Introduction

Skyrme energy density functionals are among the most commonly used in the self-consistent mean-field nuclear structure calculations. The pairing component of the functional usually corresponds to a zero-range interaction in the coordinate space [1], which is equivalent to a constant (infinite range) interaction in the momentum space. Therefore, an energy cutoff followed by a pairing strength refit is necessary to regularize the results, and the number of active quasiparticle states becomes finite. On the other hand, the dimension of the particle space is either infinite (coordinate representation) or truncated for reasons that are not related to the pairing regularization. This implies different dimensions of particle and quasiparticle spaces and, therefore, renders the Bogoliubov transformation non-unitary. As a result, the pairing tensor is no longer antisymmetric, but it acquires a finite symmetric component.

In this work, we propose a method of restoring the unitarity of the Bogoliubov transformation, while keeping the number of quasiparticle states limited. The method is based on a truncation of the particle space and solving the Hartree-Fock-Bogoliubov [2] (HFB) equations in this truncated Hilbert space. The proposed truncation scheme accommodates all the particle states that are needed within a given truncation of the quasiparticle space.