Generator coordinate method with optimum basis

The generator coordinate method (GCM) has been a well-known method to describe nuclear collective motions. In GCM, one a priori specifies collective degrees of freedom (collective coordinates), such as nuclear deformations, and superposes many Slater determinants (SDs) within the selected collective subspace. However, there always exists arbitrariness in this approach in the choice of collective coordinates, for which one has to rely on an empirical and phenomenological theory. With such choice, it is not trivial whether the collective motion of interest can be optimally described. Therefore, a description of the collective motion without pre-set collective coordinates is desirable in order not to miss important degrees of freedom.

Recently, we are developing a new extension of GCM, by optimizing both the basis SDs and the weight functions according to the variational principle. With such simultaneous optimization of the basis states, one does not have to specify beforehand the relevant collective degrees of freedom covered by the set of basis SDs. In this presentation, I will present results for sd-shell nuclei with the Skyrme energy functional. Our results indicate that collective coordinates often assumed in conventional GCM calculations, such as quadrupole moment, may not provide optimal basis to describe the ground states. This work would be an important step towards consistent description of nuclear collective motions.