Positive energy Generalized Sturmian functions applied to atomic photoionization

I.A. GOMEZ, G. GASANEO, D.G. ARBO, D.M. MITNIK, AND B. PIRAUX

Canakkale

Conferencia; Molecular Electronic Structure at Troy; 2012

A technique based on the use of Generalized Sturmian functions (GSFs) [1] have been implemented recently to study both structure [2,3] and scattering two- and three-body problems [4]. GSFs are the solutions of a Schrödinger type equation which includes one generating potential and one auxiliar potentials. This last one dictates the asymptotic behavior to all the basis functions. The eigenvalues are defined by the boundary conditions imposed at the origin and at large distances and by the generating potential. The wave function are written as a linear combination of products GSF, and for each situation an appropriated asymptotic condition is imposed to the basis functions. Bound or scattering type behavior is imposed to the basis functions depending on the problem to be solved. Situations where both functions are bound [2], one is bound and the other is in the continuum [3], or both are in the continuum can be easily considered [4]. In this report we study the physical information contained on the GSF in detail. We define a set of functions with a Coulombic auxiliar potential and a Yukawa generating potential, for negative and positive energies. The GSF are re-expanded in terms of hydrogenic eigenfunctions and the weights are studied for different situations. This analysis is performed all together with the study of ionization of atomic hydrogen interacting with an electromagnetic field. A perturbative approach allows us to include the absorption of photons one by one. A set of driven equations is obtained and solved analytically. The solution is also written as a linear combination of GSF, thus, the driven equation is transformed into a linear set of equations which is solved by standard matrix methods. The time-dependent Schrödinger equation for the hydrogen atom in the field is solved also using a pseudospectral method. A comparison of the results obtained with the different methods is performed and the advantages of the use of the GSF are discussed. This is the natural starting point to the extension to three-body problems.