Correlation energies by the generator coordinate method: Computational aspects for quadrupolar deformations

We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are available. These include a strongly deformed nucleus, $^{156}\mathrm{Sm}$, a nucleus with strong pairing, $^{120}\mathrm{Sn}$, the krypton isotope chain which contains examples of soft deformations, and the lead isotope chain which includes the doubly magic $^{208}\mathrm{Pb}$. We find that the Gaussian overlap approximation (GOA) for angular-momentum projection is effective and reduces the computational cost by an order of magnitude. Cost savings in the deformation degrees of freedom are harder to realize. A straightforward Gaussian overlap approximation can be applied rather reliably to angular-momentum projected states based on configuration sets having the same sign deformation (prolate or oblate), but matrix elements between prolate and oblate deformations must be treated with more care. We propose a two-dimensional GOA using a triangulation procedure to treat the general case with both kinds of deformation. With the computational gains from these approximations, it should be feasible to carry out a systematic calculation of correlation energies for the nuclear mass table.