Beyond-Mean-Field with an Effective Hamiltonian Mapped from an Energy Density Functional

A method for beyond-mean-field calculations based on an energy density functional is described. The main idea is to map the energy surface for the nuclear quadrupole deformation, obtained from an energy density functional at the mean-field level, into an effective Hamiltonian expressed as a many-body operator. The advantage of this procedure is that one avoids the problems with density dependence which can arise in beyond-mean-field methods. The effective Hamiltonian is then used in a straightforward way in the generator-coordinate-method with the inclusion of projections onto good particle numbers and angular momentum. In the end, both spectra and wave functions are obtained. As an example of the method, calculations for the nucleus $^{62}$Zn is performed with three different parametrizations of the Skyrme functional. The results are compared with experiment.