Theoretical understanding of the nuclear incompressibility: where do we stand ?

The status of the theoretical research on the compressional modes of finite nuclei and the incompressibility $K_\infty$ of nuclear matter, is reviewed. It is argued that the recent experimental data on the Isoscalar Giant Monopole Resonance (ISGMR) allow extracting the value of $K_\infty$ with an uncertainity of about $\pm$ 12 MeV. Non-relativistic (Skyrme, Gogny) and relativistic mean field models predict for $K_\infty$ values which are significantly different from one another, namely $\approx$ 220-235 and $\approx$ 250-270 MeV respectively. It is shown that the solution of this puzzle requires a better determination of the symmetry energy at, and around, saturation. The role played by the experimental data of the Isoscalar Giant Dipole Resonance (ISGDR) is also discussed.Comment: To appear in the proceedings of the COMEX1 conference (special issue of Nucl. Phys. A). Few changes and corrections compared to the previous version. General conclusion unchange

A self-consistent QRPA study of quadrupole collectivity around 32Mg

On the basis of the Hartree-Fock-Bogoliubov (HFB) plus quasiparticle random phase approximation method (QRPA) based on the Green's function approach with Skyrme force, we discuss the anomalous E2 properties of the first 2+ states in neutron-rich nuclei 32Mg and 30Ne. The B(E2) values and the excitation energies of the first 2+ states are well described within HFB plus QRPA calculations with spherical symmetry. We conclude that pairing effects account largely for the anomalously large B(E2) values and the low excitation energies in 32Mg and 30Ne.Comment: 5 pages, 5 figures, Proceedings of the international symposium "A new era of nuclear structure physics", 19-22 November 2003, Niigata, Japa

Isospin corrections for superallowed Fermi beta decay in self-consistent relativistic random phase approximation approaches

Self-consistent random phase approximation (RPA) approaches in the relativistic framework are applied to calculate the isospin symmetry-breaking corrections $\delta_c$ for the $0^+\to0^+$ superallowed transitions. It is found that the corrections $\delta_c$ are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections $\delta_c$, the nucleus-independent $\mathcal{F}t$ values are obtained in combination with the experimental $ft$ values in the most recent survey and the improved radiative corrections. It is found that the constancy of the $\mathcal{F}t$ values is satisfied for all effective interactions employed. Furthermore, the element $V_{ud}$ and unitarity of the Cabibbo-Kobayashi-Maskawa matrix are discussed.Comment: 7 pages, 2 figures, 4 table

Proton decay of high-lying states in odd nuclei

In the framework of the quasiparticle-phonon model, we study the non-statistical proton decay of excited states in odd nuclei towards low-lying collective states. Partial cross sections and branching ratios for the proton decay of the high angular momentum states in $^{41}$Sc, $^{59}$Cu and $^{91}$Nb %{\it excited by means of the ($^{7}$Li,$^{6}$He) reaction} are evaluated. The calculated branching ratios predict strong direct proton decays to the low-lying vibrational states in $^{41}$Sc and $^{91}$Nb. A general agreement with existing experimental data is found.Comment: 12 pages, 2 figures, Latex, accepted for publication in Nucl. Phys.

Pairing interactions and the vanishing pairing correlations in hot nuclei

Finite temperature Hartree-Fock-Bogoliubov calculations are performed in Sn isotopes using Skyrme and zero-range, density-dependent pairing interactions. For both stable and very neutron-rich nuclei the critical temperature at which pairing correlations vanish is independent of the volume/surface nature of the pairing interaction. The value of the critical temperature follows approximatively the empirical rule T$_c$ $\simeq$ 0.5 $\Delta_{T=0}$ for all the calculated isotopes, showing that the critical temperature could be deduced from the pairing gap at zero temperature. On the other hand, the pairing gap at temperatures just below T$_c$ is strongly sensitive to the volume/surface nature of the pairing interaction.Comment: 6 pages, 7 figures revised versio

Nuclear structure calculations with a separable approximation for Skyrme interactions

A finite rank separable approximation for the quasiparticle RPA calculations with Skyrme interactions that was proposed in our previous work is extended to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. It is shown that characteristics calculated within the suggested approach are in a good agreement with available experimental data.Comment: 6 pages, proceedings of the International Symposium on Physics of Unstable Nuclei (ISPUN02), Halong Bay, Vietnam, November 20-25, 200

Relativistic Hartree-Fock theory. Part I: density-dependent effective Lagrangians

Effective Lagrangians suitable for a relativistic Hartree-Fock description of nuclear systems are presented. They include the 4 effective mesons $\sigma, \omega, \rho$ and $\pi$ with density-dependent meson-nucleon couplings. The criteria for determining the model parameters are the reproduction of the binding energies in a number of selected nuclei, and the bulk properties of nuclear matter (saturation point, compression modulus, symmetry energy). An excellent description of nuclear binding energies and radii is achieved for a range of nuclei encompassing light and heavy systems. The predictions of the present approach compare favorably with those of existing relativistic mean field models, with the advantage of incorporating the effects of pion-nucleon coupling.Comment: 26 pages, 5 table

Effects of the tensor force on the ground and first 2+2^{+} states of the magic 54^{54}Ca nucleus

The magic nature of the $^{54}$Ca nucleus is investigated in the light of the recent experimental results. We employ both HFB and HF+BCS methods using Skyrme-type SLy5, SLy5+T and T44 interactions. The evolution of the single-particle spectra is studied for the N=34 isotones: $^{60}$Fe, $^{58}$Cr, $^{56}$Ti and $^{54}$Ca. An increase is obtained in the neutron spin-orbit splittings of $p$ and $f$ states due to the effect of the tensor force which also makes $^{54}$Ca a magic nucleus candidate. QRPA calculations on top of HF+BCS are performed to investigate the first $J^{\pi}$=$2^{+}$ states of the calcium isotopic chain. A good agreement for excitation energies is obtained when we include the tensor force in the mean-field part of the calculations. The first $2^{+}$ states indicate a subshell closure for both $^{52}$Ca and $^{54}$Ca nuclei. We confirm that the tensor part of the interaction is quite essential in explaining the neutron subshell closure in $^{52}$Ca and $^{54}$Ca nuclei.Comment: 8 pages, 3 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.