THEORY AND COMPUTATION OF ELECTRON CORRELATION IN THE CONTINUOUS-SPECTRUM - DOUBLE PHOTOIONIZATION CROSS-SECTION OF H- AND HE NEAR AND FAR FROM THRESHOLD

We present a theoretical approach to the ab initio calculation of sing le or multiphoton double electron ionization cross sections, sigma(++) (E), of polyelectronic atoms, near (Wannier region) and far from thres hold. The overall computational method is variational, uses functions of real as well as of complex coordinates, and follows the many-electr on, many-photon theory proposed by Mercouris and Nicolaides [J. Phys. B 21, L285 (1988); 23, 2037 (1990)]. It incorporates the electronic st ructure and the pair correlations in the continuum via configuration-i nteraction techniques. sigma(++)(E) is obtained as the imaginary part of a complex eigenvalue that is computed by diagonalizing a state-spec ific non-Hermitian matrix constructed from separately optimized functi on spaces Q and P representing the field-induced resonance state. Q co ntains correlated wave functions of bound or quasibound states expande d over numerical and analytic orbitals of real coordinates. P is compo sed, in principle, of subspaces P-1 and P-2, representing the one- and the two-electron channels, respectively, which are optimized separate ly and then are allowed to mix via the construction of the total non-H ermitian matrix. Both are spanned by basis sets of real coordinates fo r the ionized core and of complex coordinates for the outgoing part of the one- and the two-electron resonance state. The two-electron squar e integrable ''continuum'' function space is made orthogonal to the av ailable single electron channels in order for sigma(++)(E) not to incl ude portions of the single electron ionization cross section sigma(+)( E). Application is made to the single photon sigma(++)(E) of the proto typical systems H- and He, but without the mixing of P-2 and P-1, due to numerical instabilities. The two-electron ionization channels were composed of Slater-type orbitals, symmetry-coupled according to (sp), (pd), and (df). Higher symmetries would also be needed at higher energ ies, with corresponding increase of angular correlation terms in the i nitial-state wave function. The continuous energy ranged from E=0 to E =250 eV. In the threshold region E=0-2 eV, the length and velocity res ults are in good agreement with experiment for H- and in reasonable ag reement with experiment for He. Far from threshold, there is discrepan cy between length and velocity forms in this as well as in previous wo rks by other methods. Apart from whatever inadequacies of the basis fu nctions, this is possibly due to the exclusion of mixing of the single electron open channels into the correlated wave function of the two f ree electrons. By comparing the results from the use of correlated wav e functions with those obtained when the calculation of the transition matrix element is done with wave functions of real coordinates, where the initial state is correlated but the final one is only a product o f Coulomb wave functions, the effect of correlation of the two free el ectrons is deduced for the case of He, without considering the mixing of one- and two-electron channels. Finally, a by-product of the presen t development was the calculation of the He sigma(+)(E) to the n=1 sin gle ionization threshold. Comparison with previous accurate experiment al results reveals very good agreement.