A two-center-oscillator-basis as an alternative set for heavy ion processes

Abstract

The two-center-oscillator-basis, which is constructed from harmonic oscillator wave functions developing about two different centers, suffers from numerical problems at small center separations due to the overcompleteness of the set. In order to overcome these problems we admix higher oscillator wave functions before the orthogonalization, or antisymmetrization resp. This yields a numerically stable basis set at each center separation. The results obtained for the potential energy surface are comparable with the results of more elaborate models.

New and efficient method for solving the eigenvalue problem for the two-center shell model with finite-depth potentials

“…The deformed oscillator basis is straightforward to use, but a large number of basis states is required at large separation distances of two potential wells. This problem can be avoided by using the non-orthogonal twocenter basis, but calculations with such basis may suffer from a numerical instability at short distances due to the overcompleteness of the basis [23]. Moreover, with these basis functions, it is not straightforward to compute matrix elements of a spin-orbit potential in single-particle potentials when they are shifted from the origin.…”