STURMIAN EXPANSION OF BOUND STATES FOR TWO-ELECTRON ATOMIC SYSTEMS

A. L. FRAPICCINI, J. M. RANDAZZO, F. D. COLAVECCHIA AND G. GASANEO

Königstein, Alemania

Simposio; Fourteenth International Symposium on Polarization and Correlation in Electronic and Atomic Collisions, and International Symposium on (e, 2e), Double Photoionization and Related Topic; 2007

The three-body Coulomb problem has been extensively studied over the past years, but no exact wave function is yet known either for the scattering or bound states. If one is dealing with scattering problems, the boundary conditions for the wave functions are known , and several ab-initio methods including the Exterior Complex Scaling (ECS) or the R-matrix have been successfully applied to (e,2e) and (γ,2e) processes. Meanwhile, in the case of bound atomic systems, a variational approach with different trial functions is known to give very good values of the ground state energy.In this contribution, we propose to use an expansion for a given total angular momentum L and projection M of the full wave function. The radial basis set are the Sturmian functions with the correct asymptotic behavior according to the energy domain: exponential decay for negative energy and outgoing (incoming or standing) wave for positive ones. The advantage of using the Sturmian basis set is that the correct boundary conditions are incorporated for any energy of each electron. In the case of atomic bound states, the Scrhödinger equation for the two electron system is solved by replacing the expansion in the equation and projecting again onto the basis set, this gives a generalized eigenvalue problem whose solution are the total energy E and the coefficient expansion.We show the convergence for the bound states of He and H- atoms including several angular momentum pairs (l1,l2) for ground states as well as singly and doubly excited states, and compare the results obtained with those given by other methods.