Sturmian wave function for Coulomb screened potentials

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

Buenos Aires, Argentina

Simposio; Thirteenth International Symposium on Polarization and Correlation in Electronic and Atomic Collisions, and International Symposium on (e, 2e), Double Photoionization and Related Topic; 2005

Recent experimental advances in the measurement of collision processes had lead to the use of more complex, many electron atoms. From the theoretical point of view, the description of such systems has significant challenges. A useful approach, is by employing many electron Coulomb Sturmian functions as a basis set, to expand the exact atomic wave function for all electrons. For negative energies, these eingencharge basis functions have the special feature of having the correct asymptotic behavior for potentials that goes to zero equal or faster than 1/r, although it is not complete for the entire negative energy spectrum. Within the independent electron model, the effect of the passive electrons on the active one can be included in several ways,  from the modelling of the Coulomb potential with effective charges, to the calculation ofthe potential with ab-initio methods. In this last approach, theresulting potential can be generally well represented by a Hermanand Skillman-type expression.In this report we introduce a set of Sturmian functions for thesepotentials, suitable to construct many electron basis sets. We use an expansion for the Sturmian function in terms of a L2 Laguerre-type basis. Finally, we write the approximate solution for the function and study its convergence for negative energies. For the pure Coulomb potential, the bound states eingencharges satisfy Zn=n(-2E)^1/2. We study how this law is modified when the screening potential is turned on. An L2 approximation of the wave function is obtained when we set E>0.