Z-DEPENDENCE OF THE ENERGY LEVELS AND AUTOIONIZATION PROBABILITIES FOR DOUBLY EXCITED STATES 2l 3l' OF THE TWO-ELECTRON SYSTEMS

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Z-DEPENDENCE OF THE ENERGY LEVELS AND AUTOIONIZATION PROBABILITIES FOR DOUBLY

EXCITED STATES 2l 3l’ OF THE TWO-ELECTRON SYSTEMS

M. Cornille, J. Dubau, F. Bely-Dubau, P. Faucher, U. Safronova

To cite this version:

M. Cornille, J. Dubau, F. Bely-Dubau, P. Faucher, U. Safronova. Z-DEPENDENCE OF THE EN-

ERGY LEVELS AND AUTOIONIZATION PROBABILITIES FOR DOUBLY EXCITED STATES

2l 3l’ OF THE TWO-ELECTRON SYSTEMS. Journal de Physique Colloques, 1989, 50 (C1), pp.C1-

583-C1-588. �10.1051/jphyscol:1989163�. �jpa-00229362�

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JOURNAL DE PHYSIQUE

Colloque C1, suppl6ment au n O l , Tome 50, janvier 1989

2-DEPENDENCE OF THE ENERGY LEVELS AND AUTOIONIZATION PROBABILITIES FOR DOUBLY EXCITED STATES 2t3t' OF THE TWO-ELECTRON SYSTEMS

M. CORNJLLE,

J.

DUBAU, F. BELY-DUBAU* , P. **FAUCHER* and U.** I. SAFRONOVA*

*

Observatoire de Paris-Meudon, F-92395 Meudon Principal Cedex, France

"~bservatoire de la C6te d'Azur, F-06003 Nice Cedex, France

"'~nstitute of Spectroscopy, Academy of Sciences of the U.S.S.R., Troistsk 142092, U.S.S.R.

Resume - Deux methodes de calcul differentes (AUTOLSJ et MZ) sont utilisees pour obtenir les niveaux d'dnergie et les probabilites d'autoionisation pour les Btats doublement excites 29. 3L'des systemes 2. deux Blectrons. Une dkpendance en Z de ces parametres pour une sequence isoelectronique des ions h6liumoides (6 < Z <44) ainsi qu'une comparaison entre les r6sultats obtenus par ces deux methodes sont presentees.

Abstract

-

'Itto different calculational methods (AUTOLSJ and MZ) are used to obtain the energy levels and autoionization probabilities for doubly excited states 29. 3i' of two-electron systems.

A

Z

dependence of these parameters for an isoelectronic sequmce of He-like ions (6

<

^Z

<

44) and a comparison between the results obtained by these two methods are presented.

1.

INTRODUCTION

Energy levels and autoionizing states of two-and three-electron systems have been the object of many investigations 111. Special attention was paid to the doubly excited states 29. 3k' of-the two-electron systems. We have focussed our efforts on the calculation of the energy levels and autoionization probabilities by two different calculational methods for the He-like ions isoelectronic sequence (6 4 Z

<

44). It is interesting firstly to study the behaviour of these parameters according to the method which is used for the calculation and secondly to exhibit a Z - dependence along the isoelectronic sequence.

2.

CALCULATIONAL METHODS

The AUTOLSJ and MZ methods being described in details by Cornille et al. 121, only a summary of them is presented in this paper. A common feature of both methods is that the energy matrix is constructed in a LS coupling scheme and the relativistic corrections are included within the framework of the Breit-Pauli operator. These methods use a perturbational approach. The main difference is in the choice of the monoelectronic wavefunctions of the N-electron system, and also by the basis size for these wavefunctions. The AUTOLSJ method uses two computer codes : "SUPERSTRUCTURE" 13

1

which calculates the wavefunctions and the energy levels and AUTOLSJ 141 which obtains the autoionization probalities. These two codes are briefly described below.

a. SUPERSTRUCTURE : In a first step the program determines a set of non-relativistic wavefunctions by diagonalization of the non-relativistic Hamiltonian using orbitals calculated in a scaled Thomas-Fermi-Dirac potential V (r). For this potential the scaling parameters hL are obtained by a self-consistent energy mtnimization procedure. In a second step the p~ogram diagonalizes the Breit-Pauli Harniltonian on this basis. Thus the multiconfigurational wavefunctions obtained contain the relativistic effects in the configuration mixing coefficients.

b. AUTOLSJ : The program calculates the autoionization probabilities. The spirit of this one is very similar to the collisional JJOM code 151. The term coupling coefficients for N and N

+

¹

electron systems are calculated by "SUPERSTRUCTURE" and are supplied as inputs to "AUTOLSJ".

The transition matrix elements betveen the bodnd and the free states are obtained in the Distorted Wave Approximation (D.W.). AUTOLSJ calculates the recoupling coefficients and afterwards the autoionization probabilities A given by formula (1) :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989163

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JOURNAI- DE PHYSIQUE

Where Es =

<

$s

1

H

I Jls >

and where J, and

JI,;

are the initial "bound" state and final "free" sfate respectively. The energy E of the fsee state $: is taken to be the same. The wavefunctions

*;

af-e normalized to the egergy wavefunction and the free wavefunction $; corresponds to an auto~onization channel.

The MZ method uses for the unperturbed monoelectronic wavefunctions of the N-electron system the unscreened hydrogenic type wavefunctions, and a complete basis set including both discrete and continuum states. This method calculates the energy of a given state by diagonalization procedure for the energy matrix elements between the states of the same Layzer complex 161, the contribution of all the states belonging to the other complexes is introduced as a second-order perturbation correction. The MZ method is appropriate for few electron systems since the hydrogenic orbitals are realistic and the method can be carried to any order of perturbation on a complete basis. On the contrary, the AUTOLSJ method is appropriate for many electron systems since an average potential is more realistic than the nuclear potential alone.

RESULTS

a. Scaling parameters and energy levels :

Fig. 1 shows the behaviour of the scaling parameters h e ( 9 , = 0,l) along the He-like ions isoelectronic sequence (6

<

Z

<

44) calculated with the AUTOLSJ method. These parameters are determined by minimization of all the terms of the 29. 39.' configurations with L = 0,l and 9. = 0,1,2.

The scaling parameter A, is taken equal to A , .

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The energy levels are calculated using the following configurational basis set : 2s3s, 2s3p, 2s3d, 2p2s, 2p3p, 2p3d. In the AUTOLSJ method we use the scaling parameters determined by the precedent minimization. The results for all energy levels are presented in tables 1,2. In order to compare these ones with those obtained by the

MZ

method we have suppressed from those ones the configurations of the other complexes, and among the levels we have selected the following ones : 2s3d3D3 (21, 2p3p3D3 (3), 2s3d3D, (181, 2p3p3Dl (19), 2p3p3Pl (201, 2p3p1P, (21) 2s3s3S, (22), 2p3p3Sl (23). The corresponding energies obtained by the two calculational methods agreeing very well, for the clearness of the figures we report only the results obtained by the AUTOLSJ method. Figures 2 and 3 give the behaviour of these atomic data along the He-like ions isoelectronic sequence.

J = 1 e v e n

I

800

r

LOO;

200

!

-

J = 3 even

Figure 2 F i g u r e 3

b . Autoionization probabilities i

The autoionization probabilities are calculated by the two methods. The AUTOLSJ and MZ methods use the same basis sets which are utilized to obtain the energy levels. We consider the autoionization probabilities for doubly excited levels 2e 31' listed above. The results obtained by the two calculational methods are given on figures 4 , s (AUTOLSJ), and 6,7 (MZ), but it is more difficult to show the behaviour of those atomic data along the He-like ions isoelectronic sequence than for the energy levels.

' A ~ 1ic3 <rn.'l

I

^J^{= I}^even

0 2 L c

I J = 3 even

Figure 4 Figure 5

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JOURNAL

DE

PHYSIQUE

J = l even

Figure 6

A, (10" c

'I

I

J

= 1 even

CONCLUSION

The comparison between the results obtained from the AUTOLSJ and HZ methods for the doubly excited states 2 1 39.' of the two-electron systems shows a good agreement for the behaviour of the energy levels along the isoelectronic sequence of the He-like ions. The agreement for the autoionization probabilities A is good for large Z values and is not good for little Z values.

REFERENCES

11) Aglitskii, E.V., ~afronova, U.I., Autoionization States Spectroscopy of Atomic Systems (Mos- cou : Energoatomizdat).

121 Cornille, M., Dubau, J., Loulergue, M., Bely-Dubau, F., Faucher, P. ,Safronova, U.I., Shli- japtseva, A.S., Vainshtein, L., J. Phys. B

2

(1988).

13; Eissner, W., Jones, M., Nuss5aumer, H., Comput. Phys. Commun.

8

(1974) 270.

141 Dubau, J., Loulergue, M., Phys. Scr.

2

51981) 136.

151 Saraph, H.E., Comput. Phys. Commun.

3

(1972) 246.

161 Layzer, D., Ann. Phys., NY

8

(1959) 271.

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