L2,3M2,3X Auger transitions of Ag, In, Sn, and Sb: experiment and theory

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UNIVERSIDADE ESTADUAL DE CAMPINAS

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REPOSITÓRIO DA PRODUÇÃO CIENTIFICA E INTELECTUAL DA UNICAMP

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https://journals.aps.org/prb/abstract/10.1103/PhysRevB.60.15790

DOI: 10.1103/PhysRevB.60.15790

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©1999 by American Physical Society. All rights reserved.

DIRETORIA DE TRATAMENTO DA INFORMAÇÃO Cidade Universitária Zeferino Vaz Barão Geraldo

CEP 13083-970 – Campinas SP Fone: (19) 3521-6493 http://www.repositorio.unicamp.br

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L

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X Auger transitions of Ag, In, Sn, and Sb:

Experiment and theory

A. de Siervo, R. Landers, G. G. Kleiman, S. G. C. de Castro, and J. Morais

Instituto de Fı´sica ‘‘Gleb Wataghin,’’ Universidade Estadual de Campinas, Caixa Postal 6165, 13081-970 Campinas, Sao Paulo, Brazil

共Received 2 July 1999兲

The possibility of measuring high-resolution Auger core-level spectra produced from the ionization of deep levels has recently stimulated interest in their properties. Of special interest are those properties involving the purely atomic and the satellite spectra: the former permits evaluation of theories of atomic spectra and the latter allows study of excited states. Most such studies have treated the L2,3M4,5M4,5 spectra of the 4d metals:

theoretical characterization of the atomic portion of the spectra facilitated separation of the satellite spectra and study of their systematics. Reports of other such spectra in the literature are sparse. In this study we present high-resolution L2,3M2,3M2,3and L2,3M2,3M4,5Auger spectra measured for Ag, In, Sn, and Sb, and compare

them with the results of nonrelativistic atomic calculations of the multiplet structure intensities using a model for closed shells with the initial state treated in the jj coupling scheme and the final state in the intermediate coupling scheme. Comparison of the theoretical results and experimental spectra shows a high degree of agreement for the L2,3M2,3M4,5spectra. Consideration of the L2,3M2,3M2,3spectra would seem to indicate the

presence of many-body effects.关S0163-1829共99兲10147-4兴

I. INTRODUCTION

High-resolution Auger spectra have been extensively used to study the physical mechanisms involved with the emission of electrons from solids molecules and atoms. Auger transi-tions that involve only core levels are particularly interesting when one is interested in such phenomena as hole-hole in-teractions, correlation effects, and the dynamics of relaxation and screening of the holes involved. Their study also lends insight into phenomena related to the decay of the primary core hole such as Coster-Kronig 共CK兲 transitions, shake-up, and, in some cases, x-ray fluorescence.1,2 Many studies of this kind can be found in the literature, notably those related to the satellites of the L2,3M4,5M4,5Auger spectra of the 3d and the L_1,2,3M_4,5M_4,5 spectra of the 4d metals. The satel-lites in Cu, Zn, Ge, and Ga were shown3–6to be associated with 3d spectator vacancies produced mainly by L2L3M4,5 CK preceding the L3M4,5M4,5 transition and by a combina-tion of initial-state shake-up and L1L2M4,5CK preceding the

L2M4,5M4,5 transition.7–10 Analogous satellites of the 4d metals Rh, Pd, and Ag, observed in conjunction with the

L1,2,3M4,5M4,5transitions, are also associated with valence-band spectator vacancies: these satellites, however, originate primarily in initial-state shake-up, and the effect of CK is minor. This conclusion is borne out by studies utilizing syn-chrotron radiation.11–13 It should be emphasized that these conclusions regarding the satellites were possible only be-cause of the adequacy of the models for the atomic line shapes, permitting separation of the atomic contribution to the total line shapes.14–17

The difference in physical origins of the satellites of the 3d and 4d L M4,5M4,5spectra suggests the experimental in-vestigation of other 4d L M M Auger transitions in order to illuminate the dependence of satellite production mecha-nisms on the nature of the core levels involved.

The L2,3M2,3M4,5and L2,3M2,3M2,3transitions correspond to the most intense such Auger spectra of the 4d metals. To

illustrate this point, we present, in Fig. 1, a long scan of these spectra for Ag excited with radiation from a Ti anode: we discuss the experimental conditions below. Combination of the results of their study with those already reached for the

L1,2,3M4,5M4,5spectra should indicate the effect on the spec-tra of gradually changing the nature of the final state. From Fig. 1, it is clear that direct identification of satellite struc-tures is made difficult by the broadness of the spectra. In order to characterize the atomic contributions to the line shapes, it is essential to theoretically model these transitions. Such atomic characterizations are important in themselves, as well as from the point of view of satellite studies.

In this paper, we present the results of theoretical calcu-lations and measurements of the L2,3M2,3M4,5 and

L2,3M2,3M2,3spectra of the closed 4d shell metals Ag, In, Sn and Sb. The calculations are based on nonrelativistic closed

FIG. 1. Long scan of LMM Auger transitions of Ag excited with Ti radiation for Auger kinetic energies between 2100 and 2650 eV before and after subtracting the background. The dashed line is the background calculated using Tougaard’s formalism共Ref. 27兲. PRB 60

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shell models with jj coupling in the initial state and interme-diate coupling共IC兲 in the final state for the L2,3M2,3M4,5and

L2,3M2,3M2,3Auger transitions. We find good agreement be-tween theory and experiment for the L2,3M2,3M4,5 Auger spectra; although such agreement may not be surprising be-cause of the closed 4d shells of these metals, similar agree-ment exists for the open shell metals Pd, Rh, and Ru.18The importance of performing nonrelativistic calculations sys-tematically for these transitions of the 4d metals is under-lined by the fact that the only reported theoretical transition probabilities for these metals are the relativistic ones of Chen14 for Rh. Comparison of the relativistic14 and nonrelativistic16,19results for the L2,3M4,5M4,5transitions of Rh demonstrates that, whereas both calculations predict similar transition probabilities, the nonrelativistic multiplet splittings reproduce the experimental spectra better共perhaps because of the use of experimental spin-orbit splittings16兲. This conclusion regarding the multiplet splitting is repeated for the L2,3M2,3M4,5 spectra of Rh 共Refs. 18–20兲 although

the relativistic intensities in this case appear to agree better with experiment.

In previous work,18,21,22 we discussed some of the

L2,3M2,3M2,3 and L2,3M2,3M4,5 Auger spectra for some of these metals, but without complete analysis of their multiplet structure. In the present study, we present experimental spec-tra and detailed discussion of the theoretical results obtained from nonrelativistic atomic calculations. The theoretical re-sults presented here are such that they can be readily used to calculate the Auger spectra.

Section II contains discussion of the experiments as well as the theoretical calculations, Sec. III has a discussion of the results, and Sec. IV presents our conclusions.

II. EXPERIMENTAL RESULTS AND CALCULATIONAL PROCEDURE

Most of our experiments involved excitation with a Ti anode. These were performed in an ion-pumped system共base pressure of 2 – 5⫻10⫺10Torr兲 with a VSW HA 100 hemi-spherical analyzer operated in the fixed analyzer

transmis-sion 共FAT兲 mode with pass energy of 44.0 eV, producing a

full width at half maximum of 1.5 eV for the Au 4 f7/2 line when excited by Al K␣ radiation. The Auger spectra were excited with Ti K␣₁ (h␯⫽4510.9 eV) and K␣₂ (h␯

⫽4504.9 eV) characteristic radiation. The energy scale was

calibrated by fixing the Au 4 f_7/2 binding energy at 84.0 eV and the Au M4,5N6,7N6,7 Auger kinetic energy at 2015.8 eV.23

We also report spectra measured using synchrotron radia-tion. These were taken at the Laboratorio Nacional de Luz Sincrotron Brazil共LNLS兲 with a double crystal monochrom-eter and an Omicron EA125 HR hemispherical analyzer

op-FIG. 2. Experimental spectra of the L2M2,3M2,3, and L3M2,3M4,5Auger spectra excited with Ti radiation and with

back-ground subtracted, for the closed shell metals Ag, In, Sn, and Sb. The solid and dotted bars’ diagrams correspond to j j-IC atomic calculations for L3M2,3M4,5and L2M2,3M2,3, respectively; their

or-der is that in Tables II and III. Plasmons and possible shake-up satellite contributions are indicated by inverted solid and open tri-angles, respectively. Auger kinetic energies are relative to that of the main (1F3) line of the M2,3M4,5configuration, corresponding to

2345.6 eV for Ag, 2545.8 eV for In, 2648.0 eV for Sn, and 2751.6 eV for Sb.

FIG. 3. Details of the Ag L3M2,3M4,5Auger spectrum excited

with monochromatic synchrotron radiation (h␯⫽3516 eV) insuffi-cient to ionize the L2 level: Auger kinetic energies are relative to

that of 1F3 multiplet component共2345.6 eV兲. The bars represent the j j-IC atomic calculation; their order is that in Table III. The theoretical envelope curves, described in the text, of the atomic and shake-up satellite contributions 共corresponding to images of the atomic spectrum and denominated Sat. 1 and Sat. 2 in Table XII兲 as well as of the total theoretical spectrum are indicated. The inset presents the results of jj-LS calculations, which are clearly inad-equate here.

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erated in the FAT mode with a pass energy of 44.0 eV. A detailed description of sample preparation and experi-mental setup are described elsewhere.24,25The samples were in the form of thick high purity foils cleaned in situ by argon ion bombardment. The Ag sample was annealed. Because of the long acquisition times, all samples presented a slight oxygen contamination at the end of the analysis: the energies of the corresponding photoelectron peaks, however, were compatible with those of the clean pure metals.

A typical long scan spectrum of Ag for the transitions under study appears in Fig. 1. Spectra of the other metals considered here show very similar features, especially with respect to the background. We should mention that, since the background increases with kinetic energy, it is very difficult to treat it with a Shirley26 type algorithm. All the back-grounds of the spectra we present were calculated using Tou-gaard’s ‘‘universal’’ parameters.27

In Figs. 2–5 we present, for Ag, In, Sn, and Sb, details of the spectra typified in Fig. 1: all the Auger spectra except those illustrated in Fig. 3 were excited with a Ti anode. In

Fig. 2, we display the overlapping L2M2,3M2,3 and

L3M2,3M4,5spectra; in Fig. 3, the L3M2,3M4,5spectra of Ag excited with synchrotron radiation below the L2 ionization threshold; in Fig. 4, the overlapping L2M2,3M4,5 and

L3M4,5M4,5 spectra; and in Fig. 5, the L3M2,3M2,3 spectra, all with background subtracted. We also exhibit the results of atomic multiplet structure calculations for each transition.

To obtain the relative energies of the multiplets we use the same general scheme employed previously for the

L_2,3M₄₅M₄₅ transitions.15,16,28 Since we treat the two-hole final state in the intermediate coupling共IC兲 scheme, we must include both residual electrostatic and spin-orbit interactions in the final-state Hamiltonian. We account for the Coulomb interactions by using the atomic direct and exchange Cou-lomb integrals 共F2, G1, and G3 in Slater’s notation29 are given in Table I兲 from the nonrelativistic neutral ground-state Hartree-Fock-Slater self-consistent field 共HFS-SCF兲 calculations of Mann.30 The spin-orbit parameters used in our IC calculations were derived from experimental M2- M3

FIG. 4. Experimental spectra of the L2M2,3M4,5, and the more

intense L3M4,5M4,5Auger transition共Refs. 11, 12, 15, 16, and 28兲,

excited with Ti radiation and with background subtracted, for the metals Ag, In, Sn, and Sb. The bars correspond to j j-IC atomic calculations for the L2M2,3M4,5transition; their order follows that in Table III. Very weak theoretical L2M2,3M4,5 intensities are

circled. Plasmon and shake-up satellites are indicated by inverted solid and open triangles, respectively. The energy scale is relative to the main (1_F

3) line of M2,3M4,5configuration. The corresponding

absolute energies are 2518.4 eV for Ag, 2754.0 eV for In, 2875.0 eV for Sn, and 2999.5 eV for Sb.

FIG. 5. Experimental spectra of the L3M2,3M2,3Auger transition

excited with Ti radiation and with background subtracted, for Ag, In, Sn, and Sb. The bars correspond to j j-IC atomic calculation in the order in Table II. The energy scale is relative to 1D2multiplet and strong plasmon features are indicated by inverted black tri-angles. The energy zeros correspond to 2143.8 eV for Ag, 2328.6 eV for In, 2421.3 eV for Sn, and 2517.0 eV for Sb.

TABLE I. Direct (F2_{) and exchange} _共G1 _{and G}3_{兲 Coulomb}

integrals 共Ref. 30兲; and spin-orbit parameters derived from XPS data, all expressed in eV.

F2_{(3 p,3p) F}2_{(3 p,3d) G}1_{(3 p,3d) G}3_{(3 p,3d)} _␰ 3 p ␰3d Ag 33.36 32.96 37.54 24.21 20.67 2.40 In 35.23 34.92 39.50 25.57 25.33 3.02 Sn 36.18 35.90 40.47 26.25 28.00 3.36 Sb 37.13 36.88 41.45 26.92 30.67 3.74

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and M₄- M₅ x-ray photoelectron spectroscopy 共XPS兲 splittings;31 and are also given in Table I. In Table II, we present the calculated multiplet energies of the M2,3M2,3 IC final state relative to that of the main (1D2) component; in Table III, we indicate the corresponding results for the

M2,3M4,5final state relative to the main (1F3) line. Tables IV and V display the corresponding IC eigenvectors for the re-spective 3 p43d10 and 3 p53d9 final states.

In Tables VI and VII, we present the numerical results for the L2,3M2,3M2,3and L2,3M2,3M4,5j j -IC transition rates rela-tive to the most intense terms 共i.e., 1D2 and 1F3, respec-tively兲. We give the general equations for nonequivalent final-state holes32,33in the Appendix, and in Tables VIII–XI, we summarize explicit expressions for the j j-IC transition rates in terms of the appropriate IC eigenvector components and of the quantities A(L,l2) defined in the Appendix. The radial integral matrix elements used in our calculations are those of McGuire34 共those of In, Sn, and Sb were extrapo-lated linearly from the tabuextrapo-lated results34兲.

III. DISCUSSION

A salient feature of the experimental spectra presented in Fig. 2 is the appearance of satellites. Based on previous work, we identify these as plasmon satellites when we treat In, Sn, and Sb共Refs. 7, 15兲 and shake-up satellites when we consider Ag.28 In Fig. 2, we indicate some strong plasmon satellites by inverted solid triangles and shake-up satellites by inverted open triangles. Comparison of the experimental

spectra with the results of theoretical calculations is compli-cated by the appearance of the plasmon satellites in In, Sn, and Sb.

Another complicating factor in making such a detailed comparison is the overlap of the individual L2M2,3M2,3and

L3M2,3M4,5 spectra. Identification of the overlap is, in fact, possible only by comparing with the theoretical predictions. In Fig. 2, we compare theoretical transition probabilities for the experimental L3M2,3M4,5 spectra by aligning the main (1F3) theoretical line with the leftmost experimental peak. The theoretical L2M2,3M2,3lines were positioned by adding the L2-L3 binding energy difference to the energies of the

L3M2,3M2,3multiplet terms, which are relatively easy to po-sition, as indicated in Fig. 5. The energy zeros in Fig. 2 correspond to absolute Auger kinetic energies of 2751.6 eV for Sb, 2648.0 eV for Sn, 2545.8 eV for In, and 2345.6 eV for Ag.

From consideration of Fig. 2, it is clear that the

L2M2,3M2,3 spectrum of Sb is masked by that of the

L3M2,3M4,5 transition. As we decrease the atomic number the spectra separate increasingly until we reach In and Ag, where there is a possibility of isolating the L2M2,3M2,3 spec-tra; the influence of the plasmon satellites in In, however, would seem to negate this possibility. For Ag, however, the

L2M2,3M2,3 theoretical intensities and energy positions ap-pear to correspond rather well to experimental peaks.

Consideration of the L3M2,3M4,5 spectrum, on the other hand, indicates similar behavior in all four metals, especially in the energy region around the right-hand main peak: the shapes of the experimental spectra in this region resemble one another and these shapes seem to be reflected in the patterns of theoretical probabilities.

In order to explore the degree of experimental and theo-retical accordance without complications from the overlap of the L2M2,3M2,3spectrum, we performed experiments for Ag utilizing synchrotron radiation below the L2 ionization threshold. Figure 3 exhibits the pure L3M2,3M4,5 spectrum measured, as well as the total theoretical spectrum resulting from applying our theoretical model28 共in the inset we indi-cate the results of j j-LS calculations, which are clearly in-adequate for describing these spectra兲. The theoretical ‘‘atomic’’ spectra were generated by convoluting each mul-tiplet term with the same Voigt function, so that each spec-trum involved only three parameters: the width, the relative TABLE II. L2,3M2,3M2,3IC relative energies in eV. The order of

the entries corresponds to that of the bars in Figs. 2 and 5. The indicated term in parentheses is the zero spin-orbit limit of the IC.

Term Ag In Sn Sb A (1_S 0) ⫺33.48 ⫺40.44 ⫺44.42 ⫺48.41 B (1_D 2) 0 0 0 0 C (3_P 1) 5.75 6.02 6.16 6.3 D (3_P 0) 24.98 31.34 35.03 38.73 E (3_P 2) 34.5 41.59 45.64 49.69

TABLE III. L2,3M2,3M4,5IC relative energies in eV. The order

of the entries corresponds to that of the bars in Figs. 2, 3, and 4. The indicated term in parentheses is the zero spin-orbit limit of the IC.

Term Ag In Sn Sb A (1_P 1) ⫺5.86 ⫺7.91 ⫺9.06 ⫺10.23 B (1F3) 0 0 0 0 C (1D2) 9.22 8.96 8.82 8.71 D (3D2) 12.42 11.10 10.33 9.54 E (3P1) 28.02 33.28 36.34 39.4 F (3D3) 30.92 35.91 38.79 41.68 G (3P0) 33.35 38.42 41.34 44.24 H (3D1) 34.46 40.06 43.31 46.62 I (3P2) 35.46 40.81 43.88 46.94 J (3F3) 41.11 47.03 50.48 53.98 K (3F2) 46.51 53.29 57.16 61.09 L (3F4) 50.64 57.85 61.94 66.07

TABLE IV. Eigenvector for 3 p4states in intermediate coupling (J, f ). The second column indicates the zero spin-orbit coupling limit of state (J, f ). CJ f(2S⫹1LJ) Ag In Sn Sb C0A(3P0) ⫺0.71 ⫺0.73 ⫺0.73 ⫺0.74 C0A(1S0)a ⫺0.70 ⫺0.69 ⫺0.68 ⫺0.67 C0D(3P0)a 0.70 0.69 0.68 0.67 C0D(1S0) ⫺0.71 ⫺0.73 ⫺0.73 ⫺0.74 C1C(3P1)a 1 1 1 1 C2B(1D2)a ⫺0.48 ⫺0.50 ⫺0.50 ⫺0.51 C2B(3P2) ⫺0.88 ⫺0.87 ⫺0.87 ⫺0.86 C2E(1D2) ⫺0.88 ⫺0.87 ⫺0.87 ⫺0.86 C2E(3P2)a 0.48 0.50 0.50 0.51 a_{The surviving term in the zero spin-orbit limit.}

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energy position, and intensity of the most intense multiplet of the transition 共1F3 for the L3M2,3M45 transition兲. The contributions of the satellites were included by applying a model developed for the L1,2,3M45M45 Auger spectra.28 In this model, the shakeup satellites are attributed to the pres-ence of single and double spectator vacancies in the initial and final Auger states and are included in intensity calcula-tions as images of the atomic multiplets. Calculation of the satellite contributions in this model is, therefore, the same as that for the atomic multiplets. The widths, energy positions, and relative intensities of the atomic and satellite spectra were determined from summing them to form the total spec-trum and making a best fit to the experimental data 共in the Voigt functions, the Gaussian portion of the width corre-sponded to the analyzer machine function兲.

In Table XII, we present the results of this fitting and compare them to those derived from similar treatment of the Ag L₃M_4,5M_4,5spectrum excited with Ti radiation. Compari-son of these results among themselves and with previous results28 for the Ag, L3M4,5M4,5 spectrum excited with Al bremsstrahlung leads to two conclusions. First, isolation of the satellite contributions and determination of their relative intensities appear to be extremely sensitive to the manner in which the background is calculated and to the nature of the data. The other conclusion is that the positions of the satel-lites relative to the main lines are quite insensitive. There is good agreement between the L3M4,5M4,5 satellite positions in Table XII and those derived previously28 and with the

L3M2,3M4,5 satellite positions in Table XII. These satellite positions, in turn, agree rather well with those calculated from the model28 共theoretical satellite energy positions are indicated in parentheses in Table XII兲.

The characteristics of strong plasmon satellites of the sp metals and overlapping Auger transitions are repeated for the

L2M2,3M4,5spectra in Fig. 4; the L2M2,3M4,5theoretical in-tensities were positioned by adding the L2-L3 binding en-ergy difference to energies of the corresponding L3M2,3M4,5 lines. Here, the spectra overlap those of the much more in-tense L3M4,5M4,5 transition, especially in the region of the circles in the figure, which indicate very weak theoretical

L₂M_2,3M_4,5intensities. Although these theoretical intensities are weak, we note that their influence should be taken into account when analyzing L3M4,5M4,5 data, especially when treating the atomic spectra of Sb, Sn and ln and the shakeup satellite structure of Ag 共indicated by inverted open tri-angles兲.

For purposes of analyzing these spectra, the overlap is TABLE V. Eigenvector for 3 p53d9states in intermediate

pling (J, f ). The second column indicates the zero spin-orbit cou-pling limit of state (J, f ).

CJ f(2S⫹1LJ) Ag In Sn Sb C0G(3P0)a 1 1 1 1 C1A(3D1) 0.57 0.59 0.60 0.61 C1A(3P1) 0.33 0.34 0.35 0.35 C1A(1P1)a 0.75 0.73 0.72 0.71 C1H(3D1)a 0.25 0.20 0.17 0.14 C1H(3P1) ⫺0.94 ⫺0.94 ⫺0.93 ⫺0.93 C1H(1P1) 0.23 0.28 0.31 0.34 C1E(3D1) 0.78 0.78 0.78 0.78 C1E(3P1)a 0.06 0.02 ⫺0.06 ⫺0.10 C1E(1P1) ⫺0.62 ⫺0.62 ⫺0.62 ⫺0.62 C2K( 3 F2)a ⫺0.36 ⫺0.35 ⫺0.34 ⫺0.33 C2K( 1 D2) 0 ⫺0.03 ⫺0.04 ⫺0.05 C2K( 3 D2) 0.84 0.83 0.83 0.83 C2K( 3 P2) 0.40 0.43 0.44 0.45 C2C( 3 F2) 0.16 0.18 0.20 0.25 C2C(1D2)a 0.65 0.65 0.65 0.66 C2C(3D2) ⫺0.26 ⫺0.26 ⫺0.26 ⫺0.23 C2C(3P2) 0.69 0.69 0.69 0.67 C2D(3F2) 0.82 0.82 0.82 0.81 C2D(1D2) 0.24 0.21 0.19 0.15 C2D(3D2)a 0.47 0.47 0.48 0.49 C2D(3P2) ⫺0.24 ⫺0.24 ⫺0.25 ⫺0.28 C2I(3F2) ⫺0.42 ⫺0.41 ⫺0.41 ⫺0.41 C2I(1D2) 0.72 0.73 0.73 0.73 C2I(3D2) 0.08 0.12 0.14 0.16 C2I(3P2)a ⫺0.55 ⫺0.53 ⫺0.52 ⫺0.52 C3B(3F3) ⫺0.33 ⫺0.36 ⫺0.38 ⫺0.40 C3B(1F3)a 0.87 0.85 0.84 0.83 C3B(3D3) ⫺0.36 ⫺0.38 ⫺0.39 ⫺0.40 C3J(3F3)a 0.77 0.72 0.70 0.67 C3J(1F3) 0.03 0.00 ⫺0.02 ⫺0.03 C3J(3D3) ⫺0.63 ⫺0.69 ⫺0.72 ⫺0.74 C3F(3F3) ⫺0.54 ⫺0.59 ⫺0.61 ⫺0.63 C3F(1F3) ⫺0.48 ⫺0.53 ⫺0.55 ⫺0.56 C3F(3D3)a ⫺0.69 ⫺0.61 ⫺0.58 ⫺0.54 C4L(3F4)a 1 1 1 1 a_{The surviving term in the zero spin-orbit limit.}

TABLE VI. Intensities of L2,3M2,3M2,3spectras calculated in jj-IC scheme relative to the 1D2terms. The

order of entries in the row corresponds to that of the bars in Figs. 2 and 5. The indicated term is the zero spin-orbit limit of the IC state.关Numbers enclosed in parentheses signify powers of 10; e.g., 5.35(⫺2)

⫽5.35⫻10⫺2_._兴 Term Ag L3M M L2M M In L3M M L2M M Sn L3M M L2M M Sb L3M M L2M M A (1S0) 5.35共⫺2兲 4.17共⫺1兲 4.98共⫺2兲 4.20共⫺1兲 4.55共⫺2兲 4.13共⫺1兲 4.08共⫺2兲 4.17共⫺1兲 B (1D2) 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 C (3P1) 4.03共⫺1兲 4.46共⫺1兲 4.07共⫺1兲 4.44共⫺1兲 4.05共⫺1兲 4.44共⫺1兲 4.12共⫺1兲 4.46共⫺1兲 D (3P0) 4.32共⫺1兲 4.56共⫺4兲 4.48共⫺1兲 2.27共⫺3兲 4.42共⫺兲 2.27共⫺3兲 4.57共⫺1兲 2.22共⫺3兲 E (3P2) 1.50共0兲 1.14共⫺2兲 1.53共0兲 1.36共⫺2兲 1.53共0兲 1.36共⫺2兲 1.55共0兲 1.33共⫺2兲

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much more serious for the sp metals because of the very pronounced plasmon structures 共indicated by inverted solid triangles兲 stretching well below the L3M4,5M4,5line. Even in this case, the strongest L2M2,3M4,5theoretical intensities ap-pear to correspond very clearly in energy and intensity with experimental features.

The theoretical L3 and L2M2,3M4,5spectra we have con-sidered until this point appear to describe the corresponding experimental spectra of all four metals at least reasonably well. The accuracy of the theoretical description of the

L2M2,3M2,3spectra is more difficult to assess, except for the spectrum of Ag in Fig. 2, discussed above. In order to make this assessment more concrete, we present, in Fig. 5, experi-mental spectra for the L3M2,3M2,3 transition, together with results for the corresponding atomic calculation. In Fig. 5, strong plasmon features are indicated by inverted black tri-angles.

In contrast to the transitions with the M2,3M4,5final state discussed here and those with the M_4,5M_4,5 final state dis-cussed previously,11–13,15,16,28where j j -IC coupling seems to describe the energies and intensities of the experimental spectra well, there is, by no means, such good agreement with the experimental L3M2,3M2,3 spectra presented in Fig. 5. The experimental spectra are characterized by a double peak structure on the right. Although intense plasmon satel-lites共indicated by inverted black triangles兲 overlap the peaks in In, Sn, and Sb, persistence of the double peak structure in Ag would suggest that it is intrinsic to the atomic multiplet. It seems that the atomic calculations reproduce neither the

peak positions nor their intensities well.

The reason for this discrepancy is not clear: similar dis-crepancies in multiplet splittings were observed for

L3M2,3M2,3 spectra of Cu, Zn, Ga, and Ge. 4,35,36

It might appear that the nonrelativistic HFS-SCF neutral ground-state calculations30yield wave functions which underestimate the electrostatic interaction of the two 3 p holes, yielding too small a multiplet splitting. Utilization of an effective

F2(3 p,3p) Coulomb integral improves the agreement in en-ergy positions between the left and rightmost peaks, but changes the transition probabilities little and fails to describe the double peak: furthermore, the same effective Coulomb integral worsens, if anything, the theoretical and experimen-tal energy position agreement for the L2M2,3M2,3spectra in Fig. 2.

In principle, including the effects of either relativity, or correlation or configuration interaction could improve the agreement between the theoretical results and the experimen-tal data. Indeed, when configuration interaction is incorpo-rated into calculations of the L3M2,3M2,3 spectra of Cu and Zn,35 agreement with experiment improves significantly. Of special relevance here are relativistic j j -IC calculations, with configuration interaction, of these spectra for Rh.14 Compari-son with experimental L₃M_2,3M_2,3 spectra of Rh 共Ref. 20兲 indicates that the positions of the relativistic multiplet TABLE VII. Intensities of L2,3M2,3M4,5spectra calculated in jj-IC scheme relative to the

1

F3terms. The

order of entries corresponds to that of the bars in Figs. 2, 3 and 4. The indicated term is the zero spin-orbit limit of the IC state.关Numbers enclosed in parentheses signify powers of 10; e.g., 5.35(⫺2)⫽5.35⫻10⫺2.兴

Term Ag L3M M L2M M In L3M M L2M M Sn L3M M L2M M Sb L3M M L2M M A (1P1) 1.17共⫺1兲 4.91共⫺1兲 1.07共⫺1兲 4.97共⫺1兲 1.04共⫺1兲 5.01共⫺1兲 1.03共⫺1兲 5.03共⫺1兲 B (1F3) 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 1.00共0兲 C (1D2) 8.92共⫺2兲 2.99共⫺1兲 9.76共⫺2兲 3.08共⫺1兲 9.90共⫺2兲 3.13共⫺1兲 9.85共⫺2兲 3.14共⫺1兲 D (3D2) 7.04共⫺2兲 1.80共⫺2兲 6.83共⫺2兲 1.80共⫺2兲 6.93共⫺2兲 2.09共⫺2兲 6.40共⫺2兲 2.33共⫺2兲 E (3P1) 4.13共⫺1兲 2.70共⫺2兲 4.29共⫺1兲 3.29共⫺2兲 4.41共⫺1兲 3.58共⫺2兲 4.48共⫺1兲 4.07共⫺2兲 F (3D3) 7.79共⫺1兲 5.39共⫺2兲 8.44共⫺1兲 8.68共⫺2兲 8.86共⫺1兲 1.04共⫺1兲 8.97共⫺1兲 1.19共⫺1兲 G (3P0) 3.52共⫺2兲 2.67共⫺2兲 3.80共⫺2兲 2.70共⫺2兲 3.96共⫺2兲 2.78共⫺2兲 3.94共⫺2兲 2.62共⫺2兲 H (3D1) 1.78共⫺1兲 2.99共⫺2兲 2.10共⫺1兲 2.70共⫺2兲 2.28共⫺1兲 2.39共⫺2兲 2.46共⫺1兲 2.04共⫺2兲 I (3P2) 3.05共⫺1兲 3.59共⫺2兲 3.32共⫺1兲 3.89共⫺2兲 3.47共⫺1兲 3.88共⫺2兲 3.64共⫺1兲 3.78共⫺2兲 J (3F3) 1.97共⫺1兲 7.49共⫺2兲 2.59共⫺1兲 7.19共⫺2兲 3.02共⫺1兲 6.87共⫺2兲 3.35共⫺1兲 6.98共⫺2兲 K (3F2) 3.76共⫺2兲 5.99共⫺3兲 3.90共⫺2兲 5.99共⫺3兲 4.46共⫺2兲 5.97共⫺3兲 4.43共⫺2兲 2.91共⫺3兲 L (3_F 4) 1.88共⫺3兲 2.99共⫺4兲 3.41共⫺3兲 2.99共⫺4兲 4.46共⫺3兲 2.99共⫺4兲 4.93共⫺3兲 2.91共⫺4兲

TABLE VIII. L2M2,3M2,3transition rates in jj IC.

J⫽0 27兩⫺Cf共1S0兲A共0,1兲⫹&Cf共3P0兲A共1,1兲兩2 J⫽1 243 2 兩Cf共 3_P_{1兲A共1,1兲兩}2 J⫽2 135 2 兩&Cf共 1 D2兲A共2,1兲⫹Cf共3P2兲A共1,1兲兩2 ⫹315兩Cf共1D2兲A共2,3兲兩2

TABLE IX. L3M2,3M2,3transition rates in jj IC.

J⫽0 27兩Cf共1S0兲A共0,1兲⫹ & 2 Cf共 3_P_{0兲A共1,1兲兩}2 J⫽1 243 4 兩Cf共 3 P1兲A共1,1兲兩2 J⫽2 27 2 兩Cf共 1_D_{2兲A共2,1兲⫺5}& 2 Cf共 3_P_{2兲A共1,1兲兩}2 ⫹315兩Cf共1D2兲A共2,3兲兩2 ⫹243 2 兩Cf共 1 D2兲A共2,1兲兩2 PRB 60 _L 15 795

(8)

terms14 agree somewhat better than do those from the non-relativistic calculations. On the other hand, the relative

L3M2,3M2,3 transition probabilities from the relativistic

j j -IC calculations with configuration interaction14 are

simi-lar to the nonrelativistic ones and also fail to describe the Rh experimental data.20A study to separate the influence of such effects as relativity, the Breit interaction, configuration inter-action, and correlation on the L3M2,3M2,3 spectra would be very interesting: such a study, however, is beyond our brief here. We should point out that multiplet splittings from the nonrelativistic calculations, including empirical spin-orbit splittings, seem to describe the Rh L2,3M2,3M4,5 共Refs. 18– 20兲, L2,3M4,5M4,5共Ref. 6兲 data better than do those from the relativistic calculations.14 In fact, the question remains why the neutral ground-state wave functions describe the multip-let splittings of the L2,3M2,3M4,5 presented here and the

L2,3M4,5M4,5spectra reported previously 15,16,28

so well. To add to the puzzle, work on the M4,5N4,5N4,5transition in Cd 共Ref. 37兲 indicates that using nonrelativistic calcula-tions with ground-state basis funccalcula-tions overestimates the multiplet splitting and suggests that the discrepancy might be caused by neglecting relativistic effects: configuration inter-action and correlation effects were eliminated as causes of the discrepancy.37Similar conclusions were reached for stud-ies of the M4,5N4,5N4,5transition of Ag, In, and Sn.38

The whole body of Auger data for Ag, In, Sn, and Sb—

that is, the L1,2,3M4,5M4,5, the L2,3M2,3M4,5, and the

L2,3M2,3M2,3 spectra—suggests that a unified description of all the transitions in terms of an independent particle model is unlikely, and it is difficult to see how relativistic correc-tions to such a model alone could explain the double peaked structure in the spectra in Fig. 5. We feel, therefore, that the root of an explanation of the L3M2,3M2,3spectra must lie in the many body nature of the final state with two 3 p holes and, possibly, include the effects of correlation and dynamic polarization associated with the two 3 p holes.

IV. CONCLUSIONS

In this paper, we present experimental data for the

L_2,3M_2,3M_2,3 and L_2,3M_2,3M_4,5 Auger transitions in Ag, In, TABLE X. L2M2,3M4,5transition rates in jj IC.

J⫽0 45 2 兩Cf共 3 P0兲A共1,0兲兩2 J⫽1 270

冏

⫺) 6 Cf共 1 P1兲A共1,0兲⫹

冑

6 6 Cf共 3 P1兲A共1,0兲

冏

2 ⫹2700

冏

冏

₂₀5 Cf共1D2兲A共2,2兲⫹ & 8 Cf共 3_P_{2兲A共1,2兲} ⫹

冑

30 40 Cf共 3 D2兲A共2,2兲

冏

2 ⫹6750

冏

ACKNOWLEDGMENTS

The authors would like to thank CNPq, FAPESP, and FINEP of Brazil for support; and Dr. Miguel Abbate and the LNLS staff for their assistance in using the SXS beam line. A.S. and J.M. acknowledge support from CAPES and FAPESP.

APPENDIX

General expressions for the intensity of Auger transitions with two holes32,33共equivalent or not兲 in the final state are given in Eqs.共A1兲–共A5兲:

Wi f⫽⌬共l3,l4兲共2J⫹1兲

兿

i⫽1 4 共2li⫹1兲

兺

x 共2x⫹1兲 ⫻

冏

兺

LS Cf共2S⫹1LJ兲共⫺1兲L

冑

共2L⫹1兲共2S⫹1兲 ⫻

再

l₂ L l₁ 1 2 j1 x

冎再

1 2 S 1 2 L x J

冎

A共L,l2兲

冏

2 , 共A1兲 ⌬共l3,l4兲⫽

再

1 if l3⫽l4 1 2 if l3⫽l4, 共A2兲 A共L,l2兲⫽

兺

k

冋

冉

l1 k l3 0 0 0

冊冉

l2 k l4 0 0 0

冊

再

l1 l3 k l4 l2 L

冎

⫻共2k⫹1兲D共k,l2兲⫹共⫺1兲S⫺L

冉

l1 k l4 0 0 0

冊

⫻

冉

l2 k l3 0 0 0

dr2␾l₁共r1兲␾l₂共r2兲 ⫻

冉

共r⬍兲 k 共r⬎兲k⫹1

冊

␾l3共r2兲␾l4共r1兲. 共A5兲

The expressions for the quantity A(L,l₂) used in the equa-tions for the L2,3M2,3M2,3transition rates in Tables VIII and IX are given in Eqs. 共A6兲–共A9兲:

A共0,1兲⫽1 9 关D共0,1兲⫹2D共2,1兲兴, 共A6兲 A共1,1兲⫽1 9 关D共2,1兲⫺D共0,1兲兴, 共A7兲 A共2,1兲⫽ 1 45关5D共0,1兲⫹D共2,1兲兴, 共A8兲 A共2,3兲⫽⫺

冑

14 35 D共2,3兲. 共A9兲

TABLE XII. Parameters resulting from fitting the experimental L3M2,3M4,5spectrum of Ag in Fig. 3 to the satellite image model 共Ref. 28兲. The multiplet splittings and transition probabilities of the

satellite spectra are the same as those of the atomic spectrum in Tables III and VII, respectively. Sat. 2共Sat. 1兲 represents the satel-lite closer to 共further from兲 the main peak, corresponding to one

共two兲 valence-band spectator vacancies. Each spectrum is formed

by multiplying each multiplet term by the same Voigt function. The Gaussian width of the Voigt functions used in fitting represents the analyzer resolution of 1.0⫾0.1 eV. Also shown are the correspond-ing parameters from fittcorrespond-ing the Ag L3M4,5M4,5spectrum. For each

transition, the second column represents the position relative to that of the atomic spectrum—the model satellite position is given in parentheses. The third column denotes the full Lorentzian width 2⌫ of the Voigt function. The quantity L Int. corresponds to the inten-sity of the spectrum relative to that of the atomic part.

L3M2,3M4,5 L3M4,5M4,5 ⌬␧ 共eV兲 2⌫ 共eV兲 L Int. ⌬␧ 共eV兲 2⌫ 共eV兲 L Int. Atomic 0.0 6.3⫾0.3 1.0 0.0 2.6⫾0.2 1.0 共0.0兲共0.0兲 Sat. 2 ⫺6.45 8.5⫾0.5 0.46 ⫺6.56 4.9⫾0.4 0.36 共⫺6.05兲共⫺6.05兲 Sat. 1 ⫺14.05 13.5⫾0.5 0.32 ⫺14.08 4.9⫾0.4 .09 共⫺12.70兲共⫺12.70兲 PRB 60 _L 15 797

(10)

Those expressions for A(L,l2) used in the L2,3M2,3M4,5 tran-sition rate equations 共Tables X and XI兲 are given in Eqs.

共A10兲–共A14兲; where S is the total spin angular momentum in

the representation 2S⫹lLj: A共1,0兲⫽

冑

2 45关D共2,0兲⫹共⫺1兲 S_E_{共1,0兲兴,} _共A10兲 A共1,2兲⫽⫺ 1 15关D共0,2兲⫺D共2,2兲兴 ⫺共⫺1兲S1 75关E共1,2兲⫹9E共3,2兲兴, 共A11兲 A共2,2兲⫽ 1 15关D共0,2兲⫺D共2,2兲兴 ⫹共⫺1兲S1 25关E共3,2兲⫺E共1,2兲兴, 共A12兲 A共3,2兲⫽⫺ 1 15D共0,2兲⫺ 2 105D共2,2兲 ⫺共⫺1兲S 1 175 关14E共1,2兲⫹E共3,2兲兴, 共A13兲 A共3,4兲⫽2

冑

15 105 关D共2,4兲⫹共⫺1兲 S_E_{共3,4兲兴.} _共A14兲

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