Influence of monopole pairing on the energies of single-nucleon states in the problem of superconducting pairing correlations

A correlation function, the chemical potential, coefficients in a special Bogolyubov transformation, and single-quasiparticle energies were calculatedwith allowance for the effect of the monopole-pairing potential on the energies of single-particle nucleon states in the mean nuclear field.     

A test of the collective correlations calculation of the dipole states of28Si

We solve a one band hopping model in the presence of a homogeneous static electric fieldF. In this case the exact eigenvalues do form a ladder:E _m =m e Fa, the corresponding eigenfunctions are localized within the “tilted” band.     

The phase fixation in the systems with e-h pairing; collective modes and current states

The interband transitions make impossible the states with the uniform superfluid quasiparticles flux in the systems with e-h pairing. However, the states with the nonuniform superfluid flux may exist. The theory is applied to the system of spatially separated electrons and holes in the presence of interfilm transitions and whiskers.     

Empirical pairing gaps and neutron-proton correlations

Analysis of various mass formulas related to neutron-proton correlations in atomic nuclei is carried out.Using the example of the N =Z chain it is shown that for self-adjoint nuclei various formulas proposed in literature for estimating the np pairing energy lead to similar results. Significant differences between the calculation methods arise when nuclei with N = Z are considered, which allows to reveal the complexity of neutron-proton correlations in different types of atomic nuclei and to make assumptions on the correspondence of the mass relation to the real effect of np pairing. The Shell Model parametrization of the binding energy makes it possible to draw additional conclusions on the structure of mass formulas and their relationship.     

$\delta$-pairing forces and collective pairing vibrations

The collective pairing Hamiltonian is obtained in the framework of the generator coordinate method in the Gaussian overlap approximation with a slightly modified BCS function used as a generator function. The collective variable , measuring the monopole moment of the pairing field, and the gauge transformation angle are chosen as generator coordinates. The vibrational ground states are calculated by diagonalisation of the collective pairing Hamiltonian in the harmonic-oscillator basis.Received: 28 April 2003, Revised: 1 October 2003, Published online: 18 June 2004PACS: 21.30.-x Nuclear forces - 21.60.Ev Collective models     

Electron pairing correlations in a Kondo metal

Using part of the s-d exchange interaction in a reduced hamiltonian, we construct a variational ground state based on electron-hole pairing. The model is motivated by and compared with de Haas-van Alphen data on Cu : Cr.     

Particle-number fluctuation of pairing correlations for Dy isotopes

Within the relativistic mean field(RMF) theory, the ground state properties of dysprosium isotopes are studied using the shell-model-like approach(SLAP), in which pairing correlations are treated with particlenumber conservation, and the Pauli blocking effects are taken into account exactly. For comparison, calculations of the Bardeen–Cooper–Schrieffer(BCS) model with the RMF are also performed. It is found that the RMF+SLAP calculation results, as well as the RMF+BCS ones, reproduce the experimental binding energies and one- and twoneutron separation energies quite well. However, the RMF+BCS calculations give larger pairing energies than those obtained by the RMF+SLAP calculations, in particular for nuclei near the proton and neutron drip lines. This deviation is discussed in terms of the BCS particle-number fluctuation, which leads to the sizable deviation of pairing energies between the RMF+BCS and RMF+SLAP models, where the fluctuation of the particle number is eliminated automatically.     

Study of weak pairing correlations in aluminum nanograins

Weak pairing correlations in aluminum nanograins have been investigated using a symmetrical polynomial method based on the wave functions projected onto states with a fixed number of electrons. It is shown that this approach does not lead to a sharp transition from the superconducting to normal state with an increase in temperature, and the intensity of the pairing correlations exceeds that obtained using traditional BCS theory.     

High spin states and pairing vibrations

The Generator-Coordinate-Method is applied to describe yrast-bands and excited vibrational bands of pairing-vibrational orβ-vibrational type in deformed rare earth nuclei. The model wave functions are supplied by the Pairing+Quadrupole-Model with angular momentum — and particle number projection. Results are shown for the nucleus¹⁷⁰Yb. The question if backbending may be produced by the intersection of the ground and the neutron pairing vibrational band is discussed.     

Interplay of pairing and quadrupole correlations in deformed nuclei

We study pairing correlations in deformed nuclei in the framework of the Nilsson+BCS theory. As in the spherical case, the pairing interaction is found to induce strong spacial correlations between the partners of each paired couple. The presence of the deformed mean field gives rise to a non-spherical pair field, whose deformation is governed by the properties of a few single-particle orbitals around the Fermi surface and does not necessarily follow the shape of the mean field. Multipole expansion of the pair field yields all the pair densities associated with the direct two-particle transfer processes to the members of the g.s. rotational band in the A+2 system. The interplay of the deformations of the mean and the pair fields can lead to different relative magnitudes and phases of these densities and therefore to different excitation patterns of the rotational bands in two-particle transfer reactions. In the case of non-collective twoquasiparticles and bands the associated pair densities display large components with high multipoles and the associated transfer processes may be favoured in heavy-ion collisions by kinematical conditions. Examples corresponding to both prolate and oblate cases are considered.     

Excited collective states of heavy even-even nuclei

Quadrupole-type collective excitations of even-even nuclei are analyzed. In this analysis, transverse γ vibrations of the nuclear surface are taken into account effectively, while longitudinal beta vibrations remain free. A potential energy of the exponential form is used for free surface longitudinal beta vibrations. The behavior of the energy levels of excited states in the ground-state, β, and γ bands of heavy nuclei is studied, and the predictive potential of the model used is demonstrated for transfermium nuclei.     

Andreev states near short-ranged pairing potential impurities

We study Andreev states near atomic scale modulations in the pairing potential in both s- and d-wave superconductors with short coherence lengths. For a moderate reduction of the local gap, the states exist only close to the gap edge. If one allows for local sign changes of the order parameter, however, resonances can occur at energies close to the Fermi level. The local density of states (LDOS) around such pairing potential defects strongly resembles the patterns observed by tunneling measurements around Zn impurities in Bi2Sr2CaCu2O8+x (BSCCO). We discuss how this phase impurity model of the Zn LDOS pattern can be distinguished from other proposals experimentally.     

Self-consistency and search for collective effects in semiclassical pairing theory

A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the isoscalar nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The density response function is explicitly evaluated and it is shown that the energy-weighted sum rule is restored to its correct value by a part of the fluctuations of the imaginary pairing field. The remaining part of these imaginary fluctuations, together with the fluctuations of the real part, could give rise to collective excitations in the density response function. A detailed analysis of the monopole and quadrupole strength functions shows that there are practically no collective effects in these channels at low excitation energy.     

Skyrme-Hartree-Fock approach to spherical nuclei with density-dependent pairing correlations

The ground-state properties of spherical nuclei over the entire periodic table are investigated by the Skyrme-Hartree-Fock approach with new force parameters SKI4 [P. G. Reinhard and H. Flocard, Nucl. Phys. A584 467 (1995)] plus a density-dependent pairing correlation. By introducing the density-dependent pairing correlation in the Skyrme-Hartree-Fock model with SKI4, both the isospin degree of freedom and the nucleon-nucleon correlation have been suitably included in the theory. The theoretical results agree very well with experimental data of binding energies, single particle energies and radii of spherical nuclei. The isotope shifts of charge radii in Ca, Ni, Sn, and Pb are also well reproduced.