Introduction

Modern nuclear structure theory is rapidly expanding from the description of phenomena in stable nuclei toward regions of exotic short-lived nuclei far from stability. Stringent constraints on the microscopic approach to nuclear dynamics, effective nuclear interactions, and nuclear energy density functionals are obtained from studies of the structure and stability of exotic nuclei with extreme isospin values, as well as extended asymmetric nucleonic matter.

The Hartree-Fock-Bogoliubov (HFB) method is a reliable tool for a microscopic self-consistent description of nuclei, which can be used in the context of the density functional theory (DFT). We solve the HFB equations by using the Transformed Harmonic Oscillator (THO) basis [1], which allows for a correct asymptotic behavior of single-quasiparticle wave functions. The method is adopted for performing massive calculations for many axially deformed nuclei including those which are weakly bound [2].

Recently, it has been shown [3] that the total energy in the particle-number-projected (PNP) HFB approach can be expressed as a functional of the unprojected HFB density matrix and pairing tensor. Its variation leads to a set of HFB-like equations with modified Hartree-Fock fields and pairing potentials. The method has been illustrated within schematic models [3], and also implemented in HFB calculations with the finite-range Gogny force [4]. In the present paper, we adopt it for the Skyrme functionals and zero-range pairing term; in this case the building blocks of the method are the local densities and mean fields. The HFB results using the Lipkin-Nogami (LN) approximation, followed by the particle-number projection after variation (PLN), are compared to the HFB results with projection before variation (PNP).