Neutron 2p2p and 1f1f spin--orbit splittings in 40^{40}Ca, 36^{36}S, and 34^{34}Si N=20N=20 isotones: tensor--induced and pure spin--orbit effects

Neutron $2p$ and $1f$ spin--orbit splittings were recently measured in the isotones $^{37}$S and $^{35}$Si by $(d,p)$ transfer reactions. Values were reported by using the major fragments of the states. An important reduction of the $p$ splitting was observed, from $^{37}$S to $^{35}$Si, associated to a strong modification of the spin--orbit potential in the central region of the nucleus $^{35}$Si. We analyze $2p$ and $1f$ neutron spin--orbit splittings in the $N=20$ isotones $^{40}$Ca, $^{36}$S, and $^{34}$Si. We employ several Skyrme and Gogny interactions, to reliably isolate pure spin--orbit and tensor--induced contributions, within the mean--field approximation. We use interactions (i) without the tensor force; (ii) with the tensor force and with tensor parameters adjusted on top of existing parametrizations; (iii) with the tensor force and with tensor and spin--orbit parameters adjusted simultaneously on top of existing parametrizations. We predict in cases (ii) and (iii) a non negligible reduction of both $p$ and $f$ splittings, associated to neutron--proton tensor effects, from $^{40}$Ca to $^{36}$S. The two splittings are further decreased for the three types of interactions, going from $^{36}$S to $^{34}$Si. This reduction is produced by the spin--orbit force and is not affected by tensor--induced contributions. For both reductions, from $^{40}$Ca to $^{36}$S and from $^{36}$S to $^{34}$Si, we predict in all cases that the modification is more pronounced for $p$ than for $f$ splittings. The measurement of the centroids for neutron $2p$ and $1f$ states in the nuclei $^{36}$S and $^{34}$Si would be interesting to validate this prediction experimentally. We show the importance of using interactions of type (iii), because they provide $p$ and $f$ splittings in the nucleus $^{40}$Ca which are in agreement with the corresponding experimental values

Two Proton Emission with Electromagnetic Probes

A model to study two-proton emission from nuclei induced by electromagnetic probes is developed. The process is due to one-body electromagnetic operators, acting together with short-range correlations, and two-body $\Delta$ currents. The model includes all the diagrams containing a single correlation function. The sensitivity of the cross section to the details of the correlation function is studied by using realistic and schematic correlations. Results for the $^{16}$O nucleus are presented.Comment: 9 pages, 8 figures, Contribution to the 6th. Workshop on "Electromagnetic Induced Two-Hadron Emission",Pavia, 200

Photo-emission of two protons from nuclei

The photo-emission of two protons from the $^{12}$C, $^{16}$O and $^{40}$Ca nuclei is investigated. Aim of the work is the study of the possibilities offered by this probe to obtain information about the characteristics of the short-range correlations. We have also evaluated the effects of the two-body $\Delta$-currents which, in this processes, compete with those produced by the short-range correlations. Our results show that ($\gamma$,pp) processes could be more useful than (e,e'pp) for the study of the short-range correlations.Comment: 21 pages, 15 figures, 3 table

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

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.

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.

Mean-field Based Approaches to Pairing Correlations in Atomic Nuclei

The evolution of the pairing correlations from closed shell to middle shell nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn isotopes. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the Lipkin-Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairing regime is also approach dependent, specially at shell closure.Comment: 14 pages, 5 figure

Self-consistent continuum random phase approximation calculations of 4^4He electromagnetic responses

We study the electromagnetic responses of $^4$He within the framework of the self-consistent continuum random phase approximation theory. In this approach the ground state properties are described by a Hartree-Fock calculation. The single particle basis constructed in this manner is used in the calculations of the continuum responses of the system. Finite-range interactions are considered in the calculations. We compare our results with photon absorption cross sections and electron scattering quasi-elastic data. From this comparison, and also from the comparison with the results of microscopic calculations, we deduce that our approach describes well the continuum excitation.Comment: 6 pages, 1 table, 4 figures, accepted for publication in Physical Review