Proton-neutron pairing in N=Z nuclei: quartetting versus pair condensation

The isoscalar proton-neutron pairing and isovector pairing, including both isovector proton-neutron pairing and like-particle pairing, are treated in a formalism which conserves exactly the particle number and the isospin. The formalism is designed for self-conjugate (N=Z) systems of nucleons moving in axially deformed mean fields and interacting through the most general isovector and isoscalar pairing interactions. The ground state of these systems is described by a superposition of two types of condensates, i.e., condensates of isovector quartets, built by two isovector pairs coupled to the total isospin T=0, and condensates of isoscalar proton-neutron pairs. The comparison with the exact solutions of realistic isovector-isoscalar pairing Hamiltonians shows that this ansatz for the ground state is able to describe with high precision the pairing correlation energies. It is also shown that, at variance with the majority of Hartree-Fock-Bogoliubov calculations, in the present formalism the isovector and isoscalar pairing correlations coexist for any pairing interactions. The competition between the isovector and isoscalar proton-neutron pairing correlations is studied for N=Z nuclei with the valence nucleons moving in the $sd$ and $pf$ shells and in the major shell above $^{100}$Sn. We find that in these nuclei the isovector pairing prevail over the isoscalar pairing, especially for heavier nuclei. However, the isoscalar proton-neutron correlations are significant in all nuclei and they always coexist with the isovector pairing correlations.Comment: 12 pages, 1 figur

Subtraction method in the second random--phase approximation: first applications with a Skyrme energy functional

We make use of a subtraction procedure, introduced to overcome double--counting problems in beyond--mean--field theories, in the second random--phase--approximation (SRPA) for the first time. This procedure guarantees the stability of SRPA (so that all excitation energies are real). We show that the method fits perfectly into nuclear density--functional theory. We illustrate applications to the monopole and quadrupole response and to low--lying $0^+$ and $2^+$ states in the nucleus $^{16}$O. We show that the subtraction procedure leads to: (i) results that are weakly cutoff dependent; (ii) a considerable reduction of the SRPA downwards shift with respect to the random--phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of 2 particle--2 hole configurations ($2p2h$) on the excitation spectra of medium--mass and heavy nuclei.Comment: 1 tex, 16 figure

Deformation effects on the coexistence between neutron-proton and particle like pairing in N=Z medium mass nuclei

A model combining self-consistent mean-field and shell-model techniques is used to study the competition between particle like and proton-neutron pairing correlations in fp-shell even-even self-conjugate nuclei. Results obtained using constant two-body pairing interactions as well as more sophisticated interactions are presented and discussed. The standard BCS calculations are systematically compared with more refined approaches including correlation effects beyond the independent quasi-particle approach. The competition between proton-neutron correlations in the isoscalar and isovector channels is also analyzed, as well as their dependence on the deformation properties. Besides the expected role of the spin-orbit interaction and particle number conservation, it is shown that deformation leads to a reduction of the pairing correlations. This reduction originates from the change of the single-particle spectrum and from a quenching of the residual pairing matrix elements. The competition between isoscalar and isovector pairing in the deuteron transfer is finally addressed. Although a strong dependence the isovector pairing correlations with respect to nuclear deformation is observed, they always dominate over the isoscalar ones.Comment: 16 pages, 14 figure

Second random-phase approximation with the Gogny force. First applications

We present the first applications of the second random-phase-approximation model with the finite-range Gogny interaction. We discuss the advantages of using such an interaction in this type of calculations where 2 particle-2 hole configurations are included. The results found in the present work confirm the well known general features of the second random-phase approximation spectra: we find a large shift, several MeV, of the response centroids to lower energies with respect to the corresponding random-phase-approximation values. As known, these results indicate that the effects of the 1 particle-1 hole/2 particle-2 hole and 2 particle-2 hole/2 particle-2 hole couplings are important. It has been found that the changes of the strength distributions with respect to the standard random-phase-approximation results are particularly large in the present case. This important effect is due to some large neutron-proton matrix elements of the interaction and indicates that these matrix elements (which do not contribute in the mean-field calculations employed in the conventional fit procedures of the force parameters) should be carefully constrained to perform calculation

Coexistence of quartets and pairs in even-even N>ZN>Z nuclei

We analyse the structure of the ground states of even-even $N>Z$ nuclei with nucleons moving in the same major shell and interacting via realistic two-body forces of shell-model type. We express the ground states of these nuclei as a product of a quartet term, which represents the $N = Z$ subsystem, and a pair condensate built with the excess neutrons. The accuracy of this approximation is discussed for nuclei with valence nucleons in the $sd$ and $pf$ major shells.Comment: 9 pages, 4 figure

Low-lying dipole response in the stable 40,48^{40,48}Ca nuclei with the second random-phase approximation

Low-energy dipole excitations are analyzed for the stable isotopes $^{40}$Ca and $^{48}$Ca in the framework of the Skyrme-second random-phase approximation. The corresponding random-phase approximation calculations provide a negligible strength distribution for both nuclei in the energy region from 5 to 10 MeV. The inclusion and the coupling of 2 particle-2 hole configurations in the second random-phase approximation lead to an appreciable dipole response at low energies for the neutron-rich nucleus $^{48}$Ca. The presence of a neutron skin in the nucleus $^{48}$Ca would suggest the interpretation of the low-lying response in terms of a pygmy excitation. The composition of the excitation modes (content of 1 particle-1 hole and 2 particle-2 hole configurations), their transition densities and their collectivity (number and coherence of the different contributions) are analyzed. This analysis indicates that, in general, these excitations cannot be clearly interpreted in terms of oscillations of the neutron skin against the core with the exception of the peak with the largest $B(E1)$ value, which is located at 9.09 MeV. For this peak the neutron transition density dominates and the neutron and proton transition densities oscillate out of phase in the internal part of the nucleus leading to a strong mixing of isoscalar and isovector components. Therefore, this state shows some features usually associated to pygmy resonances

Excitation of Pygmy Dipole Resonance in neutron-rich nuclei via Coulomb and nuclear fields

We study the nature of the low-lying dipole strength in neutron-rich nuclei, often associated to the Pygmy Dipole Resonance. The states are described within the Hartree-Fock plus RPA formalism, using different parametrizations of the Skyrme interaction. We show how the information from combined reactions processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.Comment: 9 Pages, 8 figures, contribution to International Symposium On Nuclear Physics, December 8-12, 2009,Bhabha Atomic Research Centre, Mumbai, Indi

Excitations of pygmy dipole resonances in exotic and stable nuclei via Coulomb and nuclear fields

We study heavy-ion inelastic scattering processes in neutron-rich nuclei including the full response to the different multipolarities. Among these we focus in particular on the excitation of low-lying dipole states commonly associated to the pygmy dipole resonance. The multipole response is described within the Hartree-Fock plus RPA formalism with Skyrme interaction. We show how the combined information from reactions processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states. We have performed calculation for the excitation of 132Sn generated in the reactions with 4He, 40Ca, and 48Ca at several incident energies, as well as for the system 17O +208Pb. Our results suggest that the investigation of the PDR states can be better carried out at low incident energies (below 50 MeV/nucleon). In fact, at these energies the PDR peak is relatively stronger than the giant dipole resonance (GDR) one and the narrow width of the low-lying quadrupole and octupole states should not blur its presence.Ministerio de Ciencia e Innovación (España) y FEDER FPA2009-07653 FIS2008-04189Programa Consolider-Ingenio 2010 (España) CSD2007-00042Junta de Andalucía P07-FQM-02894 FQM16