Nuclear pairing: New perspectives

Nuclear pairing correlations are known to play an important role in various single-particle and collective aspects of nuclear structure. After the first idea by A. Bohr, B. Mottelson, and D. Pines on similarity of nuclear pairing to electron superconductivity, S.T. Belyaev gave a thorough analysis of the manifestations of pairing in complex nuclei. The current revival of interest in nuclear pairing is connected to the shift of modern nuclear physics towards nuclei far from stability; many loosely bound nuclei are particle-stable only due to the pairing. The theoretical methods borrowed from macroscopic superconductivity turn out to be insufficient for finite systems such as nuclei, in particular, for the cases of weak pairing and proximity of continuum states. We suggest a simple numerical procedure of exact solution of the nuclear pairing problem and discuss the physical features of this complete solution. We show also how the continuum states can be naturally included in the consideration bridging the gap between the structure and reactions. The path from coherent pairing to chaos and thermalization and perspectives of new theoretical approaches based on the full solution of pairing are discussed.     

Nuclear pairing from chiral pion-nucleon dynamics

We use a recently improved version of the chiral nucleon-nucleon potential at next-to-next-to-leading order to calculate the ¹S₀ pairing gap in isospin-symmetric nuclear matter. The pairing potential consists of the long-range one- and two-pion exchange terms and two short-distance NN-contact couplings. We find that the inclusion of the two-pion exchange at next-to-next-to-leading order reduces substantially the cutoff dependence of the ¹S₀ pairing gap determined by solving a regularised BCS equation. Our results are close to those obtained with the universal low-momentum nucleon-nucleon potential V_low-k or the phenomenological Gogny D1S force.     

Nuclear moments of inertia in the absence of pairing

The nuclear moments of inertia in the absence of pairing are not equal to the rigid-body values because of quantal corrections due to the finite size of the system.     

The continuity equation and the Hamiltonian formalism in quantum mechanics

The relationship between the continuity equation and the HamiltonianH of a quantum system is investigated from a nonstandard point of view. In contrast to the usual approaches, the expression of the current densityJ is givenab initio by means of a transport-velocity operatorV _T, whose existence follows from a weak formulation of the correspondence principle. Once given a Hilbert-space metricM, it is shown that the equation of motion and the continuity equation actually represent a system in theunknown operatorsH andV _T, due to the arbitrariness on the initial condition of the quantum state. The general solution is given in some cases of special interest and a straightforward application to relativistic quantum mechanics is performed.This work was partially supported by the Ministero della Pubblica Istruzione.     

Nuclear matter equation of state with single particle correlations

Symmetrical nuclear matter at finite temperature is studied in the framework of the Brueckner-Hartree-Fock approximation extended to include single-particle correlations. A liquid-vapor phase transition is observed, wtih a critical temperature of about 20 MeV, in close similarity with Skyrme force calculations. The inclusion of single-particle correlations introduces a significant temperature dependence in the single-particle potential as well as in the nucleon effective mass. In this scheme the Hughenholtz-Van Hove theorem is well satisfied throughout the range of density and temperature considered.     

Nuclear equation of state and compression modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K _nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K _nm and the experimental and theoretical methods used to determine the value of K _nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.     

Nuclear matter equation of state and three-body forces

The energy per particle, symmetry energy, pressure, and free energy are calculated for symmetric nuclear matter using BHF approach with modern nucleon-nucleon CD-Bonn, Nijm1, Argonne v₁₈, and Reid 93 potentials. To obtain saturation in nuclear matter we add three-body interaction terms which are equivalent to a density-dependent two-nucleon interaction a la Skyrme force. Good agreement is obtained in comparison with previous theoretical estimates and experimental data.     

Nuclear shadowing and antishadowing in a unitarized BFKL equation

The nuclear shadowing and antishadowing effects are explained by a unitarized BFKL equation.The Q2-and x-variations of the nuclear parton distributions are detailed based on the level of the unintegrated gluon distribution.In particular,the asymptotical behavior of the unintegrated gluon distribution near the saturation limit in nuclear targets is studied. Our results in the nuclear targets are insensitive to the input distributions if the parameters are fixed by the data of a flee proton.     

Nuclear shadowing and antishadowing in a unitarized BFKL equation

The nuclear shadowing and antishadowing effects are explained by a unitarized BFKL equation. The Q²- and x-variations of the nuclear parton distributions are detailed based on the level of the unintegrated gluon distribution. In particular, the asymptotical behavior of the unintegrated gluon distribution near the saturation limit in nuclear targets is studied. Our results in the nuclear targets are insensitive to the input distributions if the parameters are fixed by the data of a free proton.     

Nuclear matter equation of state and σ-meson parameters

We try to determine phenomenologically the extent of in-medium modification of σ-meson parameters so that the saturation observables of the nuclear matter equation of state (EOS) are reproduced. To calculate the EOS we have used Brueckner-Bethe-Goldstone formalism with Bonn potential as two-body interaction. We find that it is possible to understand all the saturation observables, namely, saturation density, energy per nucleon and incompressibility, by incorporating in-medium modification of σ-meson-nucleon coupling constant and σ-meson mass by a few per cent.     

LOFF and breached pairing with cold atoms

We investigate here the Cooper pairing of fermionic atoms with mismatched Fermi surfaces using a variational construct for the ground state. We determine the state for different values of the mismatch of chemical potential for weak as well as strong coupling regimes including the BCS BEC cross over region. We consider Cooper pairing with both zero and finite net momentum. Within the variational approximation for the ground state and comparing the thermodynamic potentials, we show that (i) the LOFF phase is stable in the weak coupling regime; (ii) the LOFF window is maximum on the BEC side near the Feshbach resonance; and (iii) the existence of stable gapless states with a single Fermi surface for negative average chemical potential on the BEC side of the Feshbach resonance.     

Quantum entanglement and pairing correlation in the reduced BCS pairing model

Using the particle-hole version of the density-matrix renormalization-group technique, the pairing correlation and the quantum entanglement of the reduced BCS pairing model are investigated. Both of them behave smoothly from the weak to the strong coupling regimes. A convergence radius (∼1/ln Ω) of condensation energy is detected by the first order derivative of the block-block entanglement. Furthermore, the block-block entanglement in the strong coupling regime shows distinct size dependence, and a logarithmic volume law is suggested numerically.     

Collective properties of superconductors with nontrivial pairing

Three-and two-dimensional models of p-and d-pairing are constructed for superconductors and superfluid quantum liquids using the functional integration formalism. In these models, the collective excitation spectra are calculated for superconductors with nontrivial pairing (such as high-temperature superconductors (HTSC) and heavy-fermion superconductors (HFSC)) for p-and d-pairing. Both three-and two-dimensional systems are considered. Some of recent ideas concerning the realization of the mixture of different states in HTSC are considered. In particular, the mixture of states $d_{x^2 - y^2 } + id_{xy} $ is analyzed. The obtained results of calculations of collective excitation spectra in superconductors with nontrivial pairing may be used for determining the type of pairing and the order parameter in HTSC and HFSC and also for interpreting the experimental results on ultrasound and microwave absorption in these system.