Weak Pairing Regimes Research Articles

Pairing correlations and symmetries in odd-A nuclei.

The pairing correlations in odd-A nuclei are analyzed in the mean field approximation and beyond. In particular the role of symmetry conservation is investigated. We find that particle number projection after the variation (PN-PAV) has little effect on the pairing correlations specially in the weak pairing regime. This is in contrast to the variation after particle number projection (PN-VAP) approach where a strong effect is found. The situation is specially critical in odd nuclei because the pairing correlations vanish due to the blocking effect and the Hartree-Fock-Bogoliubov wave function collapses to the Hartree-Fock one. The PN-VAP, however, handles perfectly the exact blocking providing highly correlated wave functions. The role of the angular momentum projection is studied only in the PAV approach. We find small changes of the pairing correlation, at least at small angular momentum. In the calculations we use the Gogny interaction well suited to this kind of studies.

Projection techniques as methods of particle-number symmetry restoration

The accuracy of the variation before (VBP) and after (VAP) particle-number projection methods, the Lipkin-Nogami (LN) prescription, and the projected Lipkin-Nogami (PLN) method have been studied using two exactly solvable models. It is shown that the VBP and the LN methods are rather dubious not only in a weak pairing regime, but also in strong pairing for the evaluation of quantities other than the ground state energy. The PLN method provides good results for the ground and the excited state energies, but it must be used with caution for the occupation probabilities and the observables that strongly depend on it. It seems that the VAP is the only suitable method for a global description of the nuclear properties.

Ground-state properties of even-evenN=Znuclei within the Hartree-Fock-BCS and higher Tamm–Dancoff approaches

We calculate the ground-state properties of well deformed, even-even $N=Z$ nuclei in the region between $^{56}\mathrm{Ni}$ and $^{100}\mathrm{Sn}$ within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parametrization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a $n$-particle-$n$-hole expansion using up to $n=4$ particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties.

Microscopic description of the twist mode in normal and superfluid trapped Fermi gases

We investigate the ``twist'' mode (rotation of the upper against the lower hemisphere) of a dilute atomic Fermi gas in a spherical trap. The normal and superfluid phases are considered. The linear response to this external perturbation is calculated within the microscopic Hartree-Fock-Bogoliubov approach. In the normal phase the excitation spectrum is concentrated in a rather narrow peak very close to the trapping frequency. In the superfluid phase the strength starts to be damped and fragmented and the collectivity of the mode is progressively lost when the temperature decreases. In the weak-pairing regime some reminiscence of the collective motion still exists, whereas in the strong-pairing regime the twist mode is completely washed out. The disappearance of the twist mode in the strong-pairing regime with decreasing temperature is interpreted in the framework of the two-fluid model.