S. S. Pankratov

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. PACS numbers: 21.60.-n, 21.65.+f, 26.60.+c, 97.60.Jd Microscopic evaluation of the pairing gap 2We 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 a few illustrative examples. The comparison of calculations of different groups on the same set of nuclei, besides agreements, also shows 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.

On the ab initio calculation of a pairing gap in atomic nuclei

The role of an effective mass in the ab initio BCS equation for a pairing gap in atomic nuclei has been analyzed.

Solution of the microscopic gap equation for a slab of nuclear matter with the Paris NN-potential

Abstract The gap equation in the S 0 1 -channel is solved for a nuclear slab with the separable form of the Paris potential. The gap equation is considered in the model space in terms of the effective pairing interaction which is found in the complementary subspace. The absolute value of the gap Δ turned out to be very sensitive to the cutoff K max in the momentum space in the equation for the effective interaction. It is necessary to take K max = 160 – 180 fm −1 to guarantee 1% accuracy for Δ . The gap equation itself is solved directly, without any additional approximations. The solution reveals the surface enhancement of the gap Δ which was earlier found with an approximate consideration. A strong surface-volume interplay was found also implying a kind of the proximity effect. The diagonal matrix elements of Δ turned out to be rather close to the empirical values for heavy atomic nuclei.

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T*, appears through a crossover at temperatures T ∼ T* > T⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T−α with the exponent α }~ 2/3.

Structure of the ground state of a nonsuperfluid dense quark-gluon plasma

The single-particle spectrum and momentum distribution of quasiparticles in a cold dense quark-gluon plasma are calculated within the Fermi liquid approach. It is shown that this system does not behave as a standard Fermi liquid: at zero temperature, the single-particle spectrum has a plateau at the Fermi surface, while the Fermi surface itself has a nonzero volume in momentum space.

Spatial correlation properties of the anomalous density matrix in a slab of nuclear matter with realistic NN forces

Spatial correlation characteristics of the anomalous density matrix x in a slab of nuclear matter with the Paris and Argonne v{sub 18} forces are calculated. A detailed comparison with predictions of the effective Gogny force is made. It is found that the two realistic forces lead to very close results that are qualitatively similar to those for the Gogny force. At the same time, the magnitude of x for realistic forces is essentially smaller than that for the Gogny force. The correlation characteristics are practically independent of the magnitude of x and turn out to be quite close for the three kinds of forces. In particular, all of them predict a small value of the local correlation length at the surface of the slab and a big one inside. These results are in agreement with those obtained recently by N. Pillet, N. Sandulescu, and P. Schuck [Phys. Rev. C, 76, 024310 (2007)] for finite nuclei with the Gogny force.

The microscopic pairing gap in a slab of nuclear matter for the Argonne v18 NN-potential

Abstract Ab initio gap equation for 1S0 pairing in a nuclear slab is solved for the Argonne v18 NN-potential. The gap function is compared in detail with the one found previously for the separable form of the Paris potential. The difference between the two gaps turned out to be about 10%. Dependence of the gap on the chemical potential μ is analyzed.

Effective pairing interaction for the Argonne nucleon-nucleon potential v18

The effective pairing interaction corresponding to the Argonne nucleon-nucleon potential v18 is found within the local potential approximation for several values of the boundary energy E0 that specifies the model subspace S0. A detailed comparison with the analogous effective interaction calculated previously for the Paris nucleon-nucleon potential is performed. It is shown that the effective interactions obtained for the two different nucleon-nucleon potentials at the same value of E0 are very close to each other. In the case of the Paris potential, a very wide subspace S′ complementary to S0 was required in calculating the effective interaction (the corresponding cutoff momentum being kmax = 160−180 fm−1), whereas a much narrower subspace S′ corresponding to kmax = 10−12 fm−1 could be used in the case of the Argonne potential.

On the topology of the Fermi surface in dense neutron matter

The model of dense neutron matter has been considered, where the topological rearrangement of the ground state of the system of Landau quasiparticles, which is associated with the appearance of the second sheet of the Fermi surface, occurs through two different scenarios. The rearrangement scenario depends on the relation between the wave vector qc of critical spin-isospin fluctuations and the Fermi momentum pF. Rearrangement at qc < pF occurs continuously with vanishing of the topological rigidity, whereas rearrangement at qc > pF occurs with the stepwise appearance of a bubble with a radius of about 0.5pF in the filled Fermi sphere.

Different scenarios of topological phase transitions in homogeneous neutron matter

We study different scenarios of topological phase transitions in the vicinity of the