Generalized Sturmian functions in prolate spheroidal coordinates for continuum

A L FRAPICCINI; D M MITNIK; F A LOPEZ; L U ANCARANI

Simposio; vCOPIAMC; 2021

Illinois State University

The molecular ion H+2, and other one electron diatomics, are the simplest molecular quantum three-body problem with Coulomb interactions. In the fixed nuclei approximation, it is well known that prolate spheroidal coordinates possess the natural symmetry and make the Schrodinger Equation separable.With the aim of describing bound and continuum states for diatomic molecules, we develop and implement a spectral method that uses Generalized Sturmian Functions (GSF) in prolate spheroidal coordinates. For atomic systems, the GSF approach in spherical or hyperspherical coordinates has been applied with success. The main advantage is that an appropriate asymptotic behavior can be set upon all basis elements: an exponential decay for negative energy bound-like elements and oscillatory behavior for positive energy continuum-type elements. Inserting the correct physics into the basis makes the expansions converge rapidly which is particularly valuable when dealing with computationally expensive scattering problems.For diatomic systems, we propose two different methods that use GSF in prolate spheroidal coordinates. The first one is an iterative 1d procedure in which one solves alternately theangular and the radial equations. The second method consists in representing the full Hamiltonian matrix in a two-dimensional GSF basis set, and its further diagonalization.