We make a systematic study of Li isotopes (A=9,10,11) in the tensor optimized shell model for 9Li and treat the additional valence neutrons in the cluster model approach by taking into account the Pauli-blocking effect caused by the tensor and pairing correlations. We describe the tensor correlations in 9Li fully in the tensor-optimized shell model, where the variation of the size parameters of the single particle orbits is essential for getting strong tensor correlations. We have shown in our previous study that in $^{10,11}$Li the tensor and pairing correlations in 9Li are Pauli-blocked by additional valence neutrons, which make the p-shell configurations pushed up in energy. As a result, the $s^2$ valence neutron component increases to reveal the halo structure of 11Li and the inversion phenomenon of the single particle spectrum in 10Li arises. Following the previous study, we demonstrate the reliability of our framework by performing a detailed systematic analysis of the structures of $^{9,10,11}$Li, such as the charge radius, the spatial correlation of halo neutrons of 11Li and the electromagnetic properties of Li isotopes. The detailed effects of the Pauli-blocking on the spectroscopic properties of $^{10,11}$Li are also discussed. It is found that the blocking acts strongly for the 11Li ground state rather than for 10Li and for the dipole excited states of 11Li, which is mainly caused by the interplay between the tensor correlation in 9Li and the halo neutrons. The results obtained in these analyses clearly show that the inert core assumption of 9Li is not realistic to explain the anomalous structures observed in $^{10,11}$Li. For the dipole excitation spectrum of 11Li, the effect of the final state interactions is discussed in terms of the dipole strength function.
We study the roles of the tensor and pairing correlations on the halo formation in 11Li with an extended 9Li+n+n model. We first solve the ground state of 9Li in the shell model basis by taking 2p-2h states using the Gaussian functions with variational size parameters to take into account the tensor correlation fully. In 11Li, the tensor and pairing correlations in 9Li are Pauli-blocked by additional two neutrons, which work coherently to make the configurations containing the 0p1/2 state pushed up and close to those containing the 1s1/2 state. Hence, the pairing interaction works efficiently …
In the latest version of the QMC model, QMC$π$-III-T, the density functional is improved to include the tensor component quadratic in the spin-current and a pairing interaction derived in the QMC framework. Traditional pairing strengths are expressed in terms of the QMC parameters and the parameters of the model optimised. A variety of nuclear observables are calculated with the final set of parameters. The inclusion of the tensor component improves the predictions for ground-state bulk properties, while it has a small effect on the single-particle spectra. Further, its effect on the deformati…
The Hartree-Fock-Bogolyubov (HFB) plus proton-neutron quasiparticle random phase approximation (pnQRPA) approach based on Skyrme interaction is applied to study the nuclear $β^+$/EC decay for nuclei near the proton magic numbers $Z=$20, 28, and 50. With properly selected Skyrme interactions that include the tensor terms, and the $T=0$ pairing interaction, the experimental $β^+$/EC decay half-lives of these nuclei can be systematically reproduced quite well. It is shown that the tensor and $T=0$ pairing interactions play different roles in different nuclei. The specific effect is relevant to th…
A shell-model study of proton-neutron pairing in $2p1f$ shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are able to assess the role of the various modes of proton-neutron pairing in the presence of nuclear deformation without violating symmetries. Results are presented for $^{44}$Ti, $^{45}$Ti, $^{46}$Ti, $^{46}$V and $^{48}$Cr to assess how proton-neutron pair correlations emerge under different scenarios. We also study how the presence of a one-body …
The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitati…
We study tensor and pairing effects on the quadruple deformation of neon isotopes based on a deformed Skyrme-Hartree-Fock model with BCS approximation for the pairing channel. We extend the Skyrme-Hartree-Fock formalism for the description of single- and double-lambda hypernuclei adopting two different hyperon-nucleon interactions. It is found that the interplay of pairing and tensor interactions is crucial to derive the deformations in several neon isotopes. Especially, the shapes of $^{26,30}$Ne are studied in details in comparisons with experimentally observed shapes. Furthermore the deform…
We perform a systematic investigation of the chemical composition of the inner crust of a neutron star, using the extended Thomas-Fermi approximation, the Strutinsky integral correction for shell effects, and the BCS approximation for pairing. Fifteen Skyrme functionals were selected, which cover the range of values of important bulk properties of infinite nuclear matter, while also having pure neutron matter (PNM) equation of states (EoS) with varying degrees of stiffness. We find that a functional's low-density PNM EoS is correlated with the number of protons found in the inner crust's nucle…
The recently-proposed effective shell-model interaction, the pairing-plus-multipole Hamiltonian with the monopole interaction obtained by empirical fits starting from the monopole-based universal force (PMMU), is systematically applied to nuclei of the pf5/2g9/2 shell region. It is demonstrated that the calculation describes reasonably well a wide range of experimental data, including not only the low-lying and high-excitation spectra, E2 transitions, quadrupole moments, and magnetic moments, but also the binding energies, for Ni, Cu, Zn, Ga, Ge, As, and Se isotopes with A=64-80. In particular…
Surface properties of neutron-neutron (T=1) pairing in semi-infinite nuclear matter in a hard wall potential are investigated in BCS approximation using the Gogny force. Surface enhancement of the gap function, pairing tensor and correlation energy density is put into evidence.
We discuss the effect of pairing on two-neutron space correlations in deformed nuclei. The spatial correlations are described by the pairing tensor in coordinate space calculated in the HFB approach. The calculations are done using the D1S Gogny force. We show that the pairing tensor has a rather small extension in the relative coordinate, a feature observed earlier in spherical nuclei. It is pointed out that in deformed nuclei the coherence length corresponding to the pairing tensor has a pattern similar to what we have found previously in spherical nuclei, i.e., it is maximal in the interior…
$^{3}P_{2}$ pairing in neutron matter is investigated using the Bonn potential models. We find pairing energy gaps in pure neutron matter comparable to the results of previous investigators when the attractive tensor coupling is included. However, taking into account that in a neutron star we have matter at $β$ equilibrium, we find that the $^{3}P_{2}$-$^{3}F_{2}$ energy gap is reduced considerably.
A systematic analysis of the ground state and fission properties of actinides and superheavy nuclei important for the $r$ process modeling has been performed within the framework of covariant density functional theory for the first time in Ref. [1]. A brief review of the results related to the heights of primary fission barriers and systematic uncertainties in their prediction is presented. In addition, new results on the potential impact of the isospin dependence of pairing on fission barriers in fission cycling regions is provided for the first time.
S-wave pairing in neutron matter is studied within an extension of correlated basis function (CBF) theory to include the strong, short range spatial correlations due to realistic nuclear forces and the pairing correlations of the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator contains central as well as tensor components. The correlated BCS scheme of Ref. [Nucl. Phys. A363 (1981) 383], developed for simple scalar correlations, is generalized to this more realistic case. The energy of the correlated pair condensed phase of neutron matter is evaluated at the two--body or…
An abrupt change in $α$ decay systematics around the N=126 neutron shell closure is discussed. It is explained as a sudden hindrance of the clustering of the nucleons that eventually form the $α$ particle. This is because the clustering induced by the pairing mode acting upon the four nucleons is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.
Absolute values of two-particle transfer cross sections along the Sn-isotopic chain from closed shell to closed shell (100Sn,132Sn) are calculated taking properly into account nuclear correlations, as well as the successive, simultaneous and non-orthogonality contributions to the differential cross sections. The results are compared with systematic, homogeneous bombarding conditions (p, t) data. The observed agreement, almost within statistical errors and without free parameters, testify to the fact that theory is able to be quantitative in its predictions.
We propose a simple systematics of low lying 2+ energy levels and electromagnetic transitions in semi-magic isotopic chains Z=28,50,82 and isotonic chains N=28,50,82,126. To this purpose we use a two-level pairing plus quadrupole Hamiltonian, within the spherical Quasiparticle Random Phase Approximation (QRPA). We derive a simple relation connecting the 2+ energy with the pairing gap and quadrupole-quadupole (QQ) interaction strength. It turns out that the systematics of energy levels and B(E2) values predicted by this simple model is fulfilled with a reasonable accuracy by all available exper…
The recently proposed Symmetry-Conserving Energy Density Functional approach [G. Hupin, D. Lacroix and M. Bender, Phys. Rev. C84, 014309 (2011)] is applied to perform Variation After Projection onto good particle number using Skyrme interaction, including density dependent terms. We present a systematic study of the Kr and Sn isotopic chains. This approach leads to non-zero pairing in magic nuclei and a global enhancement of the pairing gap compared to the original theory that breaks the particle number symmetry. The need to consistently readjust the pairing effective interaction strength is d…
Stimulated by the still puzzling competition between spin-singlet and spin-triplet pairing in nuclei, the 3SD1 neutron-proton pairing is investigated in the framework of BCS theory of nuclear matter. The medium polarization effects are included in the single particle spectrum and also in the pairing interaction starting from the G-matrix, calculated in the Brueckner-Hartree-Fock approximation. The vertex corrections due to spin and isospin collective excitations of the medium are determined from the Bethe-Salpeter equation in the RPA limit, taking into account the tensor correlations. It is fo…
This work aims at a global assessment of the effect of the density dependence of the zero-range pairing interaction. Systematic Skyrme-Hartree-Fock-Bogoliubov calculations with the volume, surface and mixed pairing forces are carried out to study the pairing gaps in even-even nuclei over the whole nuclear chart. Calculations are also done in coordinate representation for unstable semi-magic even-even nuclei. The calculated pairing gaps are compared with empirical values from four different odd-even staggering formulae. Calculations with the three pairing interactions are comparable for most nu…
A survey of pairing properties of nucleonic matter is presented that includes the off-shell propagation associated with short-range and tensor correlations. For this purpose, the gap equation has been solved in its most general form employing the complete energy and momentum dependence of the normal self-energy contributions. The latter correlations include the self-consistent calculation of the nucleon self-energy that is generated by the summation of ladder diagrams. This treatment preserves the conservation of particle number unlike approaches in which the self-energy is based on the Brueck…
We perform a systematic study of Gamow-Teller (GT) transitions in the 2p1f shell, using the nuclear shell model with two schematic Hamiltonians. The use of the shell model provides flexibility to analyze the role of different proton-neutron pairing modes in the presence of nuclear deformation. The schematic Hamiltonians that are used contain a quadrupole-quadrupole interaction as well as isoscalar (T=0) and isovector (T=1) pairing interactions, but differ in the single particle energies. The objective of the work is to observe the behavior of GT transitions in different isoscalar and isovector…
Effects of pairing with isospin $T=0$ and $T=1$ are systematically studied in a model, which is based on a realistic nucleon-nucleon interaction and allows to describe the transition from infinite nuclear matter to finite nuclei. Special attention is paid to the development of the spin-orbit term in the mean field of nucleons in finite nuclei. The spin-orbit term yields a drastic suppression of $T=0$ proton-neutron pairing but does not lead to a complete disappearance in finite nuclei. Arguments are presented, why no clear evidence of $T=0$ pairing can be observed in the binding energies of fi…
We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the $T=1$ pairing condensate offers a quantitative description of the binding-energy differences of open-shell superfluid nuclei. We conclude that the pairing-rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-…
The isoscalar (IS) and isovector (IV) quadrupole responses of nuclei are systematically investigated using the time-dependent Skyrme Energy Density Functional including pairing in the BCS approximation. Using two different Skyrme functionals, Sly4 and SkM*, respectively 263 and 304 nuclei have been found to be spherical along the nuclear charts. The time-dependent evolution of these nuclei has been systematically performed giving access to their quadrupole responses. It is shown that the mean-energy of the collective high energy state globally reproduces the experimental IS and IV collective e…
The present contribution reports the first systematic finite-nucleus calculations performed using the Energy Density Functional method and a non-empirical pairing functional derived from low-momentum interactions. As a first step, the effects of Coulomb and the three-body force are omitted while only the bare two-nucleon interaction at lowest order is considered. To cope with the finite-range and non-locality of the bare nuclear interaction, the 1S0 channel of Vlowk is mapped onto a convenient operator form. For the first time, neutron-neutron and proton-proton pairing correlations generated i…
We analyze the localization properties of two-body correlations induced by pairing in the framework of relativistic mean field (RMF) models. The spatial properties of two-body correlations are studied for the pairing tensor in coordinate space and for the Cooper pair wave function. The calculations are performed both with Relativistic-Hatree-Bogoliubov (RHB) and RMF+Projected-BCS (PBCS) models and taking as examples the nuclei $^{66}$Ni, $^{124}$Sn and $^{200}$Pb. It is shown that the coherence length have the same pattern as in previous non-relativistic HFB calculations, i.e., it is maximum i…
The neutron and proton odd-even mass differences are systematically studied with Hartree-Fock+BCS (HFBCS) calculations with Skyrme interactions and an isospin dependent contact pairing interaction. The strength of pairing interactions is determined to reproduce empirical odd-even mass differences in a wide region of mass table. By using the optimal parameter, we perform global HF+BCS calculations of nuclei and compare with experimental data. The importance of isospin dependence of the pairing interaction is singled out for odd-even mass differences in medium and heavy isotopes. The proton and …
Rotating $N=Z$ nuclei in the mass $A=58-80$ region have been studied within the framework of isovector mean field theory. Available data is well and systematically described in the calculations. The present study supports the presence of strong isovector $np$ pair field at low spin, which is, however, destroyed at high spin. No clear evidence for the existence of the isoscalar $t=0$ $np$ pairing has been found.
Much interest has been devoted to the shape evolution of neutron-rich Si isotopes recently both experimentally and theoretically. We provide our study of $^{28-42}$Si by Skyrme-Hartree-Fock model with BCS approximation for the pairing channel. We use an empirical pairing parameter deduced from the experimental binding energy data for each nuclei and each Skyrme parametrization. The recent highlight of the deformation change from a prolate shape of $^{38}$Si to an oblate shape of $^{42}$Si is confirmed in the present model. We also emphasize the role of tensor force on deformations of neutron-r…
In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree-Fock-Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like-particle and proton-neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the g…
Exotic and drip-line nuclei as well as nuclei immersed in a low density gas of neutrons in the outer crust of neutron stars are systematically investigated with respect to their neutron pairing properties. This is done using Skyrme density-functional and different pairing forces such as a density-dependent contact interaction and a separable form of a finite-range Gogny interaction. Hartree-Fock-Bogoliubov and BCS theories are compared. It is found that neutron pairing is reduced towards the drip line while overcast by strong shell effects. Furthermore resonances in the continuum can have an i…
An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a fermion system trapped in a harmonic potential to test its feasability by comparison with the exact solution. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant.
We study the correlation energy associated with the pair fluctuations in BCS theory. We use a schematic two-level pairing model and discuss the behavior of the correlation energy across shell closures, including the even-odd differences. It is shown that the random phase approximation (RPA) to the ground state energy reproduces the exact solutions quite well both in the normal fluid and in the superfluid phases. In marked contrast, other methods to improve the BCS energies such as Lipkin-Nogami method, only work when the strength of a pairing interaction is large. We thus conclude that the RPA…
A systematic study of the pairing correlations as a function of temperature and angular momentum has been performed in the sd-shell region using the spherical shell model approach. The pairing correlations have been derived for even-even, even-odd and odd-odd systems near N=Z and also for the asymmetric case of N=Z+4. The results indicate that the pairing content and the behavior of pair correlations is similar in even-even and odd-mass nuclei. For odd-odd N=Z system, angular momentum I=0 state is an isospin, t=1 neutron-proton paired configuration. Further, these t=1 correlations are shown to…
The $^3P_2$-$^3F_2$ pairing model is generally considered to provide an adequate description of the superfluid states of neutron matter at densities some 2-3 times that of saturated symmetrical nuclear matter. The problem of solving the system of BCS gap equations expressing the $^3P_2$-$^3F_2$ model is attacked with the aid of the separation approach. This method, developed originally for quantitative study of S-wave pairing in the presence of strong short-range repulsions, serves effectively to reduce the coupled, singular, nonlinear BCS integral equations to a set of coupled algebraic equat…
The linear response approach to nuclear transport has been extended to pair correlations. The latter are treated within a mean field approximation to a pairing interaction with constant matrix elements $G$. The constraint of particle number conservation has been accounted for on a time dependent average, which leads to modified response functions, both in the pairing degree of freedom as well as in the shape variable. The former is expressed by the gap parameter $Δ$ and the latter by a $Q$ which specifies the elongation of a fissioning nucleus. The tensors for friction and inertia correspondin…
Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes. To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of $^{264}$Fm and $^{240}$Pu using the state-of-the-art self-consistent frame…
Pairing gaps in neutron matter need to be computed in a wide range of densities to address open questions in neutron star phenomenology. Traditionally, the Bardeen-Cooper-Schrieffer approach has been used to compute gaps from bare nucleon-nucleon interactions. Here, we incorporate the influence of short- and long-range correlations in the pairing gaps. Short-range correlations are treated including the appropriate fragmentation of single-particle states, and substantially suppress the gaps. Long-range correlations dress the pairing interaction via density and spin modes, and provide a relative…
The separation method developed earlier by us [Nucl. Phys. {\bf A598} 390 (1996)] to calculate and analyze solutions of the BCS gap equation for $^1$S$_0$ pairing is extended and applied to $^3$P$_2$--$^3$F$_2$ pairing in pure neutron matter. The pairing matrix elements are written as a separable part plus a remainder that vanishes when either momentum variable is on the Fermi surface. This decomposition effects a separation of the problem of determining the dependence of the gap components in a spin-angle representation on the magnitude of the momentum (described by a set of functions indepen…
We have done systematic Hartree-Fock-Bogoliubov calculations in coordinate space on the one-quasi-particle energies and binding energy odd-even staggering (OES) in semi-magic nuclei with the zero-range volume, mixed and surface pairing forces in order to explore the influence of their density dependence. The odd-$N$ isotopes are calculated within the blocking scheme. The strengths for the pairing forces are determined in two schemes by fitting locally to reproduce pairing gap in $^{120}$Sn and globally to all available data on the OES of semi-magic nuclei with $Z\geq8$. In the former calculati…
A systematic study of the effect of tensor force on the evolution of shell structure in even-even super-heavy nuclei in the region of proton numbers Z=114, 120 and 126 and in the region of neutron numbers 178 $\le$ N $\le$ 188 is presented. We use, in this investigation, the Hartree-Fock framework by means of different types of Skyrme functionals in two cases with and without tensor force. The Bardeen-Cooper-Schriefer (BCS) approximation has been used to treat the pairing correlations. By investigating structural and decay properties of nuclei under consideration, it is found that N=184 shell …
The collective ground-state correlations stemming from low-lying quadrupole excitations are computed microscopically. To that end, the self-consistent mean-field model is employed on the basis of the Skyrme-Hartre-Fock (SHF) functional augmented by BCS pairing. The microscopic-macroscopic mapping is achieved by quadrupole-constrained mean-field calculations which are processed further in the generator-coordinate method (GCM) at the level of the Gaussian overlap approximation (GOA). We study the correlation effects on energy, charge radii, and surface thickness for a great variety of semi-magic…
We address consequences of strong tensor and weak spin-orbit terms in the local energy density functional, resulting from fits to the $f_{5/2} - f_{7/2}$ splittings in $^{40}$Ca, $^{48}$Ca, and $^{56}$Ni. In this study, we focus on nuclear binding energies. In particular, we show that the tensor contribution to the binding energies exhibits interesting topological features closely resembling that of the shell-correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to $N(Z)$=14, 32, 56, and 90, and t…
A direct fit of the isoscalar spin-orbit (SO) and both isoscalar and isovector tensor coupling constants to the f5/2-f7/2 SO splittings in 40Ca, 56Ni, and 48Ca nuclei requires a drastic reduction of the isoscalar SO strength and strong attractive tensor coupling constants. The aim of this work is to address further consequences of these strong attractive tensor and weak SO fields on binding energies, nuclear deformability, and high-spin states. In particular, we show that contribution to the nuclear binding energy due to the tensor field shows generic magic structure with tensorial magic numbe…
Excitation energies and transition probabilities of the first 2+ excitations in even lead, tin and nickel isotopes are calculated within the self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al. A reasonable agreement with available experimental data is obtained. The effect of the density dependence of the effective pairing interaction is analyzed in detail by comparing results obtained with volume and surface pairing. The effect is found to be noticeable, especially for the 2+ energies which are systematically higher at 200-300 keV for the volu…
A systematic study of the pairing-correlations derived from various particle-number projection methods is performed in an exactly soluble cranked-deformed shell model Hamiltonian. It is shown that most of the approximate particle-number projection methods including the method of Lipkin-Nogami, which is used quite extensively in nuclear structure studies, breakdown in the weak pairing limit. The results obtained from the recently formulated number-projected Hartree-Fock-Bogoliubov (PHFB) equations, on the other hand, are in complete agreement with the exact solutions of the model Hamiltonian. T…
A model combining self-consistent mean-field and shell-model techniques is used to study the competition between particle like and proton-neutron pairing correlations in fp-shell even-even self-conjugate nuclei. Results obtained using constant two-body pairing interactions as well as more sophisticated interactions are presented and discussed. The standard BCS calculations are systematically compared with more refined approaches including correlation effects beyond the independent quasi-particle approach. The competition between proton-neutron correlations in the isoscalar and isovector channe…
The effect of pairing correlation on transfer reaction below the Coulomb barrier is investigated qualitatively and quantitatively using a simplified version of the Time-Dependent Hartree-Fock + BCS approach. The effect of particle number symmetry breaking on the description of reaction and dedicated methods to extract one and two-nucleon transfer probabilities (P_{1n} and P_{2n}) in a particle number symmetry breaking approach are discussed. Influence of pairing is systematically investigated in the ^{40}Ca+ ^{40,42,44,46,48,50}Ca reactions. A strong enhancement of the two-particle transfer pr…
In this paper we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction $V_{pn}$ thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the $V_{pn}$ in even-even nuclei with $N\neq Z$ are dominated by the contribution from the proton-neutron monop…
The relative current density $n^i$ of conduction neutrons in a neutron star crust beyond the neutron drip threshold can be expected to be related to the corresponding particle momentum covector $p_i$ by a linear relation of the form $n^i=K^{ij}p_j$ in terms of a physically well defined mobility tensor $K^{ij}$. This result is describable as an ``entrainment'' whose effect - wherever the crust lattice is isotropic - will simply be to change the ordinary neutron mass m to an effective mass $m_\star$ such that in terms of the relevant number density n of unconfined neutrons we shall have $K^{ij}=…
Pairing correlation of Cooper pair is a fundamental property of multi-fermion interacting systems. For nucleons, two modes of the Cooper-pair coupling may exist, namely of $S_{12}=0$ with $L_{12}=0$ (spin-singlet s-wave) and $S_{12}=1$ with $L_{12}=1$ (spin-triplet p-wave). In nuclear physics, it has been an open question whether the spin-singlet or spin-triplet coupling is dominant, as well as how to measure their role. We investigate a relation between the magnetic-dipole (M1) excitation of nuclei and the pairing modes within the framework of relativistic nuclear energy-density functional (R…
For the first time, a wide range of collective magnetic g-factors g$_{\rm R}$, obtained from a novel analysis of experimental data for multi-quasiparticle configurations in high-K isomers, is shown to exhibit a striking systematic variation with the relative number of proton and neutron quasiparticles, N$_{\rm p}$ - N$_{\rm n}$. Using the principle of additivity, the quasi-particle contribution to magnetism in high-K isomers of Lu - Re, Z = 71 - 75, has been estimated. Based on these estimates, band-structure branching ratio data are used to explore the behaviour of the collective contribution…
A new method has been proposed to determine the strength of the isoscalar proton-neutron pairing interaction applicable to many nuclei. The principle is the equivalence between the double charge change and the double transfer of like-particle pair, and a constraint is derived to the effective interactions used in approximations. This method was applied to the quasiparticle random-phase approximation for determining that interaction strength. In this paper, detail of this method is explained thoroughly, and applications are made to nuclei of several instances of the double-$β$ decays. The syste…
