Theories for large amplitude collective motion and constrained Hartree-Fock

Abstract

For a large amplitude collective motion the adiabatic time dependent Hartree-Fock theory (ATDHF), the infinitesimal generator approach (IG), the constrained random phase approximation (CRPA) and the cranking model (CR) are compared, the only assumption made being that the system moves along a collective path generated by constrained Hartree-Fock (CHF). Without restricting to a certain model it is shown, that CRPA and IG yield identical expressions for the collective mass, which depend explicitly on the constraining operator and are therefore not unique. ATDHF is shown to depend only on the collective path rather than on the constraining operator as well. The nuclear monopole vibrations in 16O are taken as an example to demonstrate the magnitude of the effect. The masses are calculated in the different theories taking the Skyrme III interaction and r 2 as constraining operator. The theories are unified by using a constraining operator, which is projected on its particle-hole subspace at each value of the time dependent collective coordinate. This choice is justified and compared with various local prescriptions for the constraining operator.