Model calculations of doubly closed shell nuclei in CBF theory III. j-j coupling and isospin dependence

Correlated Basis Function theory and Fermi Hypernetted Chain technique are extended to study medium-heavy, doubly closed shell nuclei in j-j coupling scheme, with different single particle wave functions for protons and neutrons and isospin dependent two-body correlations. Central semirealistic interactions are used. Ground state energies, one-body densities, distribution functions and momentum distributions are calculated for 12C, 16O, 40Ca, 48Ca and 208Pb nuclei. The values of the ground state energies provided by isospin dependent correlations are lower than those obtained with isospin independent correlations. In finite nuclear systems, the two--body Euler equations provide correlation functions variationally more effective than those obtained with the same technique in infinite nuclear matter.Comment: 29 Latex pages plus 6 Postscript figure

Low-lying magnetic excitations of doubly-closed-shell nuclei and nucleon-nucleon effective interactions

We have studied the low lying magnetic spectra of 12C, 16O, 40Ca, 48Ca and 208Pb nuclei within the Random Phase Approximation (RPA) theory, finding that the description of low-lying magnetic states of doubly-closed-shell nuclei imposes severe constraints on the spin and tensor terms of the nucleon-nucleon effective interaction. We have first made an investigation by using four phenomenological effective interactions and we have obtained good agreement with the experimental magnetic spectra, and, to a lesser extent, with the electron scattering responses. Then we have made self-consistent RPA calculations to test the validity of the finite-range D1 Gogny interaction. For all the nuclei under study we have found that this interaction inverts the energies of all the magnetic states forming isospin doublets.Comment: 19 pages, 13 figures, 7 tables, accepted for publication in Phys. Rev.

Weak response of nuclei

We discuss some differences and similarities between electron and neutrino scattering off atomic nuclei. We find that, in the giant resonance region, the two processes excite different nuclear modes, therefore the weak and the electromagnetic nuclear responses are rather different. In any case, the scattering of electrons and photons is the best guide we have to test the validity of our nuclear models and their prediction power. The experience in describing electromagnetic excitations of the nucleus, suggests that, when the nucleus is excited in the continuum, the re-interaction between the emitted nucleon and the remaining nucleus should not be neglected. A simple model taking into account this final state interaction is proposed, and applied to the neutrino scattering off 16O nucleus.Comment: To appear in the proceedings of the workshop "Electron-Nucleus Scattering VIII", Marciana Marina, Elba (It), jUNE 21-2

Proton emission induced by polarized photons

The proton emission induced by polarized photons is studied in the energy range above the giant resonance region and below the pion emission threshold. Results for the 12C, 16O and 40Ca nuclei are presented. The sensitivity of various observables to final state interaction, meson exchange currents and short range correlations is analyzed. We found relevant effects due to the virtual excitation of the $\Delta$ resonance.Comment: 12 pages, 11 figures, 1 tabl

Self-consistent Continuum Random Phase Approximation calculations with finite-range interactions

We present a technique which allows us to solve the Random Phase Approximation equations with finite-range interactions and treats the continuum part of the excitation spectrum without approximations. The interaction used in the Hartree-Fock calculations to generate the single particle basis is also used in the Continuum Random Phase Approximation calculations. We present results for the electric dipole and quadrupole excitations in the $^{16}$O, $^{22}$O, $^{24}$O, $^{40}$Ca, $^{48}$Ca and $^{52}$Ca nuclei. We compare our results with those of the traditional discrete Random Phase Approximation, with the continuum mean-field results and with the results obtained by a phenomenological approach. We study the relevance of the continuum, of the residual interaction and of the self-consistency. We also compare our results with the available total photoabsorption cross section data. We compare our photoabsorption cross section in $^4$He with that obtained by a calculation which uses a microscopic interaction.Comment: 25 pages, 14 figs., 4 tables, accepted for publication in Physical Review

Matter distribution and spin-orbit force in spherical nuclei

We investigate the possibility that some nuclei show density distributions with a depletion in the center, a semi-bubble structure, by using a Hartree-Fock plus Bardeen-Cooper-Schrieffer approach. We separately study the proton, neutron and matter distributions in 37 spherical nuclei mainly in the $s - d$ shell region. We found a relation between the semi-bubble structure and the energy splitting of spin-orbit partner single particle levels. The presence of semi-bubble structure reduces this splitting, and we study its consequences on the excitation spectrum of the nuclei under investigation by using a quasi-particle random-phase-approximation approach. The excitation energies of the low-lying $4^+$ states can be related to the presence of semi-bubble structure in nuclei.Comment: 15 pages, 7 tables, 11 figures. Version accepted for publication in Phys. Rev. C; the number of nuclei analysed has been reduced; some figure have bee redrawn, and a new figure and some references have been adde

A study of self-consistent Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations with finite-range interactions

In this work we test the validity of a Hartree-Fock plus Bardeen-Cooper-Schrieffer model in which a finite-range interaction is used in the two steps of the calculation by comparing the results obtained to those found in a fully self-consistent Hartree-Fock-Bogoliubov calculations using the same interaction.Specifically, we consider the Gogny-type D1S and D1M forces. We study a wide range of spherical nuclei, far from the stability line, in various regions of the nuclear chart, from oxygen to tin isotopes. We calculate various quantities related to the ground state properties of these nuclei, such as binding energies, radii, charge and density distributions and elastic electron scattering cross sections. The pairing effects are studied by direct comparison with the Hartree-Fock results. Despite of its relative simplicity, in most of the cases, our model provides results very close to those of the Hartree-Fock-Bogoliubov calculations, and it reproduces rather well the empirical evidences of pairing effects in the nuclei investigated.Comment: 28 pages, 13 figures. Accepted for publication in J. Phys.

Coulomb and spin-orbit interactions in random phase approximation calculations

We present a fully self-consistent computational framework composed by Hartree-Fock plus ran- dom phase approximation where the spin-orbit and Coulomb terms of the interaction are included in both steps of the calculations. We study the effects of these terms of the interaction on the random phase approximation calculations, where they are usually neglected. We carry out our investigation of excited states in spherical nuclei of oxygen, calcium, nickel, zirconium, tin and lead isotope chains. We use finite-range effective nucleon-nucleon interactions of Gogny type. The size of the effects we find is, usually, of few hundreds of keV. There are not simple approximations which can be used to simulate these effects since they strongly depend on all the variables related to the excited states, angular momentum, parity, excitation energy, isoscalar and isovector characters. Even the Slater approximation developed to account for the Coulomb exchange terms in Hartree-Fock is not valid in random phase approximation calculations.Comment: 14 pages, 5 figures; accepted for publication in Phys. Rev.

Ground state of medium-heavy doubly-closed shell nuclei in correlated basis function theory

The correlated basis function theory is applied to the study of medium-heavy doubly closed shell nuclei with different wave functions for protons and neutrons and in the jj coupling scheme. State dependent correlations including tensor correlations are used. Realistic two-body interactions of Argonne and Urbana type, together with three-body interactions have been used to calculate ground state energies and density distributions of the 12C, 16O, 40Ca, 48Ca and 208Pb nuclei.Comment: Latex 10 pages, 3 Tables, 10 Figure