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.

Designed by A. Sergeev.