Effect of time-odd fields on odd-even mass differences of semi-magic nuclei

The effect of time-odd fields of Skyrme interaction on neutron odd-even mass differences is studied in the framework of axially deformed Skyrme Hartree-Fock(DSHF)+BCS model. To this end, we take into account both the time-even and time-odd fields to calculate the one-neutron and two-neutron separation energies and pairing gaps of semi-magic Ca, Ni, and Sn isotopic chains. In the calculations, a surface-type pairing interaction(IS pairing) and an isospin dependent contact pairing interaction(IS+IV pairing)are adopted on top of Skyrme interactions SLy4, SLy6 and Sk M*, respectively. We find that the time-odd fields have in general small effects on pairing gaps, but achieve better agreement with experimental data using SLy4 and Sly6 interactions, respectively.It is also shown that the calculations with IS+IV pairing reproduce the one-neutron separation energies of Sn isotopes better than those with the IS pairing interaction when the contributions of the time-odd fields are included.     

The peninsula of neutron nuclear stability in the vicinity of N = 258

The properties of extremely neutron-excessive nuclei with Z ?? 70, including the region of transuranium elements, are calculated beyond the previously theoretically known neutron drip line (NDL). The calculations are based on the Hartree-Fock approach using Skyrme forces (SkM*, SkI2, SLy4, Ska) with allowance for axial deformation and pairings in the BCS approximation. It is shown that the series of isotones with neutron number N = 258 outside of 2n NDL forms a peninsula of stable nuclei (PSN) with respect to the emission of one neutron. For SkM* forces, a PSN is formed by ³⁴⁴Rn, ³⁴⁶Ra, ³⁴⁸Th, and ³⁵⁰U nuclides.     

Low-Lying electric dipole transitions in tin isotopic chain within the RPA model

A nuclear structuremodel based on a finite rank approximation of Skyrme interaction is applied to calculate the distribution of dipole strength in tin isotopes. The model is based on the quasiparticle random phase approximation. The results obtained with the three types of parametrizations of the Skyrme forces (SLy4, SkM*, and SIII) are compared. The low-lying part of dipole strength distribution reveals the existence of a group of slightly collective states, and the corresponding E1 transition strength increases with the enlargement of neutron excess. The group is associated with the pygmy resonance. The text was submitted by the authors in English.     

能量密度泛函中不同对关联处理方式对原子核形变描述影响的探讨

在Skyrme能量密度泛函理论的框架下,研究了不同对关联处理近似,如Hartree-Fock-Bogoliubov(HFB)、Hartree-Fock-Bogoliubov Lipkin-Nogami (HFBLN)及在HFBLN基础上考虑粒子数投影,对于原子核势能曲面计算及基态结合能的影响。同时,也研究了不同对力,如体积对力、表面对力及混合对力对结果的影响。研究的对象为典型的双幻核16O,40Ca,100Sn和208Pb,它们的基态为球形;还有典型的形变核48Cr,也研究了相应的Cr和Fe同位素链的结合能,最后讨论了对超重核298Fl的势能面计算。研究发现,对关联基本不改变形变极小点,但是由于对关联能的引入,对结合能会带来几个MeV的修正能量,HFB、HFBLN及投影计算的修正能量逐渐递增。对关联可以改变位能面最小点附近曲线的软度,使得形变较小点变浅,而在HFBLN基础上考虑粒子数投影,又可以让形变极小点变得更加明显。对关联也降低了位垒高度。在相同对关联处理近似下,混合对力与体积对力计算的势能面结果相接近,表面对力带来了更多的对关联能,对关联的效果更加显著。     

Nuclear structure investigation of neutron-rich Mn isotopes

Structural evolution of odd-even and odd-odd Mn isotopes from the valley of stability up to neutron dripline is studied in the framework of the self-consistent mean-field theory of Hartree–Fock–Bogoliubov. Three Skyrme effective interactions, namely, SLy4, SLy5 and SLy5T, are employed to investigate the tensor force effect on the ground-state properties. It is shown that the calculated quantities with the SLy4 interaction correctly reproduce the available experimental data and agree well with finite range droplet model and relativistic mean-field predictions. An inconsistency has been observed between the curves of the separation energies and that of the charge radius around N = 40. It is explained by the flatness of the potential energy curves in this region. The SLy5 and SLy5T results point to the necessity to refit all the Skyrme parameters after including the tensor terms.     

Peninsula of neutron stability of nuclei in the neighborhood of neutron magic number N = 126

The properties of the ground state of even-even nuclei with extreme neutron excess that are remote from the known neutron drip line (NDL) are calculated. The calculations are based on the Hartree-Fock method with Skyrme forces SkM*, SkI2, Sly4, Ska) with allowance for axial deformation and the BCS pairing approximation. It is shown that the isotone chain at the neutron number N = 126 beyond the NDL forms a peninsula of nuclei that are stable with respect to the emission of one neutron (PNS). The neutron and proton density distributions of the PNS nuclei have spherical symmetry. A mechanism for restoring the stability of nuclei beyond the NDL is discussed. The obtained results are compared with those from Hartree-Fock-Bogoliubov calculations for long isotope chains of Zr and Pd up to the NDL.     

Neutron-deficient and neutron-rich Fe and Ni isotopes near the drip line

Positions of the proton and neutron drip lines and characteristics of the neutron-deficient and neutron-rich Fe and Ni isotopes have been studied by the Hartree-Fock method with the Skyrme forces (Ska, SkM*, Sly4) with allowance for deformation. Pairing was taken into account on the basis of the BCS approximation with the pairing constant G = (19.5/2)[1 ± 0.51(N ? Z)/A]. Manifestation of magic numbers for the nickel isotopes ⁴⁸Ni, ⁵⁶Ni, and ⁷⁸Ni and for the nucleon-stable isotope ¹¹⁰Ni which is beyond the drip line is discussed.     

Effects of 2 particle–2 hole configurations on dipole states in neutron-rich <Emphasis Type="Italic">N</Emphasis> = 80–84 isotones

Starting from the Skyrme interaction SLy4 we study the effects of 2 particle–2 hole configurations on the low-energy electric dipole response in ^130–134Sn. It is shown that the pygmy dipole resonance properties are correlated with the neutron skin thickness. The two-phonon configurations give a considerable contribution to the low-lying E1 strength.     

Properties of giant dipole resonance and the elimination of center-of-mass motion

The accuracy of eliminating the spurious state from the E1-transition strength distribution is investigated within the random-phase approximation with separabelized Skyrme forces. The E1-transition strength distribution in ¹³²Sn is considered as an example.     

On microscopic theory of radiative nuclear reaction characteristics

A survey of some results in the modern microscopic theory of properties of nuclear reactions with gamma rays is given. First of all, we discuss the impact of Phonon Coupling (PC) on the Photon Strength Function (PSF) because it represents the most natural physical source of additional strength found for Sn isotopes in recent experiments that could not be explained within the standard HFB + QRPA approach. The self-consistent version of the Extended Theory of Finite Fermi Systems in the Quasiparticle Time Blocking Approximation is applied. It uses the HFB mean field and includes both the QRPA and PC effects on the basis of the SLy4 Skyrme force. With our microscopic E1 PSFs, the following properties have been calculated for many stable and unstable even–even semi-magic Sn and Ni isotopes as well as for double-magic ¹³²Sn and ²⁰⁸Pb using the reaction codes EMPIRE and TALYS with several Nuclear Level Density (NLD) models: (1) the neutron capture cross sections; (2) the corresponding neutron capture gamma spectra; (3) the average radiative widths of neutron resonances. In all the properties considered, the PC contribution turned out to be significant, as compared with the standard QRPA one, and necessary to explain the available experimental data. The results with the phenomenological so-called generalized superfluid NLD model turned out to be worse, on the whole, than those obtained with the microscopic HFB + combinatorial NLD model. The very topical question about the M1 resonance contribution to PSFs is also discussed.     

Description of low-lying state structures with Skyrme interaction

We use the quasiparticle random phase approximation to study properties of the low-lying 2⁺ states in the even-even nuclei around ¹³²Sn. Starting from a Skyrme interaction in the particle-hole channel and a density-dependent zero-range interaction in the particle-particle channel, the calculation within the finite-rank separable approximation for the residual interaction is performed.     

Peninsulas of the neutron stability of nuclei in the vicinity of neutron magic numbers

On the basis of the Hartree-Fock method as implemented with Skyrme forces (Ska, SkM*, Sly4, and SkI2) and with allowance for an axial deformation and nucleon pairing in the Bardeen-Cooper-Schrieffer approximation, the properties of extremely neutron-rich even-even nuclei were calculated beyond the neutron drip line known earlier from theoretical calculations. It was shown that the chains of isotopes beyond the neutron drip line that contain N = 32, 58, 82, 126, and 184 neutrons form peninsulas of nuclei stable against the emission of one neutron and, in some cases, peninsulas of nuclei stable against the emission of two neutrons. The neutron- and proton-density distributions in nuclei forming stability peninsulas were found to be spherically symmetric. A mechanism via which the stability of nuclei might be restored beyond the neutron drip line was discussed. A comparison with the results of calculations by the Hartree-Fock-Bogolyubov method was performed for long chains of sulfur and gadolinium isotopes up to the neutron drip line.     

Investigation of the properties of nuclei with extreme neutron excess in the vicinity of neutron magic numbers

Properties of even-even nuclei with extreme neutron excess in the vicinity of neutron magic numbers up to and beyond the neutron drip line (NDL) are calculated by the Hartree-Fock (HF) method using Skyrme forces (Ska, SkM*, Sly4, SkI2, SkP) with allowance for axial deformation and BCS-approximation pairing. It is shown that chains of isotones with the neutron numbers N = 32, 58, 82, 126, 184, and 258 beyond the NDL form peninsulas of nuclei stable with respect to emission of one neutron, and occasionally peninsulas of nuclei stable with respect to the emission of two neutrons. The length of these peninsulas in (N, Z) space depends on the choice of the Skyrme forces, while their locations are at the same N = 32, 58, 82, 126, 184, and 258 and do not depend on the choice of forces. The investigated isotones restore stability beyond the NDL due to the complete filling of subshells with high angular momentum and to the intrusion of corresponding neutron levels in the region of discrete bound states. The stability of the numerical solution to the HF equations for nuclei belonging to the peninsulas of stability is analyzed.     

Study of weakly-bound odd-A nuclei with quasiparticle blocking

The coordinate-space Hartree-Fock-Bogoliubov(HFB) approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei ~(17,19)B and ~(37)Mg,in which halo structures have been reported in experiments.The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations.The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects.In our calculations,~(19)B and ~(37)Mg have remarkable features of deformed halos.     

Potential energy surface and formation of superheavy nuclei with the Skyrme energy-density functional

With the Skyrme energy-density functional theory, the nucleus–nucleus potential is calculated and the potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM^*, SkP, SIII, Ska, and SLy4, which correspond to the different equations of state for the isospin symmetry nuclear matter. It is found that the nucleus–nucleus potential is associated with the collision orientation and Skyrme forces. A more repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter, which hinders the formation of superheavy nuclei. The available data in the fusion-evaporation reaction of ⁴⁸Ca+²³⁸U are nicely reproduced with the SkM^* parameter by implementing the potential into the dinuclear system model.     

Investigation of neutron and proton distributions of He,Li, and Be isotopes using the new Skyrme-Force parameters

The proton and neutron densities, root-mean-square (rms) radii of proton density and neutron density, and neutron skin thickness of ^4–10He, ^6–11Li, and ^7–12Be isotopes are calculated using Skyrme-Hartree-Fock method with SLy4, SLy5, SLy6, and SLy7 force parameters. The evaluated results are compared with experimental data. Also, the results of halo nuclei (^6,8He, ¹¹Li, and ¹¹Be) are compared with the results of other isotopes for selected nuclei having the same neutron configuration.     

Non-empirical pairing energy density functional

We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a non-empirical pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.     

Pygmy and Giant Dipole Resonances in Proton-Rich Nuclei ~(17,18)Ne

The pygmy and giant dipole resonances in proton-rich nuclei~(17,18)Ne are investigated with a fully self-consistent approach. The properties of ground states are calculated in the Skyrme Hartree-Fock with the Bardeen-CooperSchrieffer approximation to take into account the pairing correlation. The quasiparticle random phase approximation(QRPA) method is used to explore the properties of excited dipole states. In the calculations the SLy5 Skyrme interaction is employed. In addition to the giant dipole resonances, pygmy dipole resonances(PDR) are found to be located in the energy region below 10 MeV in both 17,18 Ne. The strength and transition density show that the low-lying states are typical PDR states. However, analyzing the QRPA amplitudes of proton and neutron 2 quasiparticle(2 qp) configurations for a given low-lying state in ~(17,18)Ne, we find that the PDR state is less collective, more like a single 2 qp excitation.     

Investigating the neutron and proton density distributions in extremely neutron-rich nuclei

Manifestations of the neutron halo in extremely neutron-rich nuclei are investigated by the Hartree-Fock method using the Skyrme forces (SkM*, Ska, Sly4, SkI2) with allowance for axial deformation. The investigated nuclei, which lie beyond the theoretical neutron drip line (NDL), form peninsulas of nuclei stable with respect to one-neutron emission and belong to chains of isotones with the neutron number N = 32, 58, 82, 126, 184, and 258.     

轻核中中子间的对相互作用和中子晕

选择Skyme势E作为两核子间唯象相互作用,在Hartree-Fock理论中结合粒子数守恒方法处理同类核子间的对相互作用,计算了Li和Be的丰中子同位素的结构,计算表明中子间的对相互作用和双中子晕之间存在紧密的联系.