83{—3)3.12( —4)
RateMCDF
1.42( —3)4.75{—4)3.01(—3)2.82( —4)2.40( —4)1.6( —6)2.28( —3)3.70( —4)2.17(—5)2.04( —5)4.65{—5)6.22( —3)4.46( —4)
the -~ 4 5&-M M (J =2) and K-MiM3(J =2) transitions,
the level-crossing interaction amongMiM4(J =2), and MiM~(J =2) levels at the neighbor-hood of Z =63 has a strong influence on these transitionrates. The L, ~- 3 3 2 3--M M ( P ) and L -M&M4 5(J =2) have
Z =63 (Fig. 6). These weak transitionsstrong peaks at = ig.Li-MiM3( Pq) and L3-MiM45(J =2) pick up their in-tensities rom coupf coupling with strong transitions L i-M M (J=2) and L -M&M&(J=2), respective y. is
P~f M P-) in-level-crossing interaction increases the L,-- 3M3 2 111-
DHS —ICCI
25 —--- DHS- JJ
2.0—Lg M3M3 (3p2)
t )
05
1.0
0.5
030 40 50
- IVI3M3 {3
-I----I-60 70
zSO 90
FIG. 6. Calculated L~-M3M3( P&) and L3 1 43 I -M M4, {J=2)
Au er rates, as xunctsons o af t' f atomic number. The Dirac-Fock-Auger rate, x t aSlater calculations in intermediate coup ing wi conlin with configuration
eak near Z=63,interaction so it' ( olid curves) exhibit a pronounced peaThe dashed curvescaused by leveling crossing (see text). The as e
represent Dirac-Hartree-Slater results in j-j coup ing.
tensity at = y aZ =60 b a factor of 50. The strong dip atZ=60 in the relative intensity of l(L3 M3M3)-I 3-M2Mi) as a function Z (Fig. 3) is also the result of level-crossing interaction.
In order to assess the reliability of the Dirac-Hartree-Slater calculations with fixed j-j basis states, we have per-f d a sample calculation using multicon iguration
M M transitions of Kr. In ihe MCDF calculations,the energies and wave functions or o
23 45
computed with extended averaged level scheme (EAI.).h EAL scheme, the orbital wave functions are ob-d b minimizing the statist&cally averaged gy
~ ~
yall the levels. We use single configuration or ahole state and 16-configuration-state functions expansion
3 ] and [3 3dj double-hole configurations forh f' 1 A er states. The Auger energies were o aine
by taking the differences between initial- and ina-energies. owever, inH
'the calculations of Auger transition
h b't 1 ave functions from an initial state wereused to avoid the complication from nonorthogona i y e-
n the initial and final orbital wave functions. Thetween t e ini iat' m wave functions were generated y
'gb solvin thecontmuum wave
to final hole stateDirac-Pock equations corresponding to ina ot includin the exchange interaction between bound
and- continuum electrons. The continuum waveh 'dt rthogonahzed to the initial orbital
wave functions. The results are listed in Table VII. eAuger energies romf DHS-ICCI agree within 0.2 eV withthe results rom t ef h MCDF model. For the Auger rates,h its from these two theories agree wit in-t e resu
in ordert for the very weak transitions. Certain y,'
pto test the relativistic intermediate couplmg t eory,precise experimental data are needed.
ACKNOWLEDGMENTS
T»s work was performed in part under the auspices ofU S. De artment of Energy by the I.awrence I.iver
more National Laboratory under Contract No.ENG-48 and the U.S. Air Force Office of ScientificResearch under Contract No. F49620-83-K0020.
MAU HSIUNCx CHEN 31
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