Quasiparticle Resonances in the BCS Approach

We present a simple method for calculating the energies and the widths of quasiparticle resonant states. The method is based on BCS equations solved in the Berggren representation. In this representation the quasiparticle resonances are associated to the Gamow states of the mean field. The method is illustrated for the case of neutron-rich nuclei $^{20-22}$O and $^{84}$Ni. It is shown that the contribution of the continuum coupling to the pairing correlations is small and largely dominated by a few resonant states close to the continuum threshold.Comment: 14 pages, 2 figure

Superfluid Properties of the Inner Crust of Neutron Stars

Superfluid properties of the inner crust matter of neutron stars, formed by nuclear clusters immersed in a dilute neutron gas, are analysed in a self- consistent HFB approach. The calculations are performed with two pairing forces, fixed so as to obtain in infinite nuclear matter the pairing gaps provided by the Gogny force or by induced interactions. It is shown that the nuclear clusters can either suppress or enhance the pairing correlations inside the inner crust matter, depending on the density of the surrounding neutrons. The profile of the pairing field in the inner crust is rather similar for both pairing forces, but the values of the pairing gaps are drastically reduced for the force which simulates the polarisation effects in infinite neutron matter.Comment: 13 pages, 6 figures. Corrected typos and new format. To appear in Phys. Rev.

Two-Particle Resonant States in a Many-Body Mean Field

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum.Comment: 11 pages, 4 figure

Treatment of pairing correlations in nuclei close to drip lines

We discuss the HFB equations in coordinate representation,a suitable method for handling the full effects of the continuous quasiparticle spectrum. We show how the continuum HFB equations can be solved with the correct asymptotic conditions instead of the discretization conditions which are commonly used in the literature. The continuum HFB method is illustrated with a model where the mean field and pairing field have simple forms. The relationship with the continuum Hartree-Fock-BCS (HF-BCS) approximation is also discussed. Realistic HFB and HF-BCS calculations based on Skyrme interactions are compared for the case of a neutron-rich nucleus.Comment: 12 pages, 4 Postscript figures, uses KapProc.cls, to appear in Proceedings of NATO School " Nuclei far from stability and astrophysics", Predeal, Romania, 200

Pairing and alpha-like quartet condensation in N=Z nuclei

We discuss the treatment of isovector pairing by an alpha-like quartet condensate which conserves exactly the particle number, the spin and the isospin. The results show that the quartet condensate describes accurately the isovector pairing correlations in the ground state of systems with an equal number of protons and neutronsComment: 4 pages, to appear in Journal of Physics: Conference Serie

Pairing and continuum effects in nuclei close to the drip line

The Hartree-Fock-Bogoliubov (HFB) equations in coordinate representation are solved exactly, i.e., with correct asymptotic boundary conditions for the continuous spectrum. The calculations are preformed with effective Skyrme interactions. The exact HFB solutions are compared with HFB calculations based on box boundary conditions and with resonant continuum Hartree-Fock-BCS (HF-BCS) results. The comparison is done for the neutron-rich Ni isotopes. It is shown that close to the drip line the amount of pairing correlations depends on how the continuum coupling is treated. On the other hand, the resonant continuum HF-BCS results are generally close to those of HFB even in neutron-rich nuclei.Comment: 9 figures, corrected ref.

Shell corrections for finite depth potentials: Particle continuum effects

Shell corrections of finite, spherical, one-body potentials are analyzed using a smoothing procedure which properly accounts for the contribution from the particle continuum, i.e., unbound states. Since the plateau condition for the smoothed single-particle energy seldom holds, a new recipe is suggested for the definition of the shell correction. The generalized Strutinsky smoothing procedure is compared with the results of the semi-classical Wigner-Kirkwood expansion. A good agreement has been found for weakly bound nuclei in the vicinity of the proton drip line. However, some deviations remain for extremely neutron-rich systems due to the pathological behavior of the semi-classical level density around the particle threshold.Comment: 18 pages, 8 figure

Temperature dependent BCS equations with continuum coupling

The temperature dependent BCS equations are modified in order to include the contribution of the continuum single particle states. The influence of the continuum upon the critical temperature corresponding to the phase transition from a superfluid to a normal state and upon the behaviour of the excitation energy and of the entropy is discussed.Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Generalized seniority scheme in light Sn isotopes

The yrast generalized seniority states are compared with the corresponding shell model states for the case of the Sn isotopes $^{104-112}$Sn. For most of the cases the energies agree within 100 keV and the overlaps of the wave functions are greater than 0.7.Comment: 8 pages, revtex. Submitted to Phys. Rev.