The Coriolis attenuation in the pairing plus recoil model

The attenuation factor of the Coriolis off diagonal matrix element has been found to be very sensitive to the pairing strength. About 10% extra reduction of the attenuation factor coming from the recoil term may be expected in the pairing plus recoil model for some Coriolis matrix elements, if a reasonable pairing gap parameter is taken.     

Pairing effects on the mass tensor for spontaneous fission

The monopole and quadrupole pairing effects on the fission mass tensor are considered. Two possible definitions of the quadrupole pairing matrix elements are investigated. They differ in dependence on deformation, leading to different behavior of the mass parameter with changing deformation. The effects of the usually neglected RPA terms are given in a simple expression. With monopole pairing alone the RPA terms do not contribute to the mass tensor, whereas the quadrupole pairing may have significant effects. Quantitative studies are carried out for a simple model which contains the important realistic features.     

Deformation properties of osmium,platinum, mercury isotopes from self-consistent calculations: Influence of the pairing treatment

The deformation properties of several isotopes of the elements Os, Pt and Hg have been computed by means of Hartree-Fock plus BCS calculations. The Hartree-Fock potential has been derived from the Skyrme interaction SIII. Two approximations have been used for the treatment of pairing correlations: the constant (versus deformation) gap method and the constant (versus deformation) pairing matrix element method. A good agreement with experimental data is obtained for ground state deformation properties except for the exact location of the prolate-oblate transition as a function of the neutron number. For one nucleus ¹⁸⁴Hg, the pairing matrix elements have been calculated from the Gogny interaction D1, in order to study their single-particle state — and deformation — dependence. From these results, the validity of the two approximations used for pairing correlations is discussed.     

Influence of pairing in double beta decay of <Superscript>48</Superscript>Ca

Two-neutrino ββ decay matrix elements and half-life of ⁴⁸Ca are calculated after including neutron-proton pairing correlations in projected Hartree-Fock-Bogoliubov (PHFB) formalism. The GT matrix elements in 2νββ decay are reduced due to broader smearing of Fermi surfaces. Half-life results for 2νββ decay of 48Ca with np pairing are better than without pairing.     

Multi-band pairing of ultrarelativistic electrons and holes in graphene bilayer

Multi-band pairing of effectively ultrarelativistic electrons and holes in asymmetrically biased graphene bilayer in strong coupling regime is considered. In this regime, the pairing affects both conduction and valence bands of the both graphene layers, and the order parameter is a matrix, which indices correspond to the bands. For band-diagonal s-wave pairing, we derive the system of multi-band gap equations for the gaps in the valence and conduction bands and solve it in the approximation of constant gaps and in the approximation of separable pairing potential. For a characteristic width of the pairing region of order of magnitude of the chemical potential, the gap values are not much different from single-band BCS estimations. However, if the pairing region is wider, then the gaps can be much larger and depend exponentially on its energy width. We also predict gapped and soliton-like oscillations of a relative phase of the gaps and unpairing of quarter-vortices at Kosterlitz-Thouless transition.     

On the influence of shell structure and matrix element fluctuations on the pairing correlation in nuclei

The uniform model for the nuclear pairing-force problem is extended to take into account the effect of fluctuations in nucleon orbital level densityρ and in pairing matrix elementsG _vv′. Simple formulas for the average dependence of level density on energy are presented, and alternative ways of estimating effects of shell bunching on the pairing correlation are derived. It is argued also that the pairing constantG might be systematically overestimated in the usual BCS numerical calculations; a semiconstant pairing force with diagonal elements larger than off-diagonal is thus suggested.     

Formal solutions for response functions of superconductors and 3He(B). I

The superfluid Fermi liquids with BCS and BW pairing are considered in the collisionless regime and with the effective quasiparticle interaction in the pairing channel, restricted to only one Legendre harmonic. In such a case, the density-density, density-current and current-current correlation functions are expressed in terms of matrix elements of some scalar operator and the gauge invariance of such expressions is proved. The expressions obtained for autocorrelation functions are discussed and some of their limiting values are established.     

Josephson current in an irradiated Weyl semimetal junction

The influence of the off-resonant circularly polarized light on the Josephson current in the time-reversal broken superconducting Weyl semimetal junctions is investigated by using the Bogoliubov–de Gennes equation and the transfer matrix approach. Both the zero momentum BCS pairing states and the finite momentum Fulde–Ferrell–Larkin–Ovchinnikov(FFLO) pairing states are considered for the Weyl superconductors. When a circularly polarized light is applied, it is shown that the current phase relation remains unchanged for the BCS pairing with the increasing of incident radiation intensity A_0. For FFLO pairing, the Josephson current exhibits the 0–π transition and periodic oscillation as a function of A_0. The dependence of free energy and critical current on A_0 are also investigated.     

Theory of superconductivity for Dirac electrons in graphene

Phonon-exchange-induced superconducting pairing of effectively ultrarelativistic electrons in graphene is investigated. The Eliashberg equation obtained for describing pairing in the Cooper channel with allowance for delayed interaction are matrix equations with indices corresponding to the valence and conduction bands. The equations are solved in the high doping limit, in which pairing is effectively a single-band process, and in the vicinity of a critical quantum point of underdoped graphene for a value of the coupling constant for which pairing is an essentially multiband process. For such cases, analytic estimates are obtained for the superconducting transition temperature of the system. It is shown that the inclusion of dynamic effects makes it possible to determine the superconducting transition temperature, as well as the critical coupling constant for underdoped graphene, more accurately than in the static approximation of the BCS type. Estimates of the constants of electron interaction with the scalar optical phonon mode in graphene indicate that an appreciable superconducting transition temperature can be attained under a high chemical doping level of graphene.     

A schematic model for monopole and quadrupole pairing in nuclei

A schematic Hamiltonian with a pairing interaction plus a quadrupole-quadrupole interaction between nucleons is presented. It is shown that all the states of the fermion system can be classified according to the number of nucleons u not coupled to coherent monopole or quadrupole pairs. The states with u = 0 are shown to have a one-to-one correspondence to the states of the interacting boson model. The spectra for these states are derived analytically for various limits of the pairing strength and the quadrupole strength. Analytical forms for the matrix elements of operators are derived for these limits. The operators in fermion space are mapped onto boson operators. The matrix elements of operators in the fermion space are shown to be equal to matrix elements of the boson operators multiplied by analytical Pauli factors which are state dependent. The two-nucleon transfer strength is calculated in two limits and is compared to experimental values.     

Coriolis attenuation in the rare earth region

It is shown that the observed rotational band structure in a number of odd-proton and odd-neutron nuclei situated in the rare earth region, can be reproduced in the particle-rotor model without any ad hoc reduction of the Coriolis matrix elements if a value of the pairing gap parameter, which is about 30–40% of that deduced from the corresponding odd-even mass difference, is used. The importance of the proper choice of the pairing gap parameter in the study of the Coriolis attenuation problem is emphasised.     

Variational approach to configuration interaction

A variational method is developed to determine configuration interaction wave functions. The method is straightforward and is applied to a pairing Hamiltonian with constant matrix elements, for which exact eigenvalues are available. Comparisons are made with the exact results. Calculations can be carried out to any desired degree of accuracy. The method is also applied to a Hamiltonian that has neutron-neutron, proton-proton, and neutron-proton pairing. No difficulties are found in extending the method to this Hamiltonian that has many collective modes. In practice, the method scales linearly with , where is the number of variational basis states.     

NUCLEAR PAIRING PHASE TRANSITION

The intrinsic structure of the eigenfunctions of Cranking Shell Model hamiltonian and the pairing phase transition at high rotational frequency are investigated with the particle-number-conserving approach.Pair-transfer matrix elements and the K-structure of the wave functions display similar behaviour under the Coriolis interaction and hence both of them may be used to indicate the pairing phase transition.The blocking effects on pairing parameter,,are much more important than the Coriolis anti-pairing effects.     

Study ofpf-shell nuclei with a symmetry conserving generator coordinate method

Bands based on the 0⁺ ground state and the first excited 0⁺ pairing vibrational state of⁴⁸Ti,⁵²Cr and⁵⁶Fe are studied with the generator coordinate method. The generating wave functions for each value of the angular momentumJ are angular momentum and particle number projected selfconsistent Hartree-Fock-Bogoliubov states where the constrained amount of pairing correlations serves as the generator coordinate. The interaction is given by reaction matrix elements derived from the Hamada-Johnston force. The basis includes the four lowest oscillator shells. The excitation energies of the pairing vibrational states can be reproduced fairly well by the present choice of the generating wave functions, whereas the ground band is not much improved compared to projected Hartree-Bogoliubov calculations. We find that the strength of the pairing correlations in the 0⁺ and 2⁺ states of the ground state and the pairing vibrational bands can be related to data of two-particle transfer reactions. The angular momentum dependence of the pairing correlations and of the moments of inertia are studied. The results show that for a strongly paired ground state the ground state band and the pairing vibrational band intersect. This may produce in the yrast band the anomaly of the moment of inertia known from rare earth nuclei.     

Role of the surface in nuclear pairing

Recent results obtained by solving the ab initio equation for the pairing gap in a slab of nuclear matter are reviewed. They conclusively prove a surface nature of nucleon pairing in nuclei. First, the effective pairing interaction in the vicinity of the slab surface makes a dominant contribution to the gap. Second, there is a sizable surface enhancement of the pairing gap Δ(X) itself. Finally, an analysis of spatial correlation features of the anomalous density matrix shows that the local correlation length at the slab surface is very small, about 1.5 fm, but, in the interior of the slab, it is rather large, about the slab thickness. These results are in qualitative agreement with those obtained recently by Pillet and his coauthors for spherical nuclei by using the phenomenological Gogny force. An increase in the concentration of Cooper pairs at the surface of nuclei was yet another result of their study, and our present analysis confirms this indirectly.