Extended quasi-particle-phonon coupling theory for odd-mass spherical nuclei

Abstract

The low-lying states of an odd-mass spherical nucleus are considered to be states of a quasi-particle coupled to an even core. The quasi-particle modes are obtained by the Bogolyubov-Valatin transformation. The coupled linearized equations for the amplitudes of excitation of the states of the odd-mass nucleus are obtained by the equation-of-motion method. The problem is formulated so that only amplitudes of single excitations appear, as this automatically ensures hermiticity, in contrast to the second random phase approximation. This is accomplished by employing an expansion in terms of a complete set of states of the even core. The states of the core are treated by RPA. This method is called extended quasi-particle-phonon coupling (EQPC) as it can be regarded as an extension of the usual quasi-particle-phonon coupling (QPC) through the inclusion of the “backward-going” amplitudes. Preliminary numerical calculations, based on the pairing plus quadrupole force effective Hamiltonian, show that the effects of “backward-coupling” are very pronounced in the odd-mass isotopes of Tc, Rh and Ag. This mechanism seems to provide an explanation for the occurrence of low-lying phonon levels in these nuclei. The self-consistency of the theory is also discussed.