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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.

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Jacek Dobaczewski
2005-01-23