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

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.

A. I. Sherstyuk page

Designed by A. Sergeev.