Mass parameters for quadrupole vibrations in the adiabatic approximation

Abstract

Nuclear quadrupole vibrations are investigated in the framework of the adiabatic time-dependent Hartree-Fock equations. Using a continuity condition satisfied by these equations, we show that a simple analytic expression can be derived for the mass parameter in the case where the collective variable α is a scaling variable i.e. changes the cartesian coordinates x, y, z into x/ α, y/ α, α 2 z. This result depends only on the existence of the continuity equation and thus holds for any nucleon-nucleon interaction. Applications are considered in the case of small amplitude motion in oxygen-16 and calcium-40.