Effect Of Pairing Correlations Research Articles

Roles of tensor force and pairing correlation in two-proton radioactivity of halo nuclei* *Supported by the National Natural Science Foundation of China (U1832120, 11675265), the Natural Science Foundation for Outstanding Young Scholars of Hebei Province, China (A2020210012), the Natural Science Foundation of Hebei Province, China (A2021210010), the Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy

The tensor force and pairing correlation effects on the two-proton radioactivity of Mg and Si with a pronounced two-proton halo are explored in the framework of spherical Skyrme-Hartree-Fock-Bogoliubov theory. It is shown that the halo sizes are enhanced with the increase in the strength of the tensor force and pairing correlation. Furthermore, the increasing halo sizes lead to the enhancement of diproton emission. Then, the tensor force is found to have a small influence on the two-proton decay energies, and the two-proton decay energies calculated with strong surface pairing are smaller than those with weak mixed pairing. Because the two-proton decay energies are relatively large, the predicted order of magnitude of half-lives within the effective liquid drop model is not sensitive to the decay energy variation caused by the tensor force and pairing correlation, which has a value of approximately 10 s.

Longitudinal and transverse coherent waves in media containing randomly distributed spheres

Multiple scattering effects due to a random distribution of identical spheres are investigated in the general case of elastic or poroelastic host media, where both longitudinal and transverse waves may co-exist. Propagation of plane coherent waves is assumed, and their dispersion equation looked for, as well as analytic approximations of those particular solutions that are close to the wavenumbers in the free host, when the product of the concentration with the scattering cross section of the spheres is low. Under this last condition, pair-correlation effects are seen to be of second order. Numerical studies are performed under the hole correction assumption, and compared to experimental data for tungsten carbide spheres in an epoxy matrix, which is a rather illustrative situation of how longitudinal and transverse waves participate to coherent propagation.

Pairing effects on vorticity of incident neutron currents at quasiparticle resonance energies in n−A elastic scattering

In this study, we analyzed how the incident neutron current is affected by the pairing effect in neutron-nucleus scattering described within the framework of Hartree-Fock-Bogoliubov theory by performing numerical calculations in terms of current, vorticity, and circulation of the incident neutron current. We found that the pairing effect on the incident neutron flux is completely different between particle-type and hole-type quasiparticle resonances. In the case of h-type quasiparticle resonance, the pairing acts to prevent the neutron flux from entering the nucleus, reducing circulation. In the case of p-type quasiparticle resonance, pairing acts to reduce circulation at energies lower than the resonance energy, but, at energies higher than the resonance energy, the effect of pairing on the neutron flux is reversed and, conversely, circulation is increased. These properties are consistent with the approximate expression for the vorticity characteristics at p-type and h-type resonances, implying that the vorticity appearing near p-type resonances due to the pair-correlation effect is inversely proportional to the resonance width (proportional to the resonance lifetime). In contrast, at h-type resonances, the pair-correlation effect has the effect of canceling out the vortex created by MF scattering and is independent of the resonance width.

A Hartree-Fock-Bogoliubov Study on the Pairing Correlations of the Isotopes of Cobalt

Background: The phenomena of nucleon pairing could be outlined from the Bethe-Weizäcker semi-empirical formula, from which the nuclear properties, viz. the binding energy, stability, shape etc. could be clearly sketched. Though the pairing correlation seems to be a small correction to the binding energy term, it plays a determinative role in defining the structure of nuclear systems. The addition to the binding energy in turn affects the position of the isotope on the dripline and hence increases the stability.
 Purpose: To study the effects of pairing on the ground state properties of the isotopes of Cobalt.
 Methods: We use Hartree-Fock-Bogoliubov (HFB) theory for the study. The general wave functions for the HFB approach are determined from variational principle. The eigen functions for the Hamiltonian are connected with the particle operators through the Bogoliubov transformations. The Hartree-Fock energy is obtained through the minimization of the variational parameter and the HFB equation is solved by iterative diagonalization by restoring the particle number symmetry.
 Results: The HFB analysis substantiates the effect of pairing correlation on binding energies, neutron and proton pairing energies, neutron and proton pairing gaps and one- and two-neutron separation energies of the Cobalt isotopes. The binding energies and one and two-neutron separation energies match with the experimental values and for pairing energies and pairing gaps, the regions where pairing is significant and the effects of shell closure at the vicinity of magic configuration of neutrons could be recognized.
 Conclusion: The Hartree-Fock-Bogoliubov calculations of the effects of pairing could be used as an efficient tool to study the nuclear structure. It can be ascertained that pairing plays an important role in determining the ground state properties of atomic nuclei.

Investigation of pairing correlations on computed Gamow–Teller strength distributions and associated [formula omitted]-decay half-lives

We investigate the effect of pairing correlations on the computed Gamow–Teller (GT) strength distributions and corresponding β-decay half-lives. The calculations are performed for a total of 47 sd-shell nuclei, for 20 < A < 30, employing the pn-QRPA model. Our calculations use three different values of pairing gaps computed using three different empirical formulae. The GT strength distribution and centroid values change considerably with a change in the pairing gap values. This in turn leads to differences in computed half-lives. The pairing gaps computed using the mass-dependent formula result in the calculated half-lives in better agreement with the measured data.

Structural evolution and shape transition in even-even Hf-isotopes within the relativistic mean-field approach

In this theoretical study, we calculate the ground state parameters like binding energy, charge radii, neutron skin-thickness, chemical potentials, quadrupole deformation parameter, neutron separation energy, and single-particle energy for Hf isotopes of mass 170 ⩽ A ⩽ 220. The potential energy surface in parallel with the Fermi energy as a function of the quadrupole deformation parameter is estimated to determine the ground state configuration. The Relativistic Hartree-Bogoliubov approach with density-dependent DD-ME2 and the relativistic mean-field formalism with the popular NL3 and NL3⁎ parameter sets are used for the present analysis. The study involves a constant gap BCS approach within NL3, & NL3⁎ and Bogoliubov transformation within DD-ME2 parameter sets to examine the effect of pairing correlations. The calculated bulk quantities are reasonably good agreement with available experimental data, the finite range droplet model predictions, and the Weizsäcker-Skyrme mass formula. We find the signature of shell/sub-shell closure at N = 126 for all the parameter sets, which indicates the stability of 198Hf in the neutron drip-line region of the Hf-isotopes.

Energy density functional analysis of the fission properties of 240Pu: The effect of pairing correlations * *Supported by National Natural Science Foundation of China (11790325, 11790320, 11790321, 11961131010, U1732138, 11505056, 11605054, U2067205, 12105369, 12047568, 12147219) and the Continuous Basic Scientific Research Project (WDJC-2019-09)

We have calculated the potential energy surfaces for 240Pu up to the scission point using the density functional theory with different pairing strengths to investigate the effect of pairing correlations on its fission properties. An enhancement in the pairing correlations lowers the barrier heights, isomeric state, and ridge between the symmetric and asymmetric fission valleys significantly. Moreover, it weakens the microscopic shell structure around the Fermi surface, shrinks the scission frontiers, especially for the symmetric and very asymmetric fission regions, and lifts the total kinetic energies (TKEs) for the symmetric fission region. It is also emphasized that the microscopic calculation qualitatively reproduces the trend of the distribution of the measured TKEs, especially for the positions of the peaks at and .

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

In this paper, we report on a study of the spectral features associated with dipole resonances in medium-mass nuclei $(E\ensuremath{\le}12 \mathrm{MeV})$, as revealed in the framework of the spd-interacting boson model. The effect of pairing correlations on the theory follows from solutions obtained through an application of the Bethe ansatz equation. In general, calculated spectra around the critical point of the vibrational to $\ensuremath{\gamma}$-soft transitions appear to approach those of a Gaussian orthogonal ensemble, while near the rotational and vibrational limits of the theory the spectra show more regular behavior. Specifically, the results reveal that the statistical features of the spectra are sensitive to the vector boson pairing strength ${c}_{p}$ in the transition region; that is, when ${c}_{p}$ is zero, or when the system approaches one of its dynamical symmetry limits, the spectra display regular features, while for stronger ${c}_{p}$ values, or when near to the critical phase transition region, the spectral features show more chaotic behavior. Overall, our results indicate that the statistical features are governed by the interplay between dipole resonant energies, pairing correlations, and interactions between and among the single and vector boson modes of the theory. As part of this work we also found out that chaoticity occurred when results were fit to a Berry-Robnik distribution. Throughout our analyses, we used experimentally known information about both positive- and negative-parity states. Our findings suggest that dipole resonances appear to be best-described by Poisson statistics for $A\ensuremath{\approx}32--138$ nuclei.

Effect of pairing correlation on low-lying quadrupole states in Sn isotopes * *Supported by the National Natural Science Foundation of China (11975096, 11875027, 11775014) and the Fundamental Research Funds for the Central Universities (2020NTST06)

We examined the low-lying quadrupole states in Sn isotopes in the framework of fully self-consistent Hartree-Fock+BCS plus QRPA. We focus on the effect of the density-dependence of pairing interaction on the properties of the low-lying quadrupole state. The SLy5 Skyrme interaction with surface, mixed, and volume pairings is employed in the calculations, respectively. We find that the excitation energies and the corresponding reduced electric transition probabilities of the first 2+ state are different, given by the three pairing interactions. The properties of the quasiparticle state, two-quasiparticle excitation energy, reduced transition amplitude, and transition densities in 112Sn are analyzed in detail. Two different mechanisms, the static and dynamical effects, of the pairing correlation are also discussed. The results show that the surface, mixed, and volume pairings indeed affect the properties of the first 2+ state in the Sn isotopes.

Effects of pairing correlation on the quasiparticle resonance in neutron-rich Ca isotopes

We investigated the effects of the pairing correlation on the quasiparticle resonant energy and width in the neutron-rich Ca isotopes by using the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method. The resonant energy and width can be read from three kinds of quasiparticle spectra, including the quasiparticle-state probability density, the occupation probability density, and the pair probability density. The results read from different quasiparticle spectra calculated with the same potential are exactly the same for the narrow resonances, while for the broad resonances, the difference among the results are relatively larger. From the comparison between the quasiparticle-state probability density calculated with and without the pairing field, we could separate the effect only from the pairing correlation on the quasiparticle resonances. We found that the pairing correlation can increase the resonant energy and width for both the hole-like and particle-like quasiparticle resonances. And this increase is larger when the state is closer to the Fermi energy, especially for the particle-like quasiparticle resonance originated from the unbound single-particle states with smaller angular momentum $l$ in weakly bound nucleus.

Collective coupling between pairing and rotational degrees of freedom within a simple model

A simple model to study the collective coupling between pairing and rotational degrees of freedom in well-deformed even-even nuclei is proposed. It relies on the description of the effects of pairing correlations on the rotational motion in terms of intrinsic vortical currents. As a result, an expression of the rotational energy within a band is provided as a polynomial of order three in the square of the angular velocity. The coefficients of this polynomial have a well-defined analytical form and their values are determined from merely three experimental pieces of data: the energy of the first ${2}^{+}$ state, the ground-state charge quadrupole moment as deduced from $B(E2,{2}^{+}\ensuremath{\rightarrow}{0}^{+})$ measurements, and a quantity deduced from the odd-even mass differences in neighboring odd nuclei. This model is tested in 24 deformed nuclei chosen across the rare-earth and actinide regions. In spite of the very restricted input of data, and moreover which is limited to nuclear properties at zero or very low excitation energies, the agreement with the data within the yrast line is in many cases, especially in actinide nuclei, excellent up to angular momenta of the order of $30\ensuremath{\hbar}$ or more. Of course, such an approach is by construction unable to reproduce physical effects which do not result from this Coriolis antipairing (CAP) type of collective quenching of pairing correlations. This is especially the case in the rare-earth region, where a backbending effect is often observed. In such cases our model may be considered as a baseline in order to disentangle the effect of the CAP collective mode from those of other existing spectroscopic phenomena.

Microscopic description of induced fission dynamics with nuclear energy density functionals

Static and dynamic aspects of the fission process are analyzed in a self-consistent framework based on energy density functionals. Multidimensionally constrained mean-field calculations in the collective space determine the potential energy surface of the fissioning nucleus, the scission line, the single-nucleon wave functions, energies, and occupation probabilities. Induced fission dynamics is described using the time-dependent generator coordinate method in the Gaussian overlap approximation. The position of the scission line is analyzed as a function of the strength of the pairing interaction, as well as the effect of static pairing correlations on charge yields and total kinetic energy of fission fragments.

Effects of pairing correlation on neutron drop

In this work, the effects of the pairing correlation on the properties of neutron drops $N$=6-50 trapped in a harmonic oscillator potential with $\hbar\omega=10$ MeV are investigated by comparing the results given by the Skyrme Hartree-Fock and Hartree-Fock-Bogoliubov theories with the density-dependent delta interaction (DDDI) pairing force. The results showed that the pairing correlation slightly made the neutron drops more bound, and increased the central neutron density, the spin-orbit and pseudo spin-orbit splittings. Thus, the pairing correlation must be accounted for to improve the Skyrme functional compared with the ab initio calculations. Furthermore, although the single-particle energy gaps with or without pairing were similar, the shell closures varied due to pair scattering. Here, the shell closures in neutron drops using the SkM* parameter set and DDDI pairing force were found at $N$=8, 16, and 32.

Importance of multicranked configuration mixing for angular-momentum-projection calculations: Study of superdeformed rotational bands in Dy152 and Hg194

Recently we investigated an effective method of multicranked configuration mixing for angular-momentum-projection calculations, where several cranked mean-field states are coupled after projection: The basic idea was originally proposed by Peierls and Thouless more than fifty years ago. With this method a good description of the rotational band has been achieved in a fully microscopic manner. In the present work, we apply the method to the high-spin superdeformed band, for which a long rotational sequence is observed, and study how a good description is obtained for the rotational spectrum as well as the ${\mathcal{J}}^{(1)}$ and ${\mathcal{J}}^{(2)}$ moments of inertia as functions of angular momentum. The Gogny D1S force is employed as an effective interaction, and the yrast superdeformed bands in $^{152}\mathrm{Dy}$ and $^{194}\mathrm{Hg}$ are taken as typical examples in the $A\ensuremath{\approx}150$ and $A\ensuremath{\approx}190$ regions, respectively. The effect of pairing correlations is examined by the method of variation after particle-number projection to understand the different behaviors of ${\mathcal{J}}^{(2)}$ moments of inertia observed in these two nuclei. The particle-number projection on top of the angular-momentum projection has been performed for the first time with the multicranked configuration mixing.

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Greens function method.Taking the weakly bound nucleus $^{66}$Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared.For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum.By switching off the pairing potential and/or the Hartree-Fock (HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential.The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here, especially for the partial waves with small angular momentum $\ell$.

Effects of deformation, pairing and tensor correlation on the evolution of bubble structure within the Skyrme-Hartree-Fock method

We study the effects of deformation, tensor and pairing correlation on the evolution of bubble structure in 46Ar, 22O and Cl isotopes using a deformed Skyrme-Hartree-Fock model with BCS and Lipkin-Nogami number projection approximation. The parameter SLy5 of the Skyrme energy functionals is adopted together with various kinds of density-dependent pairing interaction and various kinds of tensor interaction. In the spherical case, considering pairing correlation (IS + IV) or switch off pairing, there is a clear bubble structure in 46Ar with interaction SLy5 + Tw, respectively. For 46Ar, we find that deformation weakens the bubble structure strongly, and pairing correlation also weakens the bubble in 46Ar and 22O , respectively. On the other hand, the SLy5 + Tw + IS + IV interaction evolves the bubble structure of neutron-rich Cl isotopes 43-47Cl in deformed cases because the occupation probability of states $ 2s_{1/2}$ decreases from 1 to 0.5.

Spatial-decomposition analysis of viscosity with application to Lennard-Jones fluid

A spatial-decomposition formula is presented for viscosity. In this formula, a time correlation function conditioned by the distance between a pair of particles is introduced for the stresses exerted on the pair and is integrated over the whole region of the pair distance to determine the pair-correlation effect on the viscosity. The spatial-decomposition formula is then applied to the Lennard-Jones fluid at three thermodynamic states. The extent of spatial localization of the stress-stress correlation of pairs of Lennard-Jones particles is analyzed, and it is found that the contribution from neighboring pairs to the viscosity is large at high densities. The presence of long-range components is further pointed out and is shown to arise due to the periodicity of a simulated cell.

Microscopic study of induced fission dynamics of Th226 with covariant energy density functionals

Static and dynamic aspects of the fission process of $^{226}\mathrm{Th}$ are analyzed in a self-consistent framework based on relativistic energy density functionals. Constrained relativistic mean-field calculations in the collective space of axially symmetric quadrupole and octupole deformations, based on the energy density functional PC-PK1 and a $\ensuremath{\delta}$-force pairing, are performed to determine the potential energy surface of the fissioning nucleus, the scission line, the single-nucleon wave functions, energies, and occupation probabilities, as functions of deformation parameters. Induced fission dynamics is described using the time-dependent generator coordinate method in the Gaussian overlap approximation. A collective Schr\"odinger equation, determined entirely by the microscopic single-nucleon degrees of freedom, propagates adiabatically in time the initial wave packet built by boosting the ground-state solution of the collective Hamiltonian for $^{226}\mathrm{Th}$. The position of the scission line and the microscopic input for the collective Hamiltonian are analyzed as functions of the strength of the pairing interaction. The effect of static pairing correlations on the preneutron emission charge yields and total kinetic energy of fission fragments is examined in comparison with available data, and the distribution of fission fragments is analyzed for different values of the initial excitation energy.

Effects of pairing correlations on the neutron skin thickness and the symmetry energy

We investigated effects of pairing correlations on the neutron skin thickness and the symmetry energy of finite nuclei. In this calculation we used Hartree-Fock-Bogoliubov (HFB) method with Skyrme forces and effective pairing interactions. The results have been compared with available experimental data, Hartree-Fock (HF) results as well as the predictions by droplet model (DM). Finally, our discussion was extended to study of the pairing interaction in nuclear matter. Roles of isospin T = 0 pairing in the nuclear matter were also discussed.

Investigation of the ^{10}Li shell inversion by neutron continuum transfer reaction.

This Letter reports a study of the highly debated ^{10}Li structure through the d(^{9}Li,p)^{10}Li one-neutron transfer reaction at 100MeV. The ^{10}Li energy spectrum is measured up to 4.6MeV and angular distributions corresponding to different excitation energy regions are reported for the first time. The comparison between data and theoretical predictions, including pairing correlation effects, shows the existence of a p_{1/2} resonance at 0.45±0.03 MeV excitation energy, while no evidence for a significant s-wave contribution close to the threshold energy is observed. Moreover, two high-lying structures are populated at 1.5 and 2.9MeV. The corresponding angular distributions suggest a significant s_{1/2} partial-wave contribution for the 1.5MeV structure and a mixing of configurations at higher energy, with the d_{5/2} partial-wave contributing the most to the cross section.