Number projected isovector neutron–proton pairing effect in odd-mass nuclei

Abstract

A formalism which enables one to strictly conserve the number of particles when taking into account the isovector pairing correlations is presented in the case of odd-mass nuclei. With this aim, we had to first establish the expression of the projector for such systems. Expressions of the ground state and its energy have been exhibited. The model has been numerically tested in the framework of a schematic model.

Neutron-proton pairing correlations in odd mass systems

“…(19), it can be seen that the level not only contributes with the energy of the blocked proton but also with that of a pair of neutrons. It was not the case with the formalism of Refs [3] and [4]. At the limit when the np paring gap parameter goes to zero, one has:…”

“…H' may be diagonalized using the generalized Bogoliubov-Valatin transformation: (4) Even-Even System…”

“…(13) and that used in Refs. [3] and [4] i.e. is that the state ν is not only occupied by the blocked proton.…”

“…[3,4]: this limit exactly reduces to the product of the usual BCS (i.e. in the pairing between like-particles case) wave-functions which correspond to an even neutron number and an odd proton number.…”

“…Wave-functions which describe odd systems have been recently proposed, in the isovector pairing case, either before [3], or after the projection [4]. Nevertheless, as outlined in Refs [3][4], these states have the same defect: they do not exactly generalize the usual wave-functions in the pairing between like-particles case. In the present contribution, a new expression of the wave-function which describes odd mass systems is proposed using the blocked level technique.…”