Four approaches to the function of inertia in a solvable model

Abstract

Four different methods of calculating the mass function for large-amplitude collective motion are applied to the Lipkin model: adiabatic time-dependent Hartree-Fock (ATDHF), infinitesimal generators (IG), constrained RPA and the generator coordinate method (GC). ATDHF and GC give identical results. IG and RPA lead to the same result only in the limit of vanishing constraint. The corresponding collective Hamiltonian gives good results for the low-lying excitation energies while the cranking approximation seems to be rather poor for this case.