Hartree-fock wave functions and oscillator strengths for the helium isoelectronic sequence

.I. Qunnt. SpeOosc.

Rodiat. Transfer. Vol. 16, pp. 49-52. Pergamon Press 1976. Printed in Great Bntain.

HARTREE-FOCK WAVE FUNCTIONS AND OSCILLATOR STRENGTHS FOR THE HELIUM ISOELECTRONIC SEQUENCE D. K. DATTA,? S. K. GHOSHALS and S. SENCUPTA Department of Physics, Jadavpur University. West Bengal, India (Received 21 January 1975) Abstract-Oscillator strengths for I’S - n ‘P transitions for some members of the helium isoelectronic sequence have been calculated by utilizingthe dipole length, velocity and acceleration forms of the transition matrix element with coupled H. F. wave functions. Good agreement has been obtained between the values of the oscillator strengths, The quantities (fA - f,.) and (f* - fv) decrease slowly with nuclear charge 2, whereas (f,. -fv) first increases to a maximum value and then decreases slowly. I. INTRODUCTION THE MAINobstacle in the accurate calculation

of oscillator strengths is the nonavailability of exact wave functions for the states involved. Variationally determined wave functions derived from energy-minimization procedures lead to inaccurate and inconsistent values for fnumbers because significant contributions to the line-strength integrals may arise from regions which do not affect the energies of either state. Approximate procedures for the calculation of oscillator strengths have been suggested.“’ SCHIFF and PEKERIS”’ have shown that, when exact wave functions are available for the combining states, elementary radiation theory provides accurate and consistent sets of intensity values. Even in the most favourable cases, the accuracy of calculated oscillator strengths is doubtful. In the absence of experimental data, agreement between the length (fL), velocity (fv) and (less frequently) acceleration CfA) forms of the oscillator strengths has been used to estimate the accuracy of calculated oscillator strengths. CHONG’~’has used Eckart-type wave functions to find the values of oscillator strengths for helium-like ions. His results for different ‘P - ‘D and “P -‘D transitions show agreement between length and velocity forms but large differences with acceleration form. Similar calculations have been performed by COHEN and MCEACHRAN’~’ with frozen-core type wave functions without, however, emphasizing the acceleration form. Calculations of oscillator strengths with Hartree-Fock wave functions have been performed by TREFFTZ,‘~’GREEN,@’FROESE,‘~’and others; acceleration form have not been used in these calculations. In this Note, we present oscillator strengths for 1S2 - 1SnP transitions for some members of the helium isoelectronic sequence using three standard forms and fully coupled H. F wave functions (see Section 3). 2. WAVE FUNCTION The dynamic polarizabilities of an atom under the influence of a perturbing electromagnetic field of varying frequency exhibit singularities. These singularities are related to one-electron excitations. Approximate wave functions for the excited states may be obtained from a study of the perturbed functions in the neighbourhood of the singularities.@’ The wave functions describe a situation where one of the electrons is excited while the others remain in their initial orbitals. The interelectronic interactions are different in the ground and excited states. Incorporating the required corrections, coupled H. F. wave functions for the excited states were obtained through a self-consistent variation-perturbation procedure.(‘.“) The wave functions which were obtained in polarizability calculations were used as starting wave functions. The final wave functions are listed in Refs. (9) and (10).

D. K. OA

r

e

1‘1 ;\

C”l

cd.

51

Helium isoelectronic sequence 0.6 o--f, c f,

I II -

06-

a 1 3

no-

Is2 Is2 -

ls2p:

‘P

ls3p : ‘P

04-

x

oz-

I

01

I

I

02

03

I 04

I/Z Fig. I. Plot of fL,fv. fA against l/Z.

o-t&-(/, A-

Cr,--r,,

o-

cr, --tL,

I-Is’-ls2p: II-

I&-

‘P ls3p

: ‘f

006

00::

2

004

OO?

002

0 01

3

II

D. K.

52

DATTA

et U/

been used. The f+,. fv, f,. values are plotted against I/Z in Fig. I. The f-values vary inversely with the nuclear charge for all transitions: close agreement is observed between the fv. f, and f,, values. This result may be contrasted with the observations of IAPAGLI~ and SINANO~LU””that, for Be, the values of fi. fiand fi calculated with H. F. wave functions differ by a factor of two. The quantities (fA -f, ) and (f,, -jv) decreases slowly with 2 (see Fig. 2). On the other hand. (fi. -.fv) first increases to a maximum value and then decreases slowly (see Fig. 2), Acknowledgenrents-We are indehted to Mr. Diwl( CHAT'ITRJWof the Institute of Radiophysics and Electronics of Calcutta University for comput:ttional asi\tance. Alw. one of the author\ (S.S.G.1 i\ indebted to 1I.Ci.C for providing financial grants. REFERENCES I. 7. 3. 4. 5.

6. 7. 8. 9. 10. 1I.

R. BATES and A. DAMGAARD.Phil. ~rans. Ro.v. Sot (London) A242. 101 (1944). SCHIFF and C. L. PEKEKIS. Phyc. Rev. A134 63X (19631. P. CHONG, J. c,hern. Phyc. 4X. 1313 1196X). COHEN and R. P. McE,~cHKA~. C~I. .I. I’hy\. 50. 1363 (lY72l. E. TREFFTZ, Z. Astrophy.!. 44, I (1957). L. C. GREED. N. C. JOHNSOYand E. K. KOI.~HIN. Astn~ph~\. J. 144. !hY (iY661. C. FROESE.Phys. Rec. 150. I (lY66). P. K. MUKHERJEF,s. SEh(w’I’4 and A. ML’kHERJEF../. dw?~. I$~,~. 51, 1317 ( IYhY). P. K. MUKHERJEE.S. SENGUPT.~and A. MUKHBRUE. W. .I. (2. Chew. 4. I!Y (19701. P. K. MIJKHERJEE.A. K. BHATTXHARI 4 ;~nd A. MLIKHFRJEE.Id. ./. Q. (‘/Hertz.5. 647 (1~71) S. R. LAPGI.IA and 0. Sl~.4NOGl11.J. c,hertl. Phyx 44. IXNX (1966). D. B. D. M.