Non-empirical pairing energy functional in nuclear matter and finite nuclei

We study 1S0 pairing gaps in neutron and nuclear matter as well as in finite nuclei on the basis of microscopic two-nucleon interactions. Special attention is paid to the consistency of the pairing interaction and normal self-energy contributions. We find that pairing gaps obtained from low-momentum interactions depend only weakly on approximation schemes for the normal self-energy, required in present energy-density functional calculations, while pairing gaps from hard potentials are very sensitive to the effective-mass approximation scheme.Comment: 14 pages, 12 figures, published versio

Chiral three-nucleon forces and pairing in nuclei

We present the first study of pairing in nuclei including three-nucleon forces. We perform systematic calculations of the odd-even mass staggering generated using a microscopic pairing interaction at first order in chiral low-momentum interactions. Significant repulsive contributions from the leading chiral three-nucleon forces are found. Two- and three-nucleon interactions combined account for approximately 70% of the experimental pairing gaps, which leaves room for self-energy and induced interaction effects that are expected to be overall attractive in nuclei.Comment: 4 pages, 3 figure

Microscopic evaluation of the pairing gap

We discuss the relevant progress that has been made in the last few years on the microscopic theory of the pairing correlation in nuclei and the open problems that still must be solved in order to reach a satisfactory description and understanding of the nuclear pairing. The similarities and differences with the nuclear matter case are emphasized and described by few illustrative examples. The comparison of calculations of different groups on the same set of nuclei show, besides agreements, also discrepancies that remain to be clarified. The role of the many-body correlations, like screening, that go beyond the BCS scheme, is still uncertain and requires further investigation.Comment: 21 pages,7 figures; minor modification, accepted for publication in J. Phys.

LOWEST-ORDER CONTRIBUTIONS OF CHIRAL THREE-NUCLEON INTERACTIONS TO PAIRING PROPERTIES OF NUCLEAR GROUND STATES

We perform a systematic study of the odd-even mass staggering generated using a pairing interaction computed at first order in low-momentum interactions. Building on previous work including the (nuclear plus Coulomb) two-nucleon interaction only, we focus here on the first-order contribution from chiral three-nucleon forces. We observe a significant repulsive effect from the three-nucleon interaction. The combined contribution from two- and three-nucleon interactions accounts for approximately 70% of the experimental pairing gaps. This leaves room for higher-order contributions to the pairing kernel and the normal self-energy that need to be computed consistently.Comment: 4 pages, 2 figures. Proceedings of the International Niigata 2010 Symposium on Forefronts of Researches in Exotic Nuclear Structures, Tokamachi, Japan, March 1 - March 4, 2010. To be published in Modern Physics Letters

Non-empirical pairing energy functional: lowest-order calculation

The nuclear Energy Density Functional (EDF) approach is used to study medium-mass and heavy nuclei in a systematic manner [1]. Even though currently used EDFs provide a satisfactory description of low-energy properties of known nuclei, their empirical character and the spreading of the results obtained from different parameterizations as one moves away from the valley of !-stability and enters experimentally-unexplored regions point to the lack of predictive power of today's calculations. Our objective is to improve on such a situation by designing non-empirical energy density functionals constrained explicitly from inter-nucleon interactions in the vacuum. As a starting point, we have performed the first systematic finite-nuclei calculations using a nuclear EDF whose pairing part is derived from low-momentum [2] two-nucleon interactions in the vacuum. At present, calculations have been performed for all semi-magic nuclei employing a pairing functional derived at lowest-order in the nuclear plus Coulomb two-nucleon interaction [3,4]. The analysis of the results and of their comparison with existing experimental data allow us to outline three important points. (i) The Coulomb interaction has a significant impact on proton-proton superfluidity in nuclei. (ii) Lowest-order calculations lead to qualitatively different results depending on whether one starts from a high-cutoff nuclear Hamiltonian or from a low-cut-off one [5]. (iii) Using a low-momentum nuclear Hamiltonian, as is recommended here, the agreement between theoretical and experimental pairing gaps put stringent constraints on the overall contribution from missing ingredients: partial waves with L > 0, the three-nucleon interaction and higher-order effects, e.g. the coupling to density/spin/isospin fluctuations. In order to reduce the computational cost of such non-empirical calculations and perform systematic symmetry-unrestricted calculations, is it of interest to design empirical local pairing functionals that reproduce the results provided by non-empirical ones. Taking our lowest-order results as an intermediate reference, we investigate the needed isoscalar- and isovector-density dependencies [6] of the empirical local pairing functional to do so. In this modeling, we explicitly separate the part of the pairing functional accounting for the Coulomb anti proton-pairing effect

Non-empirical pairing energy functional: lowest-order calculation

The nuclear Energy Density Functional (EDF) approach is used to study medium-mass and heavy nuclei in a systematic manner [1]. Even though currently used EDFs provide a satisfactory description of low-energy properties of known nuclei, their empirical character and the spreading of the results obtained from different parameterizations as one moves away from the valley of !-stability and enters experimentally-unexplored regions point to the lack of predictive power of today's calculations. Our objective is to improve on such a situation by designing non-empirical energy density functionals constrained explicitly from inter-nucleon interactions in the vacuum. As a starting point, we have performed the first systematic finite-nuclei calculations using a nuclear EDF whose pairing part is derived from low-momentum [2] two-nucleon interactions in the vacuum. At present, calculations have been performed for all semi-magic nuclei employing a pairing functional derived at lowest-order in the nuclear plus Coulomb two-nucleon interaction [3,4]. The analysis of the results and of their comparison with existing experimental data allow us to outline three important points. (i) The Coulomb interaction has a significant impact on proton-proton superfluidity in nuclei. (ii) Lowest-order calculations lead to qualitatively different results depending on whether one starts from a high-cutoff nuclear Hamiltonian or from a low-cut-off one [5]. (iii) Using a low-momentum nuclear Hamiltonian, as is recommended here, the agreement between theoretical and experimental pairing gaps put stringent constraints on the overall contribution from missing ingredients: partial waves with L > 0, the three-nucleon interaction and higher-order effects, e.g. the coupling to density/spin/isospin fluctuations. In order to reduce the computational cost of such non-empirical calculations and perform systematic symmetry-unrestricted calculations, is it of interest to design empirical local pairing functionals that reproduce the results provided by non-empirical ones. Taking our lowest-order results as an intermediate reference, we investigate the needed isoscalar- and isovector-density dependencies [6] of the empirical local pairing functional to do so. In this modeling, we explicitly separate the part of the pairing functional accounting for the Coulomb anti proton-pairing effect