ENERGIES OF THE K-LL AUGER LINES

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ENERGIES OF THE K-LL AUGER LINES

Wadie Asaad

To cite this version:

Wadie Asaad. ENERGIES OF THE K-LL AUGER LINES. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-132-C4-138. �10.1051/jphyscol:1971424�. �jpa-00214625�

ENERGIES OF THE K-LL AUGER LINES

WADIE N. ASAAD (*)

Faculty of Engineering, Cairo University, Egypt ;

Institute of Nuclear Physics, University of Miinster, Western Germany ; and Solid State and Materials Research Center, The American University in Cairo

Rksumk. - Nous avons calcule les energies des raies Auger K-LL en utilisant, pour l'integrale de Slater, la forme A(Z - Z s ) (1

+

La constante a dans le facteur relativiste est la moyenne ponder& des valeurs de a calculees par Asaad pour les integrales de Slater correspondantes. Nous avons ajustk le paramktre A de manikre a obtenir les valeurs experimentales de l'energie des raies Auger K-LL des 6lements 16gers Z = 11 et 12, en utilisant le couplage intermediaire ainsi que l'interaction de configuration. Nous parve- nons a un bon accord avec les energies mesurees des raies Auger d'un certain nombre d'elements mais, pour d'autres elements, l'accord porte seulement sur l'intervalle entre les raies.

Abstract. - The energies of the K-LL Auger lines have been calculated with use of the form

A(Z - Z,) (1

+

The constant a in the relativistic factor was taken as the weighted average of the values of a for the relevant Slater's integrals as calculated by Asaad. The parameter A was adjusted to fit the experimental energy values of the K-LL Auger lines of the light elements Z = 11 & Z = 12,

intermediate coupling as well as configuration interaction being used. Good agreement with measured values for the Auger line energies for a variety of elements has been achieved, but the agreement for other elements is only in the separations between lines.

1. Introduction. - Knowledge of the energies of the different lines in a n Auger spectrum is essential for the identification and interpretation of the different lines in the spectrum. In studying the L spectrum, for example, different workers interpreted the lines differently [l]. Before trying to study such complex spectra, it is felt that the study of the simplest spectrum, the K-LL, has not yet ended with a theoretical or even semi-empirical formula for the accurate calculation of the energies of the different lines. Asaad and Bur- hop [2] studied the K-LL Auger spectrum, applying intermediate coupling theory, and were able to calculate the energies using known values for the electron binding energies together with the Slater's integrals P and G that expressed the electrostatic interaction between pairs of electrons. The form they took for the variation of Slater's integrals with the atomic number Z was :

where Z , was a screening constant and the factor 1 - aZ2 was to take account of the variation with Z of the relativistic effects. The values of ^a! used were all positive. The values of the constants Zs and a were adjusted to yield agreement with the experimental

(*) Present address : Department of Mathematics and Physics, Faculty of Engineering, Cairo University.

results of Mladjenovic and Slatis [3] for Z = 83.

For other elements the values obtained differed from the experimental results by some tens of electron volts.

To get closer agreement with experiments done for elements in the intermediate coupling region, Horn- feldt, Fahlman and Nordling [4] modified only the values of A. The new constants failed, however, to give satisfactory results for all 2.

In another attempt, Hornfeldt [5] expressed the Slater's integrals in the form

taking the same Zs as originally introduced by Asaad and Burhop, and adjusting the remaining constants so as to get excellent agreement with the experimental values of the energy of the strongest line, the 'D, line, over the wide range of Z from 20 to 100. While this attempt gives by far the best agreement with experimental results, the factor 1

+

In a theoretical investigation of the correct form of the factor that takes account of the relativistic effects, Asaad [6] found that this form should be 1

+

for all the matrix elements of electrostatic interaction for the K and L electrons, with the exception of G1(l S, 2 p) and G2(2 P, 2 p) for which a was found to be negative.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971424

ENERGIES OF THE K-LL AUGER LINES C4-133 In the present paper we give the results obtained (hereafter denoted by configurations I, II and III,

for the energies of the K-LL Auger lines, calculated respectively). For configuration I, the total angular on the basis of intermediate coupling theory together momentum quantum number / is equal to zero ; with configuration interaction (see Asaad [7]), with for configurations II and III, J may have the values the form 0,1 and 2. Since both / and the parity p are conserved,

A(Z — Z^s) (1 + aZ²) the matrix of the Hamiltonian will reduce to a set of for the involved Slater's integrals. While good agree- independent submatrices, each for a definite pair of ment with measured values for the Auger line ener- quantum numbers J, p. If we limit our consideration gies of some heavy elements has been achieved, the t o t h e a t o m d o u b iy 1 0 n l z e d m t h e L shell> ^{t h}f^{e W l U} agreement is still not as good for other elements, b e n o configuration interaction except between although there is still good agreement as regards the configurations I and III which are of the same parity, separations between lines. Suggestions for future a n d o n ly f o r t h e J ~ ° s t a t e-

refinement are discussed. If the rows and columns of this submatrix are so ordered that they correspond successively to the terms 2. Theory. — For the K-LL Auger spectrum, the 3po; IS Q (b o t h for configuration III) and % (of confi- atom in the final state may have one of the following g u r at i o n I ; from now on this term will be denoted three configurations : b y l g ^ t h e n t h i s s ubmatrix of the Hamiltonian is

(2 s)° (2 p)6 , (2 s) (2 p)5 , (2 s)2 (2 p)4 , (see Asaad — 1965 — [7]) :

£ a v - ^ i^{7 2}( 2 p , 2 p ) + C^2p V2C^2p 0

H= V2C^2P £^av + g F²( 2 p , 2 p ) - - ^ G¹( 2 s . 2 p ) 0 - 4= Gl(2 s, 2 p) £a'v

V³ J

Here £^{a v} and E^ are the average energies of configu- and the brackets < > indicate an integration over rations III and I, respectively : rx and r2 ;

2 ² , £^2p = i\.E(L²) - E(L³)1 .

£av = 2 E(L2) + F°(2 p, 2 p) - — F\l p, 2 p) - 2 £2p

The eigenvalues of the matrix H above, when orde- E*v = 2 E{L^X)+F (2 s, 2 s) , ^{r e (}j ^{a c c 0}r d i n g to increasing values, correspond to the where E(Lj) is the energy required to remove an terms :

Lj ( j = 1, 2, 3) electron from the L shell of the atom. ^ £3(3P0) , L2 Z,2CS0) , Lt LifSo) . The quantities F, G and C are the matrix elements of

the electrostatic and spin-orbit interactions : The energies of the corresponding lines

F\nl, n' V) = < Rnl(ri) Rnr(r2) yv(r1; r2) x K - L3 L3(3P0) , K - L2 L2CS0) ,[K - Lx L^So) x R (v ^ R <(Y ) ~>

can then be readily computed by subtracting these G\nl, n' I') = < Rmirj) K„T(r2) x RnT(ri) Rm^2) > , eigenvalues from E{K), where E{K) is the ionization

w h e r e energy for the K shell.

/ v, v+i < The energies of the remaining six lines of the K 7v(ri> ri) — j ' * 2 Auger spectrum are as given on intermediate coupling

I rl/r\⁺¹, r² <r^± basis by Asaad and Burhop (1958) [2] :

3 ( / l 1 \2 1 11/2

K-L^x L ^ P O : E{K) - £(L^X) - E(L²) - F°(2 p, 2 s) + ^ C^2p - ( ( j G\2 p, 2 s) - ^ £^2pJ + 5 & j K-L^t L³CPi):E(K) - E(L^t) - E(L²) - F°(2p, 2 s) + | C^{2 p} + { (5 G\2p, 2 s) - \Cz^P) + \z\^p J * K- L^t L²(³P⁰) : E(K) - £(Lj) - E(L²) - F°(2 p, 2 s) + ^ G\2 p, 2 s)

K-Lt L3(3P2): E{K) - E(Lt) - E(L2) - F°(2 p, 2 s) + i G1(2 p, 2 s) + | C2p

K - L2 LsC'Da) : £(K) - 2 £(L2) - f ° (2 p, 2 p) + J r f 2(2 p, 2 p) +

+

i ^ - {(i

(

P'

p)

i^p)

i^p)

+ |c

+ {(|f

(2p,2p)

ic

)

+^a}

3. Mathematical Details. — To be able to use the In table 1, we have displayed the values of A (in results obtained by Asaad [6] for the relativistic electron volts) obtained theoretically by Asaad [6]

Slater's integrals 5s" and 8 we took weighing factors using hydrogenic wave functions. Because the posi-

as follows : tion of the Auger lines is very insensitive to G^l{2 s, 2 p)

j 2 a n^ t o F2Q P» 2 p), we took our trial values At for A F°(2 s, 2 p) = - 3r°(2 s, 2 p) + - 5r°(2 s, 2 p) equal to these theoretical values for these two e. s.

matrix elements. The values of At for the remaining

1 1 t - 2 x three matrix elements were adjusted to give good

G (2 s, 2 p) = - S (2 s, 2 p) + - S (2 s, 2 p) agreement with the measured values of the energies of the K-LL Auger lines in the spectrum of magnesium, F°(2 p, 2 p) = - F°(2 p, 2 p) + £ 5^°(2 p, 2 p) + Z = 12- T h e measured values for Z = 11 and Z = 12 15 15 were given by Fahlman, Nordberg, Nordling and

6 Siegbahn (1966) [8]. For these elements with such low

+ T55 r ( 2 p'2 p) -

atomic numbers, relativistic effects can be neglected, the factor 1 + a Z² being very nearly equal to one.

Now 3^r2(2 p, 2 p) = S²(2 p, 2 p) but is not equal The trial values A^t obtained by such an adjustment to S2(2 p, 2 p), whereas F2(2 p, 2 p) = G2(2 p, 2 p). are given also in Table I.

As we could not trace back the origin of F2(2 p, 2 p) As for the binding energies E(K), E(Lj) (j = 1,2,3), to see if it was an fr2 or one of the S2's, we decided the values used for Z ^ 30 were taken from to take « Alpha-Beta-and-Gamma-Ray Spectroscopy » [9]. The

F2(2 p, 2 p) = 3r2(2 p, 2 p ) . same applies to the binding energies for Z between 25 and 29 inclusive except for EiLj) which was taken This is further justified because the position of the f r o m R e f [ 1 Q ] T h e e l e c t ro n binding energies for Z Auger hues is very insensitive to this F [2]. [The b e t w e e n 1 0 an d 24 inclusive were taken as in Table II coefficient a of Z2 m these matrix elements was less w h e r e t h e r e f e r e n c e s a r e indicated.

than 0.4 of the corresponding coefficient in other

matrix elements and F2(2 p, 2 p) was to be divided TABLE II

b y 2 5 i n all t h e f o r m u l a e i n w h i c h i t a p p e a r e d . ] T h u s Electron Binding Energies in eV for 10 < Z < 24

the form taken for the electrostatic matrix elements _ „.„, _.r , _,r , _/ r .

„ , ^ . Z E(K) E(L{) E(L²) E{Li)

F and G is

AC7 7 ^ / , x - 7 ^ ^{1 0} 870.1(11) 48.48(12) 21.6(12) 21.6(12)

A\A — ^^s) (i- + a& ) 1 1 1 072.1 (13) 63.3 (10) 30.58 (14) 30.58 (14)

„ . . , . , . 12 1 305.0 (13) 89.4 (10) 49.50 (14) 49.50 (14) where Zs is a screening constant which is taken as j3 1559.6(13) 117.7 (10) 73.1 (13) 72.9 (13) in Asaad and Burhop's paper [2], and a is the weigh- 14 1 838.9 (13) 148.7 (10) 99.6 (13) 99.0 (13) ted average of a computed as above from Asaad's 15 2145.5 (10) 189.3 (10) 135.4 (13) 134.5 (13) relativistic calculations [6]. The values of Z^s and of J« l^Al\l^{B, i P ^ S S \⁶JA ?,ll l^A ?³⁾,

. ^ir. , ^x }• ^J , _ _ , , ^{S T} 17 2 822.4(13) 270.2 (10) 201.6 (13) 200.0 (13) a are given in the last two columns of Table I. ^{l g 320}2.o(i3) 326.5(15) 250.5(15) 248.5(15)

19 3 607.3 (13) 377.1 (10) 296.5 (13) 293.5 (13) TABLE I 20 4038.0(13) 437.8 (10) 350.0 (13) 346.3 (13) A A Z a 2 1 4 492.7(13) 500.4 (10) 407.2 (13) 402.6 (13)

matrix'element eV eV ' 22 4 966.4(10) 563.7 (10) 460.4 (13) 454.4 (13) matrix ^ l e n i e n t eV eV ^ ^ 2 3 5 4 6 5 0 ( 1 3 ) m 2 ( 1 0 ) 5 2 0 4 ( 1 3 ) 5 n 9 ( ] 3 )

F 0 ( 2 s , 2 s ) 4.092 2.75 3.8 1.983 x 10-5 24 5 989.1(13) 6 9 4 . 6 ( 1 0 ) 5 8 3 . 6 ( 1 3 ) 5 7 4 . 4 ( 1 3 ) F ° ( 2 s , 2 p ) 4.411 3.03 4.0 1.680 x 10"= . _ , . , _,. . „ . .i U t, . ,

GH2 s 2 D) 2 392 2 39 2 6 1566 x 10"5 Results and Discussion. — With the electron F<>(2p, 2p) 4.942 3.47 4.5 1.158 x 10-s binding energies and the e. s. matrix elements taken F2(2p, 2p) 2.392 2.39 5.1 0.403 6 x 10-s as mentioned in the previous section, the energies of

ENERGIES OF THE K-LL AUGER LINES C4-135 the K-LL nine lines were calculated using the formu-

lae given at the end of § 3. A program written in Algol incorporating a subroutine for obtaining the eigen- values of the symmetrical matrix H was run on ZUSE

Z 2 3 at the Institute of Applied Physics, University of Minister, Western Germany. The line energies obtained for Z from 10 to 100 with the trial values At

as in Table 1, are given in Table III.

TABLE III

Calculated Energies (in eV) of the K-LL Auger Lines

z

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

"-'X J-11 ^ 0

753.9 923.4 U01.2 1 296.2 1 510.5 1 732.9 1 976.8 2 242.3 2 506.4 2 807.5 3 113.9 3 440.4 3 784.7 4 151.2 4 539.5 4 938.6 5 353.4 5 788.5 6 244.4 6 711.7 7 188.7 7 681.8 8 191.7 8 720.7 9 261.7 9 816.7 10 386 10 971 11571 12 188 12 826 13 479 14 153 14 842 15 548 16 272 17013 17 772 18 542 19 328 20 131 20 953 21790 22 644 23 526 24 404 25 309 26 229 27 181

Li L2 Pi 775.9 950.3 1 134.3 1 333.3 1 551.5 1 778.0 2 031.0 2 300.5 2 571.3 2 876.8 3 189.8 3 521.3 3 875.5 4 246.5 4 638.1 5 043.2 5 465.7 5 907.8 6 368.3 6 844.4 7 329.3 7 830.9 8 346.5 8 881.0 9 429.0 9 994.5 10 572 11 166 11774 12 400 13 046 13 708 14 390 15 089 15 803 16 537 17 287 18 053 18 833 19 628 20440 21270 22118 22 982 23 880 24 760 25 674 26 608 27 568

L j L2 "o 787.7 963.7 1 149.3 1 349.8 1 569.3 1 797.3 2 051.6 2 322.5 2 594.7 2 901.1 3 215.3 3 548.0 3 902.9 4 274.7 4 666.9 5 072.7 5 496.3 5 938.5 6 399.7 6 876.5 7 361.2 7 862.8 8 378.5 8 913.2 9 460.8 10 026 10 604 11 198 11 805 12 431 13 078 13 739 14 422 15 120 15 835 16 568 17 319 18 085 18 865 19 661 20 473 21303 22 151 23 015 23 914 24 794 25 709 26 643 27 604

L2 Li o⁰ 805.2 985.0 1 175.7 1 379.1 1 601.7 1 832.9 2 095.3 2 369.5 2 647.4 2 957.5 3 277.5 3 614.4 3 978.4 4 353.9 4 748.6 5 159.5 5 589.8 6 037.9 6 502.6 6 987.2 7 478.2 7 987.0 8 506.8 9 045.5 9 598.4 10 173 10 758 11358 11972 12 604 13 258 13 927 14 616 15 323 16 043 16 784 17 543 18 315 19 103 19 906 20 726 21564 22 420 23 293 24 206 25 087 26 009 26 956 27 923

L'l L3 Pt

787.7 963.7 1 149.3 1 349.8 1 569.5 1 797.6 2 052.0 2 323.1 2 595.4 2 902.2 3 216.7 3 549.7 3 905.2 4 277.6 4 670.6 5 077.2 5 501,2 5 944.9 6 407.1 6 884.9 7 371.8 7 875.8 8 393.9 8 931.0 9 482.7 10 052 10 633 11232 11 846 12 479 13 132 13 802 14 494 15 202 15 927 16 673 17 436 18 217 19 012 19 824 20 654 21 505 22 373 23 260 24 181 25 088 26 031 26 995 27 987

-L-1 ^3 ?2 787.7 963.7 1 149.3 1 350.0 1 569.9 1 798.2 2 052.8 2 324.1 2 596.7 2 904.1 3 219.0 3 552.6 3 908.9 4 282.2 4 676.1 5 083.7 5 508.3 5 953.5 6 416.7 6 895.5 7 384.2 7 889.8 8 409.5 8 948.2 9 501.8 10 072 10 655 11 256 11 872 12 507 13 162 13 833 14 527 15 236 15 964 16 711 17 476 18 258 19 055 19 869 20 700 21 552 22 422 23 310 24 233 25 141

26 086 27 051 28 045

L2 L3 D2

807.3 987.8 1 179.3 1 383.4 1 606.6 1 838.4 2 101.8 2 376.6 2 655.3 2 966.2 3 287.2 3 624.9 3 990.3 4 367.0 4 763.0 5 175.5 5 607.0 6 057.7 6 524.2 7 010.8 7 505.4 8 018.0 8 541.6 9 084.2 9 642.8 10 222 10 812 11419 12 042 12 683 13 345 14 023 14 724 15 441 16 175 16 930 17 703 18 491 19 295 20 117 20 956 21 816 22 694 23 590 24 528 25 437 26 389 27 367 28 367

•^3 -^3 "0

810.1 991.2 1 183.2 1 387.8 1611.4 1 843.6 2 107.4 2 382.6 2 661.7 2 973.0 3 294.3 3 632.5 3 998.4 4 375.7 4 772.5 5 186.1 5 618.3 6 070.7 6 538.6 7 026.5 7 524.0 8 039.6 8 566.3 9 112.1 9 675.7 10 259 10 853 11467 12 097 12 747 13 416 14 104 14 814 15 542 16 288 17 056 17 842 18 646 19 466 20 305 21 163 22 043 22 943 23 863 24 823 25 760 26 741 27 749 28 782

L3 L3 P² 810.1 991.2 1 183.2 1 388.0 1611.9 1 844.4 2 108.5 2 384.1 2 663.6 2 975.6 3 297.6 3 636.5 4 003.3 4 381.6 4 779.4 5 193.8 5 626.6 6 080.3 6 549.0 7 037.7 7 536.3 8 053.0 8 580.6 9 127.3 9 691.9 10 277 10 871 11486 12 117 12 768 13 438 14 126 14 838 15 566 16 313

17 082 17 869 18 674 19 495 20 335 21 193 22 075 22 975 23 896 24 857 25 795 26 777

27 786 28 819

TABLE III (Cont'd)

Calculated Energies (in eV) of the K-LL Auger Lines

Z Ly L^x S⁰ L± L² Pi L¹L² PQ L² L² S⁰ L¹L³ P J Lⁱ L³ P² L² L³ D² L³ L³ P⁰ L³ L³ r² 59

60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

28 153 29 146 30 153 31 183 32 235 33 303 34 392 35 503 36 633 37 784 38 956 40 151 41 365 42 594 43 838 45 108 46 403 47 717 49 034 50 377 51778 53 169 54 593 56 033 57 504 58 992 60 506 62 042 63 601 65 184 66 819 68 428 70 103 71 802 73 539 75 273 77 045 78 844 80 670 82 516 84 402 86 317

28 550 29 553 30 572 31 612 32 673 33 752 34 852 35 974 37 114 38 275 39 459 40 666 41892 43 133 44 388 45 670 46 977 48 303 49 641 51002 52 405 53 813 55 247 56 702 58 189 59 691 61220 62 772 64 347 65 945 67 596 69 215 70 904 72 621 74 367 76 115 77 904 79 715 81561 83 417 85 323 87 249

28 586 29 589 30 609 31 649 32 710 33 791 34 891 36 013 37 154 38 316 39 500 40 707 41934 43 176 44 431 45 714 47 021 48 348 49 687 51049 52 452 53 861 55 295 56 751 58 238 59 741 61271 62 823 64 399 65 998 67 650 69 269 70 958 72 676 74 423 76 172 77 961 79 773 81620 83 477 85 383 87 310

28 914 29 926 30 955 32 005 33 074 34164 35 274 36 405 37 554 38 726 39 920 41 138 42 374 43 627 44 892 46 186 47 504 48 842 50 199 51 579 52 982 54 407 55 849 57 319 58 820 60 336 61 880 63 445 65 036 66 649 68 315 69 944 71645 73 379 75 134 76 896 78 701 80 523 82 388 84 254 86 179 88 114

29 003 30043 31 100 32 181 33 287 34 413 35 561 36 736 37 932 39 152 40 397 41668 42 963 44 277 45 608 46 972 48 363 49 779 51212 52 672 54180 55 698 57 246 58 823 60 435 62 076 63 747 65 448 67 178 68 938 70 746 72 558 74 434 76 350 78 305 80 273 82 291 84 341 86 416 88 531 90 687 92 882

29 062 30 103 31 162 32 244 33 351 34 479 35 628 36 804 38 002 39 223 40 470 41742 43 039 44 354 45 686 47 052 48 444 49 861 51296 52 758 54 267 55 786 57 336 58 914 60 528 62 170 63 843 65 545 67 277 69 038 70 848 72 661 74 538 76 456 78 413 80 382 82 401 84 453 86 530 88 647 90 803 93 000

29 393 30 443 31512 32 603 33 718 34 855 36 014 37 199 38 406 39 637 40 894 42 177 43 483 44 809 46 151 47 528 48 931 50 359 51 812 53 292 54 801 56 336 57 894 59 486 61 114 62 769 64 456 66 172 67 919 69 693 71518 73 341 75 229 77 164 79 129 81 110 83 146 85 207 87 303 89 429 91 604 93 810

29 842 30 930 32 036 33 169 34 329 35 513 36 720 37 959 39 221 40 510 41830 43 177 44 553 45 951 47 369 48 829 50 316 51 833 53 382 54 961 56 575 58 219 59 893 61607 63 361 65 154 66 983 68 848 70 750 72 686 74 669 76 685 78 761 80 895 83 069 85 269 87 534 89 835 92 160 94 545 96 970 99 445

29 880 30 969 32 076 33 210 34 371 35 555 36 764 38 003 39 266 40 557 41877 43 225 44 601 46 001 47 420 48 880 50 368 51 886 53 436 55 016 56 631 58 276 59 950 61 665 63 420 65 214 67 044 68 910 70 813 72 750 74 733 76 750 78 827 80 962 83 136 85 338 87 604 89 906 92 232 94 617 97 043 99 519 To compare our results with experimental values,

we give in Table IV a list of the calculated values (as given in Table III) together with the corresponding measured energies for the K-LL Auger lines for some typical Z.

We stated before that the trial values A ^t for A in the electrostatic matrix elements F°(2 s, 2 s), F°(2 s, 2 p) and F°(2 p, 2 p) were obtained by adjusting the out- come of theoretical calculations to fit the experi- mental values for magnesium, Z = 12 [8]. Therefore,

the very good agreement between theory and experi- ment for Z = 12 is not surprising. But the agreement is also very good for the neighbouring element Z = 11 and for the elements Z = 52, Z = 55, Z = 66 and Z = 79 which are of intermediate and heavy atomic numbers. For these latter elements, relativistic effects cannot be neglected. The factor (1 + aZ2) with the weighted averaged values a for a as taken in table 1 according to the relativistic calculations by Asaad [6]

seems to be justified.

TABLE IV Comparison of Calculated K-LL Auger Line Energies with Experimental Results {For any Z, the first row gives the calculated values, the 2nd row gives the experimental results ; energies are in eV for Z < 50 ; in ktVfor Z > 50) 94

LtL, % ( 753.9 [ 748.0 ( 923.4 [ 922.8 + .4 ( 1 101.2 [ 1 101.3 + .4 | 4 151.2 [ 4 159 ± 6 | 5 353.4 ( 5 365 + 7 f 6 711.7 ( 6 739 + 6 J 8 191.7 [ 8 212 + 6 ( 11 571 i 11 584.4 + 1.6 | 21.790 I 21.787 i 22.644 i 22.652 ( 24.404 i 24.39 ± .02 ( 35.503 ( 35.492 ± .006 { 51.778 { 51.78 + .02 f 75.273 1 75.18 ± .015 Lj L2 1 Pi 775.9 771.5 950.3 950.8 + .4 1 134.3 1 134.7 + .4 4 246.5 4 254 + 4 5 465.7 5 475 + 5 6 844.4 6 867 ± 4 8 346.5 8 367 ± 4 11774 11 789.1 ± 1.5 22.118 22.116 22.982 22.990 24.760 24.75 ± .02 35.974 35.963 +.007 52.405 52.42 ± .02 76.115 76.05 ± .015 Lj L2 3p 787.7 963.7 1 149.3 4 274.7 5 496.3 6 876.5 8 378.5 11805 11 823 ± 4 22.151 22.168 23.015 23.019 24.794 36.013 52.452 76.172 — Lx L3 3 P, 787.7 782.0 963.7 963.4 ± .4 1 149.3 1 149.6 ± .4 4 277.6 4 284+1 5 501.2 5 508 + 7 6 884.9 6 909 + 6 8 393.9 8 41ff+6 11846 11862.8 ± 1.8 22.373 22.380 23.260 23.272 25.088 25.08 + .02 36.736 36.732 + .007 54.180 54.20 + .02 54.172 80.273 80.24 ± .015 L1 L3 3 P2 787.7 963.7 1 149.3 4 282.2 5 508.3 6 895.5 8 409.5 11872 11885 + 4 22.422 22.423 23.310 23.317 25.141 25.14 + .03 36.804 36.806 + .010 54.267 54.253 80.382 80,40 + .06 L2L2 805.2 800.5 985.0 985.6 + .4 1 175.7 1174.8 + .4 4 353.9 4 357 + 6 5 589.8 5 595 + 7 6 987.2 7 006 + 2.5 8 506.8 8 524 + 4 11 972 11 989 + 4 22.420 — 23.293 — 25.087 25.08 + .02 36.405 36.369 52.982 52.95 + .03 76.896 76.78 + .04 L2 L3 X D2 807.3 804.2 987.8 989.8 + .4 1 179.3 1 179.7 + .4 4 367.0 4 374 + 4 5 607.0 5 618 + 5 7 010.8 7 034.5 + 1.0 8 541.6 8 561 + 2.5 12 042 12 059.9 + 1.1 22.694 22.699 23.590 23.602 25.437 25.43 ± .02 37.199 37.195 + .006 54.801 54.81 + .02 81.110 81.06 ± .015 L3 L3 3p 810.1 991.2 — 1 183.2 4 375.7 5 618.3 7 026.5 8 566.3 12 097 12 109 + 4 22.943 22.945 23.863 23.884 25.760 37.959 56.575 85.269 — L3l3 Ref. forExpt. 3 P2 810.1 991.2 — 1 183.2 4 381.6 5 626.6 5 639 + 7 7 037.7 7 063 ± 2.5 8 580.6 8 601 + 2.5 12 117 12135.2+ 1.2 22.975 22.983 23.896 23.912 25.795 25.79 + .02 38.003 l8!o02T^009 56.631 56.63 + .02 85.338 85.30 + .015 Results [11] [8] [8] [16] [16] [17] [17] [4] [18] [18] [19] [20] [21] [22]

m Z en ?3 2 55 </3 o H r > C O ^{IS 70} r 2 i/J o -J