Precise description of the odd parity energy levels in the spectrum Ge I

Physica 141C (1986) 219-229 North-Holland, Amsterdam

PRECISE DESCRIPTION

OF THE ODD PARITY ENERGY LEVELS IN THE SPECTRUM

Ge I

J. DEMBCZYNSKI Politechnika

Poznariska,

Instytut Fizyki,

ul. Piotrowo 3, 60-965 Poznari, Poland

Received 18 July 1985 Manuscript received in final form 19 November

1985

A fine structure analysis for the system 4s24pn’s (n’ = 5 to 14) + 4s24pn”d (n = 4 to 14) + 4s4p3 is performed on the basis of available experimental data. The Slater integrals and spin-orbit parameters are determined. The configuration 4s4p3 is shown to influence strongly the odd level system of GeI. On the basis of the theoretical results precise spectroscopic assignments of 154 odd parity electronic energy levels are given. The quantum numbers n’ and I’ for excited electron states fail to be good quantum numbers in many cases.

1. Introduction The purpose of this work is the study of an electronic structure of the germanium atom and a precise description of the odd level system. In the case of the germanium atom we have a large body of experimental data which gives a possibility of accurate studies of interactions between electrons in an atom. Early investigations of Ge I have been summarized by Moore [l]. The spectrum of germanium was investigated by Andrew and Meissner [2], Kaufman and Andrew [3] and Humphreys and Andrew [4]. The Zeeman effect and configuration interaction have been studied by Andrew et al. [5]. In 1977 Brown et al. [6] studied the absoOrption spectrum of Ge I between 1500 and 1900 A and published a table of odd levels of Ge I. Considerations concerning coupling in two-electron spectra taking Ge I as an example have been discussed by Cowan and Andrew [7]. In an analysis performed for the spectrum Sn I [8] it has been shown that the quantum numbers n’ and 1’ for excited electron states fail to be good quantum numbers in many cases. It has been explained as an effect of strong interactions between configurations with the same parity. In the case of the spectrum Sn I quantum numbers n’ and 1’ are defected by very strong interactions between the configuration 5s5p3 and each configuration 5pn”d. The germanium atom has an electronic

structure similar to that of the tin atom. Therefore, strong perturbations of the odd level system are expected as an effect of interactions with the configuration 4s4p3 having an open inner 4s shell. Hence, n’ and 1’ are expected to fail to be good quantum numbers for electron states of the germanium atom.

2. Method The method has been described in detail in a previous paper [B]. I only briefly remind the reader that this method takes into account the electrostatic and spin-orbit interactions. Secondorder effects on the term structure are also included. One has to consider the interaction between the configurations ns’npn’s or n&rpn”d the interaction between the and nsnp3, configurations ns*npn’s and ns*npn”d, as well as the interaction between configurations of the type ns*npn’l’. If one would include completely all interactions mentioned above for a system consisting of 10 configurations of the type 4s24pn’s (n’= 5 to 14), 11 configurations of the type 4s24pn”d (n” = 4 to 14) and 1 configuration 4s4p3), the description would necessarily involve 574 electrostatic and spin-orbit radial integrals, which can be taken into account as free, dependent or fixed parameters. This is an intolerably large number as the system comprises not more

0378-4363 / 86 /$03.50 0 Elsevier Science Publishers B .V. (North-Holland Physics Publishing Division)

220

J. Dembczyhki

I The spectrum of neutral germanium, Ge I

than 182 electron levels. The number of free parameters has been reduced similarly as in previous work [8], by introducing the following relation between Slater integrals, differing only by the principal quantum numbers of the electrons:

Rk(a,b) = Rk@, 4

[n*(c)n*(d)/(n*(a)n*(b))]3R,

(1)

where a, b, c and d each stand for a two-electron configuration nln’l’, and n* is the effective quantum number. This is the effective quantum number of the configuration ns%Zn’l rather than that of the electronic level. By introducing relation (1) the number of free parameters can be reduced to 82. The above required quantum numbers n*(nln’Z’) are determined by the following relation [8]: n*(dn’l’)

=

R

E,(d) - E,(nln’l’)

1R

1’

(2)

where E,(nl) is the position of the centre of gravity of the two *L,+iR ionization limits, E,(nfn’l’) is the mean energy [8], to secondorder perturbation theory, of all the terms of the configuration ns’npn’l’. The value of E,(4p) can be calculated by using relation (2.2) from ref. 8, giving Em(4P) = =

[~ce(*p1,2)

+

2~%(%2)1/3

64891.48 cm-’ ,

(3)

where the values E,(*P,,J = 63713.24 cm-’ , Em(*P3J = 65480.60 cm-’ , R,,

=

109736.49 cm-’ ,

are taken according to ref. 6. 3. Calculation and results As in the analysis of the spectrum Sn I [8], taking into account only low configurations, the

acquisition of a reasonable description of the level spectrum proves to be rather difficult, but in particular the successive inclusion of higher configurations 4s24pn”d into the energy matrix systematically improves the agreement between the calculated and experimental level values. While assigning the experimental levels [6] to appropriate configurations, we corrected the effective quantum numbers 1z*(4pn’l’) [eq. (2)]; the results were subsequently used in relation (I). The available computer memory (5000 kB) did not allow to introduce all radial integrals which should be used for the system studied. Therefore the number of electrostatic and spin-orbit integrals must be reduced and not all interactions within the system could be taken into account. Table I shows which interactions were included. It is seen that interactions between distant configurations (e.g., 4p4d and 4plOd; 4p4d and 4~8s) and interactions between some configurations with high values of n’ and n” (e.g.: 4~10s and 4plOd; 4plOd and 4p14d) have been neglected. Finally, the energy matrix for the system studied 4s24pn’s (n’ = 5 to 14) + 4s24pn”d (n” = 4 to 14)+ 4s4p3, has been constructed with the limited number of 258 radial integrals. In computer calculations the radial integrals @, ,&,(4pn’l’), a(4pn”d) and P(4pn”d) have been treated as free parameters. The 10 radial integrals G1(4p, n”s) appearing in the configurations 4s24pn’s have been coupled by means of relation (1) so as to be represented by one adjustable parameter. Similar procedures have been applied for the radial integrals F2(4p, n”d), G’(4p, n”d), G3(4p, n”d), and f&4pn”d). Taking into account the interactions between all configurations in the system would require 451 radial integrals. However, only those integrals were included which could affect the fit significantly, namely: a) All integrals coupling the configuration 4s4p3 with other configurations, b) the integrals coupling intertwined configurations, c) the integrals coupling configurations in which states having identical main SL-components are not far apart. Under these conditions the number of off-

J. Dembczyhki

I 7he spechum

of neutral germanium,

221

Ge Z

Table I Scheme of the energy matrix used for the system 4s4p3 + 4s24pn’s (n’ = 5 to 14) + 4s24pn”d (n” = 4 to 14)

Config. 4s4p’ 4s24pSs 6s 7s 8s 9s 10s 11s 12s 13s 14s 4s24p4d 5d 6d 7d 8d 9d 1Od lld 12d 13d 14d

No. of config. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

x -configurations

1

2

3

xxxxxxxxxx x x x x x x x X x X x X x X

4

x x x x x

5

x x x x x

6

x x x x x

7

8

9

10

15

16

17

18

19

20

21

22

x

x

x

x

x

x

x

x

x

x

x

x

x x

x x x x

x x x x

x x x

x x x

x x

x x

x x

x

x

X X X

X

X

14

X

X

X

13

X

X

X

12

x x x x x

X

x x

11

x x

x x x

x x x x

x x x x

x x x

x x x x x x

x

X

x x x x x x

X X X

x x x x x x

x x x x x x x x x

x x x x x x x x x

X

X

X

X

between which interactions have

x x x x x x

X X X X X

been taken into account.

diagonal Slater integrals was reduced to 125. The integrals differing only in the principal quantum numbers of the electrons can be represented by one adjustable parameter by using relation (1). In this way, the essential contributions from the interactions between the configurations constituting the system studied have been taken into account by means of 8 adjustable parameters (see table IV). The radial integral 5,,(4s4p3) has been taken into account by a fixed parameter with a value 12OOcm-‘. A variation by 200 cm-’ had no significant influence on the quality of the fit and on the eigenvector compositions of the states. By means of the above-described procedure a very good fit has been achieved with a mean deviation of 16cm-‘. It may be remarked here that other authors [9] could not obtain a satisfactory fit without introducing U-dependent parameters. On the other hand, it should be realized that relation (1) is an approximation the validity range of which should perhaps be studied more cautiously.

The results are given in table II, where the first column gives the configurations as well as its percentage participation in the level, while the second column contains the assignment defining the state of the first component. For the explanation of the letters C and N in this column, see section 4. The experimental level values given in the fourth column were taken from ref. 6 except the one at 85046cm-‘, which originates from Wilson [lo]. Column 7 gives the percentage of the first component in the level. Column 8 gives the next component, originating from either the 4pn’s or the 4pn”d configuration. Admixtures from 4s4p3 larger than 0.1 percent are given in column 9. In several cases, the same state is present as the first component in two distinct energy levels, e.g. 6d 3D, is the first component of the level at 58551 cm-’ as well as that of the level at 61091 cm-‘. In these cases the letters ‘a’ or ‘b’ have been added to the assignment. If certain states occur twice as the first components, others are bound to fail in this role.

4s*4p5s 4~~4~5s 4~~4~5s 4s24pss 4s4p’ 4s*4p4d 4s24p4d 4s24p4d 4s24p4d &4p4d 424p4d 4s24p4d 4s*4p4d 4S4p4d 4s*4p4d 4s24p6s 4s*4p& 4s*4p4d 4s*4p4d 4s24p& 4s24p6s 4s24p5d 4s24p5d @4p5d 4&@5d 4s24p5d @4p5d 4s*4p7s 4s24p7s 4s24p5d 4s24p5d

4s24p5d 4s24p5d 4s24p5d 4s24p5d 4s24p6d 424p6d 4s24p6d

99.9 99.8 99.8 99.3 99.9 94.7 87.2 83.2 87.5 93.5 92.0 98.9 95.0 94.3 89.9 83.6 93.0 94.9 73.1 99.6 89.6 75.6 68.7 95.9 78.5 75.1 78.8 99.1 95.0 74.2 90.1

98.4 95.2 80.4 79.9 63.5 41.7 95.6

Configuration First component 5s ‘P 5s ‘P 5s 3P 5s ‘P 4p3 5s 4d’D 4d3D 4d’D 4d3D 4d’F 4d3F 4d3F 4d3P 4d’P 4d3P 6s ‘P 6s’P 4d ‘F 4d ‘P 6s3P 6s ‘P 5d 3D 5d 3D 5da’F 5d 3D Sd 3F 5db3F 7s 3P 7s 3P 5d ‘P 5d ‘P 5d ‘F 5d ‘P 5d ‘P 5d ‘F 6da’D 6da’D 6d3F C

C

C

C

Designation 37451.69 37702.31 39117.90 40020.56 41926.73 BM30.05 48882.26 48962.78 49144.40 50068.95 50323.46 50786.79 51437.80 51705.02 51978.15 52148.73 52170.51 52592.24 52847.21 53911.60 54174.90 55372.61 55474.66 55686.67 55718.56 56828.43 56921.35 57168.38 57180.21 57398.85 57430.94 57556.17 57828.78 58058.07 58093.37 58551.41 58741.04 58747.66

2 4 0 1 3 2 1 2

Observed

48940 49145 50046 50297 50818 51454 51713 51972 52149 52176 52594 52829 53883 54212 55394 55505 55646 55714 56831 56951 57163 57190 57389 57427 57549 57807 58061 58098 58566 58757 58736

41927 484%

37458 37704 39140

Calculated

Value in cm~’

0 1 2 1 2 2 2 1 3 2 3 4 2 1 0 1 0 3 1 2 1 2 1 2 3 3 2 0 1 1

.I

Table II Experimental and calculated odd-parity levels of Ge I

First 99.9 86.2 99.8 85.6 99.7 74.1 57.3 77.3 55.9 59.4 66.5 98.9 88.2 82.1 88.9 55.9 93.0 90.4 65.1 99.6 69.1 47.3 57.8 52.1 41.9 51.0 30.8 99.1 65.1 52.0 57.2 98.4 95.2 40.0 63.0 31.9 29.0 57.6

o-c -6 -2 -22 16 - 1 - 16 -6 23 -1 23 27 - 31 - 16 -8 7 0 -6 -2 18 28 -37 -21 -30 40 5 -3 -30 6 - 10 10 4 7 22 -3 -5 - 14 - 16 12 14.2 25.3 3.2 28.0 17.8 23.9 0.7 4.8 8.8 6.8 27.7 6.9 4.2 23.1 0.1 20.5 15.0 10.4 36.9 29.2 16.4 24.0 0.5 29.9 20.7 27.8 0.8 0.7 37.0 15.8 20.8 16.4 30.0

4d3F 4d3F 4d3P 4d3F 4d ‘D 4d3D 5d’F 4d3D 4d’P 6s3P 6s’P 4d3P 4d3F 6s3P 4d3P 6s3P 5d3P 4d3D 5d’D 5d3F 5d3D 5d’D 5d3P 7s’P 5d ‘P 5d ‘D 4d ‘F 7s3P 5d3P 5d’F 5d’D 5d’P 6d’D

13.7 5s3P

13.6 5s ‘P

Next

Leading component %

3P + 1.4 3D + 0.1 ‘D 3P + 1.4 3D ‘P ‘P + 0.1 3D + 0.1 ‘D

0.43P

3.9 3P 2.8 3D + 2.6 3P + 0.1 ‘P 1.1 ‘D 5.8 3D + 2.3 ‘P 3.5 3D + 0.5 3P + 0.1 ‘P

0.4 3D 0.7 ‘D + 0.3 ‘P + 0.2 ‘P 0.2 ‘P 0.3 3D + 0.1 ‘P 11.1 3D + 1.1 3P 13.0 ‘D + 0.5 3P 0.2 3P + 0.2 ‘D 9.5 3D 13.1 ‘D 10.3 3D + 0.1 ‘D 0.3 3P 0.5 3D + 0.1 3P 8.9 ‘D + 1.1 3P + 0.1 ‘P 1.5 3D + 1.5 3P + 0.3 ‘P

2.2 2.2 3.2 0.5

0.1 3P 0.1 ‘P 0.1 ‘P 0.1 ‘P 0.3 ‘P 1.1 ‘D+0.53D+ 0.1 ‘P 10.3 3D + 0.3 ‘P 13.8 3D + 0.2 3P 10.2 3D 3.9 3D + 0.3lD + 0.1 ‘P 6.1 3D

Admixture of the conf. 4s4p3

97.7 4s24p7s 65.3 &4p6d 78.3 4s24p7s 99.6 @4pfk 97.0 &4p8s 42.2 424p6d 44.5 424p6d 42.8 &4p6d 82.0 4s24p7d 53.6 4&p7d 71.0. &4p7d 65.5 4?4@d 57.7 &4p6d 98.5 4s?4p6d 91.0 4?4p6d 54.1 4G4p9s %.2 4s24p9s 45.3 4?4p9s 69.3 4!Ap6d 33.7 4sz4p6d 45.4 424p6d 92.0 4.?4pas 48.9 4?4* 92.1 4sJ4p8d 79.6 @4p8s 57.3 &4p8d 99.5 4s24plOs 58.4 4.G4p8d 77.5 4.?4plOs 47.1 &4p8d 94.9 4G4p9d 80.7 u4p9d 83.1 4s’4p9d 70.0 G4p9d 93.3 4s24plls %.7 4?4plls 86.3 4?4p7d 87.7 ti4p7d 98.4 4s=4p7d 71.1 4s24p7d 59.3 4s24plOd 62.8 &4plOd 96.6 4s24plOd 57.6 &4plOd 55.8 4s=4p7d

C

7s 3P 6da’F 7s ‘P 8s 3P 8s ‘P 6d b ‘F 6da’P 6d ‘P 7d a”F 7d b ‘F 7d 3F 6db’P 6da”P 6d’F 6d3P 9sa3P 9s’P 9sb’P 6d’F 6db3D 6db’D 8s 3P 6d’D 8dF 8s ‘P 8d ‘F 10s 3P 8d ‘P 10s 3P 8da3D 9da3F 9db3F 9da3F 9da3D 1ls’P 11s ‘P 7d ‘D 7d 3P 7d 3F 7d ‘P 10da3F 1Od’P 1Od3F 1Od3D 7d ‘F N N N N N

C N C

C C

C C

C

C

62232.87 62264.43 62355.15 62370.79

58931.49 58943.42 59114.72 59494.52 59524.27 5%58.38 59690.60 59727.51 60270.24 cQ403.38 60429.91 60516.30 60549.% 60552.37 606cn.25 60749.36 60769.25 60857.12 60886.20 61091.48 61152.37 61253.99 61268.40 61269.05 61343.17 61522.73 61539.12 61542.72 61546.23 61571.41 61849.22 61922.47 61930.04 61997.14 62041.45 62044.93 62054.73 62124.89 62125.25 62169.26 62217.75

62344 62380

62260

61079 61155 61255 61251 61286 61342 61502 61538 61543 61546 61581 61852 61938 61922 61984 62037 62048 62052 62134 62130 62175 62236

60739 60779 60844

60399 60411 60521 60561 60568

59103 59497 59524 59640 59681 59744

58939 7 11 -2 0 18 9 - 16 - 14 4 19 -5 - 11 - 15 1 10 - 10 13 - 14 12 -3 -1 17 - 17 1 21 1 0 0 - 10 -3 - 15 8 13 4 -4 3 - 10 -5 -6 - 19 -3 4 11 -9

-8

97.7 31.4 56.4 99.6 66.7 23.9 24.6 26.2 39.5 33.2 37.0 34.0 47.0 98.5 91.0 35.4 %.2 31.9 48.8 27.8 22.8 92.0 35.4 57.5 55.4 31.1 99.5 27.2 51.9 19.8 41.9 32.1 38.9 31.6 93.3 65.0 48.5 87.7 98.4 55.1 26.4 29.8 69.5 28.9 40.1

6d’D 6d’D 7s3P 5d3P 8s’P 5d’D 5d 3D 7d ‘D 7d’D

25.2 6d’D 21.6 7d’F 21.3 6d’D 16.1 7d’D 0.7 5d ‘F 3.6 9s3P 18.7 9s ‘P 3.8 6d’P 15.0 6d’P 20.4 6d’F 16.9 8d’D 22.5 6d’P 4.3 8d3F 13.4 6d’F 26.9 8d’D 24.2 8s’P 19.7 8d’F 0.2 6d’P 15.2 8d3D 25.6 1Os’P 17.5 8d’P 34.3 9d’D 26.0 9d 3D 28.1 9d’F 25.0 9d’P 5.8 7d’P 31.7 1ls’P 29.3 7d3P 6.6 lls3P 0.6 6d3F 10.0 7d’D 19.5 1Od ‘F 22.5 10d 3D 21.8 10d ‘D 25.2 7d’P 14.8 10d’F

0.6 25.1 21.9 0.1 30.3 20.0 13.4 16.3 30.9

Q r

0.2 ‘D + 0.1 ‘P 0.1 3D

0.2 ‘D 1.03P+0.4’D

2.5 ‘P + 0.5 ‘D

3.3 3P

0.5 3P O.l’P+O.l’D 1.23P+0.1’D+0.13D

.S 0.63D 2.0 3D + 0.8 ‘P + 0.1 ‘P

ii g. 0.13P+0.13D 0.9 ‘D + 0.3 ‘P

6.5 3D 1.1 ‘D 3.9 3D

% t? B B 2

3

P

1.43D+0.43P+0.1’P 0.6 ‘D 6.5’D+ 1.3’P 4.8 ‘D + 0.3 ‘P 0.2 ‘D + 0.1 ‘P 6.5 0.1 ‘D ‘P l.O’D 6.2 ‘D 0.1 ‘P

!i

P

5

4.4 ‘P 0.9 ‘D + 0.7 3P + 0.1 ‘P

2.9 ‘D 0.8 ‘D 0.1 3P 0.3 3D + 0.1 3P 18.6 ‘D 16.7 ‘D + 0.1 ‘P 15.3 ‘D 0.1 ‘D 0.3’D+O.l ‘D 0.4 ‘D 2.8 3P + 0.5 ‘D + 0.1 ‘D 3.0 ‘P + 0.7 ‘D

4s24p12s 4s24p12s 4?4p7d 4s24p7d 4t?4p7d 4?4p9s 4&plld 4s24p9s 4s24plld &4plld 4s24plld 4s24p13s 4s24p13s 4s24p12d &4p12d 4s24pl2d 424plZd 4s24p14s 4s24p14s 4s24p13d

87.0 92.9 78.3 78.7 93.6 44.1 85.5 88.8 94.3 98.6 52.1 81.6 61.3 60.7 71.8 97.1 87.6 %.l

4&&d 4!+4p13d 4s24pl3d 4&$&l 4s24p8d G4p8d 4s24pMd 4s24p14d &4p14d &4p8d 4?4p8d M4p8d 4?4p8d 424p8d 4s24p8d 4s24plOs 4?4plOs 4s24p9d 90.2 424p9d

99.3 98.9 25.7 41.6 53.4 95.7 97.0 89.1 70.4 63.5 65.3 99.7 98.4 98.6 89.1 80.1 76.8 99.5 99.3 93.1

Configuration First component

C C C

Table II (continued)

12s3P 12s3P 7d3D 7d ‘P 7d3D 9s 3P lld3F 9s ‘P 1lda’F lld3P 1ld’D 13s3P 13s’P 12d3F 12da3F 12da3D 12d3D 14s3P 14s3P 13daF 13db3F 13daF 13d3D 8d’D 8d3P 8da’P 14d3P 14d3F 14d3F 8d”F 8db3P 8d’ 8d3D 8db3D 8d’D 1Os’P 1Os’P 9d ‘D 9d3P

Designation

N

N N N N N N N N N N N N N N N N N N N N F N C N N N

C C

N

N N C C C

0 1 2 1 3 2 2 1 3 2 1 0 1 2 3 2 1 0 1 2 2 3 1 2 0 1 2 3 2 4 1 3 2 1 3 2 1 2 0

J

63625.69

63089.10 63168.53 63244.22 63251.20 63271.31 63305.19 63330.45

62390.37 62398.94 62454.86 62467.79 62522.98 62531.56 62545.56 62576.74 62629.23 62635.22 62639.17 62639.15 62647.61 62751.67 62791.97 62793.56 62814.88 62823.67 62826.79 62906.37 62926.05 62930.26 62948.76 62995.59 63032.91 63033.47 63033.89 63037.26 63046.08

Observed

Value in cm-’

63034 63101 63170 63252 63258 63277 63305 63329 63585 63614

63034 63033 63042 63041

62392 62397 62443 62466 62497 62531 62557 62579 62631 62634 62646 62638 62641 62754 62796 62790 62813 62824 62827 62906 62927 62930 62952 62982

Calculated

11

- 12 -2 -9 -6 -6 0 1

2 12 2 26 0 -11 -3 -2 1 -7 1 -6 -2 -4 4 2 0 0 0 -1 0 -3 14 5 -1 1 -5 5

-2

o-c

59.0 97.1 59.5 58.7 90.2

98.6 31.2 53.5 42.8 30.5

99.3 66.3 19.0 21.4 41.8 95.7 58.2 61.0 33.5 25.3 30.5 99.7 65.9 52.0 41.3 28.5 37.0 99.5 66.4 38.0 37.2 42.4 38.1 44.3 93.6 35.5 39.2 39.8 68.6

First

7d3P 14d3D 14d’D 14d’F 14d3D 0.6 7d’F 20.7 8d’P 27.9 8d’F 7.8 8d3P 29.9 8d’P 7.1 8d’F 1.1 8d3D 28.1 10s3P 25.4 9d3P 2.8 10d3P

1.3 25.7 24.7 29.3 17.1

0.7 7d3P 32.6 12~ ‘P 12.8 lld3D 20.2 7d3D 10.1 7d’F 1.6 lld 3F 28.3 lid ‘D 28.1 9s3P 23.5 lid ‘F 22.0 lld3D 23.1 1ld’P 0.2 7d3P 32.5 13s ‘P 30.6 12d’D 28.9 12d’F 27.3 12d3P 26.0 12d’P 0.3 8d3P 32.9 14s ‘P 31.5 13d’D 29.3 13d3D 30.4 13d’F 26.4 13d ‘P 27.2 8d3P

Next

Leading component %

4.13D+0.13P 5.2 ‘D 0.1 ‘D 0.3 3D 0.4 3P 2.3 3P

0.3 3D 6.3 “D + 0.4 ‘P

1.2 ‘D + 0.7 3P + 0.1 ‘P

0.3 ‘D 0.1 ‘D 0.8 ‘D + 0.3 3P 0.9 ‘P + 0.1 3D + 0.1 ‘D 2.8 3P 1.33P 0.5 3P

0.6 ‘D 1.3 3D + 0.1 3P 1.5’D+0.13P

0.1 3D 2.3 3D 2.6 3D 2.4 3D

3.4 ‘D + 0.3 3P 3.0 3D + 0.1 3P 4.3 ‘D 0.1 3D

Admixture of the conf. 4s4p3

ti4p9d &4p9d 4?4p9d ti4p9d 4s24plls 4s24plls 4sT4plOd 4s24plOd 4s24plOd 4s24plOd 4s24plOd 4?4plOd 4s24plOd 4s24plOd 4s24p12s 4s24p12s &4plld 4?4plld 4s24plld

4s24plld 4?4plld 4s24plld 4?4plld 424plld 4?4p13s &4p13s 4s24p12d 4s24p12d 4s24pl2d 4s24pm 4s24pl2d 4s24p12d 4s24p12d 4s24p12d 4s24p14s 4s24pl4s 4s24p13d

424p13d 4s24p13d 4s24p13d 4?4p13d 4?4p13d 4s24p13d

97.6 85.9 83.6 80.9 %.5 99.1 %.5 99.8 91.1 92.7 90.0 98.9 89.7 81.2 97.3 99.2 %.8 92.2 93.4

99.9 92.0 97.8 91.5 81.1 97.7 99.3 %.8 94.2 99.9 93.7 93.8 94.5 92.7 82.3 98.3 99.4 97.6

95.2 95.2 loo 95.5 97.9 93.7

92.0 4?4p9d 99.4 4s=4p9d

9d 3P 9d ‘F 9db’F 9d ‘D 9db3D 9d ‘D lls3P 1ls’P 1Od ‘D 1Od3F 1Od3P 1Od3P 1Od‘D 10db3F 1Od ‘P 1Od‘D 12s 3P 12s ‘P lld ‘D lld3P lld3P lld3F lld3D lld b 3F Ild’P lld3D 13s 3P 13s ‘P 12d ‘D 12cl3P 12d 3F 12d 3P 12db’D 12db’F 12d ‘P 12d 3D 14s 3P 14s ‘P 13d ‘D 13d 3D 13d ‘P 13d ‘F 13d ‘P 13d b ‘F 13d ‘P N N N

N N

N N N

N

N

N N

N

N

N

N

N N

N

N N

N

N

N

N N

N

3 1

4

2 2 0

2 3 1 3 2 1 2 0 1 4 2 3 1 3 2 1 2 1 4 0 2 3 1 3 2

3 2 1 3 2 1 2 4 0

1 4

64680.00 64702.00 64717.90

64671.62

64556.00 64572.90 64581.60 64590.78 64597.3

64505.00

64357.00 64382.40 643%.00 64405.8 64415.0

64298.98 64320.00

64084.00 64127.00 64144.00 64156.72 64168.9

64040.00

63763.10 63790.00 63809.51 63827.3

63715.00

64675 64677 64701 64718

64597 64667 64697 64673

-2

-2

3 1 0

0 0

4 2

-4

1

1 0

7

1

1

5

64505 64509 64525 64504 64541 64552 64571

-1 -1

-8

-1

-2

-4

- 13 -6 -2 2

6

64414

64079 64129 64143 64158 64168 64295 643l-n 64313 64330 64353 64356 64382

63812 63825 64005 64050 64037

63709 63740 63777

63629 63683

9d ‘P 8d3F 9d’F 9d3P 9d ‘P 9d ‘F 9d3D 1ls’P 1Od’P 8d3F 9d3P 1Od ‘P 1Od3P 10d ‘F 10d3D 1Od ‘F 10d3D 12s3P lld3P 1Od3P 1ld’D 8d3F lld 3P lld ‘F lld 3D lld ‘F lld3D 13s3P 12dP 12d’D lld3P 12d3F 12d ‘F 12d3D 12d ‘F 12d3D 14s3P 13d 3P 13d’F 12d3P

14.0 0.4 42.4 17.4 41.0 19.6 1.6 32.5 27.7 0.2 4.8 10.7 17.7 45.1 40.4 19.8 1.1 32.7 31.4 3.2 8.4 0.1 14.7 38.9 38.8 26.3 0.9 32.8 37.7 11.2 3.0 16.3 28.4 35.9 37.0 0.6 32.9 33.7 14.3 2.1

10.7 13d3D 43.2 13d ‘F 36.8 13d3D

49.4 57.2 41.3 59.4 %.5 66.6 58.6 99.8 91.1 75.5 58.2 49.3 48.9 59.4 97.3 66.5 56.3 92.2 76.8 99.9 57.5 50.9 52.7 54.3 97.7 66.5 49.2 77.6 99.9 93.7 53.8 50.8 56.6 45.1 98.3 66.5 55.0 57.7 95.2 100 79.0 49.9 56.8

73.5 99.4 “D ‘D + 0.9 ‘P ‘D + 0.1 ‘P ‘D ‘D

0.4 3P 0.1 3D 0.6 ‘D

0.3 3P

0.13P 0.6 ‘D + 0.4 3P

0.5 3P 0.7 3D + 0.4 ‘P 0.4 ‘D 0.7 ‘D 0.9 3D

0.3 3P 0.53P+0.13D

0.9 ‘D+ 0.5 ‘P 0.2 ‘D 0.1 3D 1.2 3D

0.3 3P 0.7 3P 0.7 3P

0.9 3P 0.93P+0.13D 1.4 3D + 0.7 3P 0.1 ‘D 1.5’D+0.13P 1.73D

0.3 ‘P + 0.1 ‘D

0.1 2.2 2.6 2.2 0.1

2.1 3P

226

J. Dembczyriski / l7ae spectrum of neutral germanium, Ge I

For instance, the states 4s4p 33 D,2,3 do not occur as the first components in any of the electron levels. In addition table II shows that the quantum numbers n’ and 1’ for excited electron states fail to be good quantum numbers in many cases. For example, the level at 60857cm-’ contains only 45 percent of the configuration 4~9s. The missing 55 percent are distributed over other configurations, mainly 4pn”d. Extremely mixed is the state at 62455 cm-‘, denoted as 7d 3D2, which contains only 25.7 percent of the configuration 4p7d. Table III gives the values of the diagonal radial parameters for the configurations studied. The parameters, with their standard deviation given in parentheses, have been used as adjustable parameters in the fitting procedure. Table IV gives the values of those off-diagonal Slater integrals which have been used as free parameters. The values of the other off-diagonal Slater integrals, which have been used as dependent parameters, can be easily obtained by means of the relations (2.8-2.13) given in ref. 8, and table III of this work. The upper limits of the off-diagonal integrals, deduced by means of a criterion introduced by Racah for W-configurations in ref. 10, are also given in table IV. In table V calculated g-values are compared with experimental values available in the literature [5], demonstrating a good agreement.

4. Discussion In table II, column 2, levels with an assignment different from the one in earlier compilations [l-4] are marked with the letter ‘C’, while those given an n’l’ X-assignment for the first time are marked ‘N’. In the light of the calculations, the changes in the present classification of levels as proposed recently by Brown et al. [6] are not justified. Thus the level at 61091 cm-’ is primarily due to the configurations 4s24pn”d (see table II) and not to the configuration 4s4p3 which contributes only 7.8%. Similarly, the proposed assignment of the levels at 55475, 55687 and 55719cm-’ to the configuration 4s4p3 proved to be unjustified. These calculations clearly show that they belong to the

2.0554 3.093 4.110 5.114 6.119 7.119 8.124 9.125 10.125 11.126 2.8177 3.780 4.779 5.774 6.771 7.783 8.777 9.788 10.761 11.768 12.788

4p5s

f - fixed.

4s4ps

4plld 4p12d 4p13d 4p14d

4p8d 4P9d

4k-I 4p7d

z 4plls 4~12s 4p13s 4p14s 4P4d

4p8s

$z

n*(4pn’ll)

4pn’l

Conf.

640%(31) 64204(33) 29598(275)

65044.76

63446W) 63732(38) 63941(33)

64007(9) 51253(x) 57271(28) 60095(35) 60614(31) 62497(38) 62%9(43)

62734(g) 63233(g) 63577(g) 63823(g)

39216(10) 53508(10) 58433(10) 60715(10) 61973(10)

F”(4pn’l’)

38916.22 53420.63 58395.88 60695.88 61%1.35 62726.36 63228.62 63573.70 63821.00 64095.04 51070.18 57211.14 6OOS.30 61600.38 62497.63 63079.72 63466.84 63746.02 63943.83 64099.14 64220.40

&(4pn’l’)

G3(4pn’l’)

1681(109) 695 344 195 121 80 56 40 30 23 18

G’(4pn’I’) 1797(33) 527 224 116 68 43 29 21 15 11 3264(33) 1349 668 378 234 155 108 78 58 45 35

22450( 1525) 33333(90)

94 72 56

5261(82) 2175 1077 609 377 250 174 126

Fr(4p, n’l’)

Values of the parameters obtained from the fit in cm-’

Table III Effective quantum numbers and other parameters for the configurations of Ge I

11(5) 4.4 2.2 1.2 0.77 0.51 0.36 0.26 0.20 0.15 0.11

1123(13) 1150(13) 1179(12) 1171(12) 1172(13) 1177(12) 1178(11) 1177(11) 1179(11) 1178(11) 1081(27) 1205(12) 1192(11) 11%(13) 1151(12) 1188(10) 1184(12) 1174(9) 1176(g) 1177(9) 1177(10) 1200 f

&(4pn”d)

&,(4pn’l’)

470(86)

5(17)

5(20) - 5(18) - l(18)

54(17) 50(16) 32( 10) 56( 20) 56( 20) 16(20) ~ _

154(17) - 3(2) - 3(2) -3(2) -3(3) l(3) l(2) 2(2) 2(2) l(2) 2(2)

P(4pn’l’)

- 16(2)

a(4pn’l’)

228

J. Detnbczyhki

I The specmm

Table IV Experimental values for the off-diagonal Slater integrals of GeI and their theoretical limits deduced from the Racah criterion

w4s5s, 4P4P) R’Wd, 4~4~) R2(4p5s,4~4d) R’(4~5s 4d4p) R’(4~4d, 4~5d) R1(4p4d,5d4~) R3(4r-W 5d4p) R’(4pSs, 6~4~)

Experimental (cm-‘)

Limit (cm-‘)

-2@+wm

- 7739 10430

7485(57) - 1614(79) - 1137(63) 3184(190) 1859(92) ll(160) 2w=J)

- 2422 3383 2098 1081 973

Table V Experimental and calculated values of g-factors of Ge I levels Designation according to table II 4p5s 4p5s 4p4d 4p4d

‘PI ‘Pi 3DI 3R ‘PI ‘P*

‘PI 3D1 4;5d 4p5d 4p5s 4s4p3 4P4d 4P4d 4P4d 4P4d 4P4d 4P4d 4P4d 4P4d

‘PI ‘PI 3p2 3% 3D2 3D2 ‘F2 “p2 3D3 ‘F3 ‘S ‘F3

configuration

Exp.

cak.

Exp.-Calc.

1.435(l) 1.068(l) 0.556(4) 1.391(3) 1.307(3) 1.140(3) 1.103(3) O&00(3) 1.207(16) 1.19(2) lsOO(2) 2.011(15) 0.981(8) 1.008(9) 0.867(7) l&O(4) 1.240(5) 1.194(8) 1.010(5) 1.17(l)

1.43261 1.06851 0.54666 1.3%94 1.30068 1.14767 1.09757 0.61338 1.18172 1.14821 1.50128 2.Om64 0.97926 1.05524 0.83707 1.46680 1.25109 1.16042 1.00778 1.17676

0.002 - 0.001 0.009 - 0.006 0.006 - 0.008 0.005 - 0.013 0.025 0.04 - 0.001 0.010 0.002 - 0.043 0.030 - 0.007 - 0.011 0.034 0.002 0.007

4p5d. As already mentioned, the states 4s4p3 3D12,3do not occur as the first components in any of the electron states but are present as small admixtures in almost all odd levels with J = 1,2 or 3 of the configurations 4s24pn”d. This results from the fact that the term 4~4p~~D, in absence of the configuration inter-

of neutral germanium,

Ge 1

actions, would be placed in the same region as the configurations 4s24pn”d, so that the interaction between the configuration 4s4p3 and the above-mentioned configurations is significantly greater (see table IV) than between other configurations. In the spectrum Ge I, like in the previously considered spectrum Sn I [8], the interaction of the configuration nsnp3 with the configurations ns’npn’s is much weaker than expected. The theoretical limit for the Slater integrals R’ (4sn’s, 4~4~) deduced based on the Racah criterion [lo] is considerably higher (see table IV) than the values obtained by means of the fitting procedure. The admixture of the configuration 4s4p3 to states in the configurations 4s24pn’s does not exceed 2% (the values found in the levels 9s a, b 3P,) and is mostly below one percent. This results from the position of the term 4~4p~~P, which is localized above the ionization limits (see eq. (4) and table II). From the spectrum of the odd electron levels reported by Brown et al. [6] the level at 61101 cm-’ with J = 1 has been omitted in the present calculation. The calculations clearly show that in the studied system there is no place for a level at this position, even so if its quantum number J would be changed. Tentatively, the level at 61101 cm-’ might be interpreted as a J = 2 level belonging to the configuration 4s24p5g. In absorption, Brown et al. [6] observed many transitions between levels of the configurations 4s24p2 and 4s24pn”‘g. These transitions are only possible when the states of the configurations 4pn”‘g are admixed by the states of the configurations 4pn”d. Hence, the transitions observed by Brown et al. prove the existence of a Coulomb interaction between the above-mentioned configurations. Therefore, some deviations between calculated and observed values of the energy levels (see table II) can have this origin. The small perturbations in the monotonic increase of the values of the parameters .?& along the series 4s24pn”d (see table III) probably also originate in interactions with configurations 4s24pn”‘g neglected in the present calculations. It can be deduced from table III that, along configurations 4s24pn’s, (n’- n*) is

J. Dembczyhki

I The spectrum of neutral germanium, Ge I

monotonic, in contrast with the behavior of (n”n*) along configurations 4s24pn”d. However, the fluctuations are rather small (not exceeding 0.02), much smaller than those presented, e.g., in ref. 2 for the individual levels of the mentioned configurations. In the presented procedure highly accurate functions in the SL-basis scheme have been obtained in intermediate coupling. These wave functions can be used in an analysis of the hyperfine structure splittings and optical isotope shifts or in predicting lifetime anomalies for the excited states.

Acknowledgement

This work has been performed in cooperation with the Kernforschungszentrum Karlsruhe, Institut fiir Kernphysik. The authors would like to thank Prof. Dr. G. Schatz and Prof. Dr. H. Rebel, Kernforschungszentrum Karlsruhe, for their interest. The study was partially sponsored

by the Project MR 151.04 “Experimental Theoretical Investigations of Interactions tween Atomic Nuclei and Electrons”.

229

and be-

References

r11 C.E.

Moore, Atomic Energy Levels, II, Natl. Bur. Stand. (US), Ciro. No. 467 (1958). 121K.L. Andrew and K.W. Meissner, J. Opt. Sot. Am. 49 (1959) 146. (31 V. Kaufman and K.L. Andrew, J. Opt. Sot. Am. 52 (1%2) 1223. [41 C.J. Humphreys and K.L. Andrew, J. Opt. Sot. Am. 54 (1964) 1134. PI K.L. Andrew, R.D. Cowan and A. Giacchetti, J. Opt. Sot. Am. 57 (1%7) 715. M CM. Brown, S.G. Tilford and M.L. Ginter, J. Opt. Sot. Am. 67 (1977) 584. 171 R.D. Cowan and K.L. Andrew, J. Opt. Sot. Am. 55 (1%5) 592. PI J. Dembczyriski and H. Rebel, Physica 12X (1984) 341. 191 J.M. Wilson, The Atomic Absorption Spectra of Silicon, Germanium, Tin and Lead, Thesis, Imperial College of Sci. and Tech., London (1964). WI G. Racah, Phys. Rev. 62 (1942) 523.