Adiabatic and non-adiabattc cranking models for the solution of the large amplitude time-dependent Hartree-Fock equations and the calculation of nuclear energy surfaces

Abstract

An analysis is made of the device of forced vibrations to reduce the difficult large amplitude TDHF (time-dependent Hartree-Fock) problem to a simpler static problem. It is shown that cranking is a perfectly valid technique if the cranking field is defined by the criterion that the constrained static wave function be identical at a given instant of time to the freely oscillating TDHF wave function. On the basis of this criterion an exact general expression is derived for the cranking field and adiabatic and non-adiabatic cranking models are proposed as practical means of solving the large amplitude TDHF equations and calculating energy surfaces for fission and heavy ion reactions. The non-adiabatic model, which is favoured, corresponds to cranking the nucleus to move always in the direction of a local decoupled “normal mode” calculated from its unconstrained time-dependent equations of motion. The familiar Belyaev cranking model and the Baranger-Kumar model are discussed in the context of the new formalism.