Finding optimal basis states for variation after projection nuclear wave functions*

Abstract

Abstract The variation after projection (VAP) method is expected to be an efficient way of obtaining the optimized nuclear wave functions, which can be as close as possible to the exact shell model ones. However, we found that there are two additional problems that may seriously affect the convergence of the VAP iteration. The first problem is the existence of irrelevant projected basis states. At a VAP iteration, the Hill-Wheeler (HW) equation is composed of all updated projected basis states. If one of these projected basis states does not mix with a calculated wave function of interest, which is obtained by solving this HW equation, it is likely that this basis state will never mix with this wave function even after the VAP iteration converges. The other problem is the poor orthonormality among the projected basis states, which seriously affects the accuracy of the calculated VAP wave function. In the present work, solutions for these two problems are proposed, and examples are presented to test the validity. With the present solutions, the most important projected basis states can be reliably obtained, and the fully optimized VAP wave functions can be accurately and efficiently calculated.