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.     

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.     

Tensor force effect on the exotic structure of neutron-rich Ca isotopes

The structure of neutron-rich Ca isotopes is studied in the spherical Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with SLy5,SLy5+T,and 36 sets of TIJ parametrizations.The calculated results are compared with the available experimental data for the average binding energies,two-neutron separation energies and charge radii.It is found that the SLy5+T,T31,and T32 parametrizations reproduce best the experimental properties,especially the neutron shell effects at N=20,28 and 32,and the recently measured two-neutron separation energy of ~(56)Ca.The calculations with the SLy5+T and T31 parametrizations are extended to isotopes near the neutron drip line.The neutron giant halo structure in the very neutron-rich Ca isotopes is not seen with these two interactions.However,depleted neutron central densities are found in these nuclei.By analyzing the neutron mean-potential,the reason for the bubble-like structure formation is given.     

原子核基态性质的系统研究

在Skyrme-Hartree-Fock-Bogoliubov（SHFB）理论框架下,利用SkOP1,SkOP2,SKC和SKD 4套新的Skyrme相互作用参数系统地研究了Ca,Ni,Sn和Pb同位素链上原子核的结合能、电荷半径等基态性质,并重点讨论了丰中子Ca核的新中子幻数以及Pb的同位素位移现象。通过与实验数据和SLy5相互作用参数的结果对比,发现这4套相互作用参数都能很好地再现结合能的实验数据,其预言精度比SLy5要高。对于丰中子Ca核,只有SKC和SKD相互作用参数能够再现N=28处的壳效应,而对于实验上发现的新幻数N=32和34,所有的相互作用参数均不能再现这一结果。对于电荷半径,发现所有的相互作用参数均不能很好地预言Ca同位素链电荷半径的演化规律以及Pb的同位素位移现象。另外,还将这些相互作用参数推广至远离β稳定线原子核的单粒子能级结构研究,发现其不适用于描述其随同位旋的演化行为。因此,为了更好地描述远离β稳定线原子核的宏观性质及单粒子能级,建议在拟合Skyrme相互作用参数时,除自旋-轨道耦合项包括合理的同位旋依赖外,还要考虑张量力成分。The nuclear ground state properties of Ca, Ni, Sn and Pb isotopes, such as the binding energies, the charge radii, are studied systematically by 4 sets of new Skyrme parametrizations SKC, SKD, SkOP1 and SkOP2 in the framework of the Skyrme-Hartree-Fock-Bogoliubov (SHFB) method. The new magic numbers of neutronrich Ca isotopes and the isotopic shift of Pb isotopes are discussed emphatically. By the comparisons between the calculations and the experimental data and results from the SLy5 interaction parametrization, it is found that the experimental binding energies can be reproduced accurately by all parametrizations. The calculated accuracies of SKC, SKD SkOP1 and SkOP2 parametrizations are higher than the ones of SLy5 parametrization. For the neutron-rich Ca nuclei, the shell effect of N=28 can be reproduced by the SKC and SKD parametrizations, but the magic numbers at N=32 and 34 are not found by the calculations of all the parametrizations. For the charge radii, the experimental evolution tendency of Ca isotopes and isotopic shift of Pb isotopes can not be reproduced by all the parametrizations. In addition, all Skyrme parametrizations are extended to study the structure of the nuclei far from the β stability line, it is shown that the single-particle energy evolutions with the isospin are not suitable for being studied by these parametrizations. Thus the tensor force component should be considered besides the isospin dependence in spin-orbit coupling term when the Skyrme interaction parametrizations are fitted.     

Nuclear properties of Z=114 isotopes and shell structure of ~(298)114

The two-neutron separation energies(S_(2n)) and α-decay energies(Q_α) of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S_(2n) and Q_α evolutions with neutron number N.Meanwhile,the single-particle energy spectra of ~(298)114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus ~(298)114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of ~(298)114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.     

Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.     

Emergence of new magic numbers,N = 16 and 32 by tensor interaction in Skyrme–Hartree–Fock theory

Melting of N = 20 shell and development of N = 16 and 32 shells for neutron-rich nuclei have been studied extensively by including tensor interaction in Skyrme–Hartree–Fock theory optimized to reproduce the splitting Δ1f shells of ^40,48Ca and ⁵⁶Ni nuclei. Evolution of gap generated by the energy difference of single-particle levels ν2s _1/2 and ν1d _3/2 has been found to be responsible for shell closure at N = 16. The splitting pattern of spin–orbit partners 2p shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates the formation of a new shell at N = 32 region.     

The origin of the spin-orbit splitting in some light nuclei using a modified interaction

The spin-orbit splittings in the spectra of nuclei with A = 5, 15, and 17 have been restudied, with a new set of matrix elements, within the framework of the shell model with core excitations. Investigated are the dependences of these splittings on core-excitation and on some of the different components of the nucleon- nucleon interaction. Our work confirms that the two-body spin-orbit interaction has a major effect whose magnitude depends on the size of the model space that is used. The effect of the tensor interaction is again seen to be considerably less important.     

Deformation properties of lead isotopes

The deformation properties of a long lead isotopic chain up to the neutron drip line are analyzed on the basis of the energy density functional (EDF) in the FaNDF⁰ Fayans form. The question of whether the ground state of neutron-deficient lead isotopes can have a stable deformation is studied in detail. The prediction of this deformation is contained in the results obtained on the basis of the HFB-17 and HFB-27 Skyrme EDF versions and reported on Internet. The present analysis reveals that this is at odds with experimental data on charge radii and magnetic moments of odd lead isotopes. The Fayans EDF version predicts a spherical ground state for all light lead isotopes, but some of them (for example, ¹⁸⁰Pb and ¹⁸⁴Pb) prove to be very soft—that is, close to the point of a phase transition to a deformed state. Also, the results obtained in our present study are compared with the predictions of some other Skyrme EDF versions, including SKM*, SLy4, SLy6, and UNE1. By and large, their predictions are closer to the results arising upon the application of the Fayans functional. For example, the SLy4 functional predicts, in just the same way as the FaNDF⁰ functional, a spherical shape for all nuclei of this region. The remaining three Skyrme EDF versions lead to a deformation of some light lead isotopes, but their number is substantially smaller than that in the case of the HFB-17 and HFB-27 functionals. Moreover, the respective deformation energy is substantially lower, which gives grounds to hope for the restoration of a spherical shape upon going beyond the mean-field approximation, which we use here. Also, the deformation properties of neutron-rich lead isotopes are studied up to the neutron drip line. Here, the results obtained with the FaNDF⁰ functional are compared with the predictions of the HFB-17, HFB-27, SKM*, and SLy4 Skyrme EDF versions. All of the EDF versions considered here predict the existence of a region where neutron-rich lead isotopes undergo deformations, but the size of this region is substantially different for the different functionals being considered. Once again, it is maximal for the HFB-17 and HFB-27 functionals, is substantially narrower for the FaNDF⁰ functional, and is still narrower for the SKM* and SLy4 functionals. The two-neutron drip line proved to be A_drip²ⁿ = 266 for all of the EDF versions considered here, with the exception of SKM*, for which it is shifted to A_drip²ⁿ(SKM*) = 272.     

Shell structure fingerprints of tensor interaction

We address the consequences of strong tensor terms in the local energy density functional, resulting from fits to the f _5/2 -f _7/2 splittings in ⁴⁰Ca , ⁴⁸Ca , and ⁵⁶Ni . In this study, we focus on the tensor contribution to the nuclear binding energy. In particular, we show that it exhibits an interesting topological feature 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 that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4_T, we show that the proton tensorial magic numbers shift with increasing neutron excess to Z = 14 , 28, and 50.     

Quantum Monte Carlo calculation for the neutron-rich Ca isotopes

We computed ground-state energies of calcium isotopes from ⁴²Ca to ⁴⁸Ca by means of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. Calculations were performed by replacing the ⁴⁰Ca core with a mean-field self-consistent potential computed using the Skyrme interaction. The energy of the external neutrons is calculated by projecting the ground state from a wave function built with the single-particle orbitals computed in the self-consistent external potential. The shells considered were the 1F _7/2 and the 1F _5/2 . The Hamiltonian employed is semi-realistic and includes tensor, spin-orbit and three-body forces. While absolute binding energies are too deep if compared with experimental data, the differences between the energies for nearly all isotopes are in very good agreement with the experimental data.     

Many-body correlations in shell model effective interactions derived by ab initio methods and the V_(low-k) approach

We investigate many-body correlations caused by two-and three-body(2-, 3bd) forces. Shell-model effective interactions derived from ab initio methods(coupled-cluster method, no-core shell model) are adopted.Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence.We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.     

Abnormal odd-even staggering behavior around 132Sn studied by density functional theory

In this work, we have performed Skyrme density functional theory (DFT) calculations of nuclei around ¹³²Sn to study whether the abnormal odd-even staggering (OES) behavior of binding energies around N = 82 can be reproduced. With the Skyrme forces SLy4 and SkM*, we tested the volume- and surface-type pairing forces and also the intermediate between these two pairing forces, in the Hartree-Fock-Bogoliubov (HFB) approximation with or without the Lipkin-Nogami (LN) approximation or particle number projection after the convergence of HFBLN (PLN). The Universal Nuclear Energy Density Function (UNEDF) parameter sets are also used. The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force. Moreover, for the pairing force that is favored more at the nuclear surface, a larger mass OES is obtained, and vice versa. It appears that the combination of volume and surface pairing can give better agreement with the data. In the studies of the OES, a larger ratio of surface to volume pairing might be favored. Additionally, in most cases, the OES given by the HFBLN approximation agrees more closely with the experimental data. We found that both the Skyrme and pairing forces can influence the OES behavior. The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one. The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around ¹³²Sn. The neutron OES of the tin isotopes given by the SkM* force agrees more closely with the experimental one than that given by the SLy4 force in most cases. Both SLy4 and SkM* DFT have difficulties in reproducing the abnormal OES around ¹³²Sn. Using the PLN method, the systematics of OES are improved for several combinations of Skyrme and pairing forces.     

Bismuth-induced enhancement of magneto-optical effects in iron garnets: A theoretical analysis

A semiquantitative model of circular magneto-optical effects in iron garnets is constructed within the concept of charge-transfer transitions and the existing qualitative notions. In the framework of the proposed model, the drastic enhancement of circular magneto-optical effects in R₃Fe₅O₁₂ iron garnets containing impurities of Bi³⁺ or Pb²⁺ ions is explained by the increase in the oxygen contribution to the spin-orbit coupling constant of the (FeO₆)^9? and (FeO₄)^5? complexes (the main magneto-optically active centers in iron garnets). This increase is associated with the covalent admixture of the Bi³⁺ (or Pb²⁺) 6p orbitals (with a giant one-electron spin-orbit coupling constant) to the oxygen 2p orbitals. The influence of the substitution does not reduce to an enhancement of the oxygen spin-orbit interaction alone but also leads to the appearance of the effective anisotropic tensor contributions to the spin-orbit interaction and circular magneto-optical effects. These contributions to the magneto-optical effects in garnets are estimated. The influence of an inhomogeneous bismuth distribution on the magneto-optical effects in Y_3?xBi_xFe₅O₁₂ garnets is investigated using computer simulation. Analysis of the available experimental data on the magneto-optical effects in garnets confirms the validity of the theoretical model proposed.     

Valence band spin-orbit splitting in CdTe and Cdf−xMnxTe and giant zeeman effect in the Γ7 band of Cd1−xMnxTe

Optical transitions from spin-orbit split-off valence band Γ₇ to the conduction band Γ₆ were directly observed in transmission measurements on thin samples of CdTe and Cd_1?xMn_xTe. Precise values of spin-orbit splittings were determined. Giant Zeeman splitting of Γ₇ - Γ₆ exciton in Cd_1?xMn_xTe was observed and found coherent with corresponding splitting of Γ₈-Γ₆ exciton.     

Effect of pairing correlation on low-lying quadrupole states in Sn isotopes

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~(112)Sn 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.     

Nuclear compression moduli and density-dependent forces

Density-dependent zero-range forces of the form of the modified delta interaction (MDI) are generalized (MDI3, MDI4) in order to yield reasonable values of the compression modulus in nuclear matter (K_N = 200 MeV). This low value can be fitted by introducing two terms with different density dependence in the force. The four free parameters of MDI3 are adjusted to reproduce the nuclear matter values of the binding energy, density and compression modulus, and to fulfil the condition that the total energy of ¹⁶O in harmonic oscillator wave functions has a minimum at the oscillator length b = 1.75 fm, corresponding to the correct rms radius. MDI4 contains in addition a two-body spin-orbit interaction. The five parameters of MDI4 are fitted to the above three nuclear matter data and by requiring that Hartree-Fock (HF) calculations in ²⁰⁸Pb yield the experimental charge rms radius and reasonable values of certain single-particle spin-orbit splittings. The quality of MDI4 is checked by comparing calculated rms radii, binding energies, and elastic electron scattering cross sections with available experimental data for doubly closed shell nuclei. As a test the energy levels and the nuclear monopole polarization of muonic ²⁰⁸Pb are calculated self-consistently yielding impressive agreement with experiment.     

Structure of 2<Subscript>1,2</Subscript> <Superscript>+</Superscript> states in <Superscript>132,134,136</Superscript>Te

Starting fromthe Skyrme interaction f_ together with the volume pairing interaction, we study the g factors for the 2_1,2⁺ excitations of ^132,134,136Te. The coupling between one- and two-phonon terms in the wave functions of excited states is taken into account within the finite-rank separable approximation. Using the same set of parameters we describe the available experimental data and give the prediction for ¹³⁶Te, g(2₁⁺) = ?0.18 in comparison to +0.32 in the case of ¹³²Te.     

Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V _n( r) and V _p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields. Received: 12 February 2000 / Accepted: 14 March 2002     

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.