SQUARE INTEGRABLE BASIS FOR THE CALCULATION

OF ABOVE-THRESHOLD MULTIPHOTON TRANSITIONS IN ATOMS

SHERSTYUK A.I., SERGEEV A.V.

S.I.Vavilov State Optical Institute, 199034, St.Petersburg, Russia

The calculation of above-threshold processes requires the

knowledge of Fourier transform of Green's function G( ) at

positive values of energy parameter . For the Hydrogen-like

atoms the great advantage was achieved with the use of Sturm-like

expansion of Green's function. The use of such expansions is

based on the methods of analytical continuation of the proper

matrix elements onto the real positive values of [1]. But for

many-electron atoms we have usually to deal with the

numerically-determined potentials and hence the above-mentioned

methods become inapplicable.

We have proposed an alternative approach based on the use as

the basis the set of eigenfunctions of the generalized

-eigenvalue problem for an equation

(1)

where h is the Hamiltonian (usually Hartree - Fock) operator, g =

g(r) is the weight operator, is the frequency of external

field, n = 1,2,... . In case we put

. Then the solutions of (1), which have at infinity the

phase equals to , do form a full

discrete set of square integrable and mutually orthogonal (with

the weight) functions . The corresponding eigenvalues are

The set determines the diagonal discrete expansion of the

one-particle Green's function of h. With the use of such

expansion we have calculated the probabilities of above-threshold

multiphoton ionization and dynamical polarizabilities for some of

alkali atoms. The convergence of the expansions in dependence on

the values and have been investigated. The comparison with

different method has been made.

1. KARULE E. JOSA, B7, 631, 1990.

Back to A. I. Sherstyuk.

Designed by A. Sergeev.