Quadrupole correlation energy by the generator coordinate method

We investigate the accuracy of several schemes to calculate ground-state correlation energies using the generator coordinate technique. Our test bed for the study is the sd-interacting boson model, equivalent to a six-level Lipkin-type model. We find that the simplified projection of a triaxial generator coordinate state using the S₃ subgroup of the rotation group is not very accurate in the parameter space of the Hamiltonian of interest. On the other hand, a full rotational projection of an axial generator coordinate state gives remarkable accuracy. We also discuss the validity of the simplified treatment using the extended Gaussian overlap approximation, and show that it works reasonably well when the number of boson is 4 or larger.