An extension of the generator coordinate method with basis optimization

TL;DR

This paper introduces an advanced generator coordinate method that optimizes basis states and weights variationally, enabling a more accurate description of nuclear collective motions and excited states.

Contribution

It extends the GCM by optimizing both basis determinants and weights, revealing complex collective coordinates for large amplitude motions.

Findings

Optimized bases correspond to excited states along a collective path.

The method provides a more nuanced understanding of collective coordinates.

Application to nuclei demonstrates improved state descriptions.

Abstract

The generator coordinate method (GCM) has been a well-known method to describe nuclear collective motions. In this method, one specifies {\it a priori} the relevant collective degrees of freedom as input of the method, based on empirical and/or phenomenological assumptions. We here propose a new extension of the GCM, in which both the basis Slater determinants and weight factors are optimized according to the variational principle. Applying this method to $^{16}$O and $^{28}$Si nuclei with the Skyrme functional, we demonstrate that the optimized bases correspond to excited states along a collective path, unlike the conventional GCM which superposes only the local ground states. This implies that a collective coordinate for large amplitude collective motions is determined in a much more complex way than what has been assumed so far.