Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.     

Skyrme-Hartree-Fock calculation of Λ-hypernuclear states from (π+,K +) reactions

We present a self consistent Skyrme-Hartree-Fock calculation of the binding energies ofΛ-hypernuclear states experimentally determined by (π⁺,K ⁺) reactions. A Skyrme type parametrization of theΛ-N interaction is derived, including two and three body terms, The importance of each of these terms is discussed. An overall agreement is reached even for deeply boundΛ states. The binding energies of thes- andp-shell hypernuclei are also well reproduced. No signal of quark deconfinement has been found. We conclude that the shell model picture works very well to describe deeply bound states for heavyΛ hypernuclei.     

Strangeness, charm, and bottom in a chiral quark-meson model

In this paper, we investigate an SU(3) extension of the chiral quark-meson model. The spectra of baryons with strangeness, charm, and bottom are considered within a “rigid oscillator” version of this model. The similarity between the quark sector of the Lagrangian in the model and the Wess-Zumino term in the Skyrme model is noted. The binding energies of baryonic systems with baryon numbers B=2 and 3 possessing strangeness or heavy flavor are also estimated. The results are in good qualitative agreement with those obtained previously in the chiral soliton (Skyrme) model.     

超重核的基态性质

用Skyrme Hartree Fock+BCS方法计算了超重核的基态性质,讨论了结合能、α衰变、形变、壳结构和自发裂变等问题.计算得到的结合能较好地反映了实验测量值,α衰变能与实验值符合很好.发现基本上有两种类型的超重核形变:在270108核附近的β2≈0.2的长椭球形变和在298114核附近的近球形形变.单粒子能级分布计算表明:在质子Z=108和中子N=162存在变形壳,在质子Z=114和中子N=184存在球形壳.用得到的α衰变能和Viola Seaborg公式估算了α衰变半寿命,能合理地符合实验测量值. The ground state properties of superheavy nuclei are investigated using the Skyrme Hartree Fock model. The pairing correlation is treated by the BCS method with the pairing δ force. Binding energies, α decays, spontaneous fissions, shell structures and deformations are discussed. Our calculations reproduce experimential binding energies and α decay energies.It is found that superheavy nuclei can be grouped with two kinds of deformations: i) well deformed prolate shapes (β2≈0.2) around 270108...     

A study of the nuclear response function

We examine the excitation properties of spherical nuclei in the Random Phase Approximation using the Green's function method. The calculations are done with interactions of the Skyrme type for nuclei from ¹⁶O to ²⁰⁸Pb. Different Skyrme interactions can have the same predictions for ground state Hartree-Fock properties, but give quite different predictions for the dynamic response. Our calculations favor a mild velocity-dependence in the interaction, such as given by Skyrme I. The level of agreement with empirical properties is as follows: energies of low-lying states, ≈25%; positions of giant resonances, ≈10%; transition rates of low states, factor of 2 typical. Inelastic scattering of electrons is reasonably accounted for by the model, but nucleon inelastic scattering has difficulties with the noncollective strength.     

Binding energies of even-even superheavy nuclei in a semi-microscopic approach

The structure of some even-even superheavy nuclei with the proton number Z = 98?120 is studied using a semi-microscopic but not self-consistent model. The macroscopic energy part is obtained from the Skyrme nucleon-nucleon interaction in the semi-classical extended Thomas-Fermi approach. A simple but accurate method is derived for calculating the direct part of the Coulomb energy. The microscopic shell plus pairing energy corrections are calculated from the traditional Strutinsky method. Within this semi-microscopic approach, the total energy curves with the quadrupole deformation of the studied superheavy nuclei were calculated. The same approach features the well known ²⁰⁸Pb or ²³⁸U nuclei. For each nucleus the model predictions for the binding energy, the deformation parameters, the half-density radii and comparison with other theoretical models are made. The calculated binding energies are in good agreement with the available experimental data.     

Modern energy density functional for nuclei and the nuclear matter equation of state

We discuss a method of determining a modern energy density functional (EDF) in nuclei. We adopt a Skyrme type EDF and fit the Skyrme parameters to an extensive set of experimental data on the ground-state binding energies, radii, and the breathing mode energies of a wide range of nuclei. We further constrain the values of the Skyrme parameters by requiring positive values for the slope of the symmetry energy S, the enhancement factor κ, associated with the isovector giant dipole resonance, and the Landau parameter G ₀^′. This is done within the approaches of Hartree-Fock (HF) and HF with the inclusion of correlation effects, using a simulated-annealing based algorithm forminimizing χ ².We also present results of HF based random phase approximation for the excitation strength function of the breathing mode and discuss the current status of the nuclear matter incompressibility coefficient.     

Strength functions of primary transitions following thermal neutron capture in strontium

The primaryE1,M1 andE2γ-radiation in^87,88,89Sr observed after thermal neutron capture was compared with the predictions of single particle and giant resonance models. The nuclei feature a wide range of neutron binding energies between 6.3 and 11.1 MeV, which makes a 5.5 MeV spectrum of primary transition energies available for investigation. The (n, γ) reaction was used to estimate the parameters of the spin-flip M1 giant resonance in strontium. The total energy weightedM1 strength of this resonance exceeds the results of shell model and random phase approximation calculations for⁹⁰Zr by a factor of 3–4. TheE1 strengths were found to agree with the established giant dipole resonance model. The few data on primaryE2 transitions do not allow to differentiate between the giant quadrupole resonance and the single particle models.     

Nuclear binding energies and liquid drop parameters in the extended Thomas-Fermi approximation

Using the extended Thomas-Fermi model, we calculate average nuclear binding energies with Skyrme type effective interactions. The total energy is minimized with respect to variations of the nucleon densities without the use of wave functions or adjustable parameters. We obtain binding energies only ～2–7 MeV higher than self consistenly averaged Hartree-Fock energies. By least-square fits we determine the liquid drop parameters of different effective interactions very accurately. Shell effects are added perturbatively and lead to total energies within 5–10 MeV of the exact Hartree-Fock results.     

Flavored exotic multibaryons and hypernuclei in topological soliton models

The energies of baryon states with positive strangeness, or anticharm (antibeauty), are estimated in the chiral soliton approach, in the “rigid oscillator” version of the bound-state soliton model proposed by Klebanov and Westerberg. Positive strangeness states can appear as relatively narrow nuclear levels (Θ-hypernuclei), and the states with heavy antiflavors can be bound with respect to strong interactions in the original Skyrme variant of the model (SK4 variant). The binding energies of antiflavored states are also estimated in the variant of the model with a sixth-order term in chiral derivatives added to the Lagrangian to stabilize solitons (SK6 variant). This variant is less attractive, and nuclear states with anticharm and antibeauty can be unstable relative to strong interactions. The chances of obtaining bound hypernuclei with heavy antiflavors increase within the “nuclear variant” of the model with a rescaled model parameter (the Skyrme constant e or e′ decreased by a out 30%), which is expected to be valid for baryon numbers greater than B ～ 10. The rational map approximation is used to describe multiskyrmions with a baryon number of up to about 30 and to calculate the quantities necessary for their quantization (moments of inertia, sigma term, etc.).     

Selfconsistent calculations of highly excited nuclei

Selfconsistent calculations of excitation energies and entropies of highly excited nuclei have been performed using the temperature-dependent constrained Hartree-Fock (HF)method with the Skyrme interaction. The selfconsistent variations of the level spectra as functions of the temperature (at a fixed deformation) are shown to be small and practically do not affect the results for the entropy versus excitationenergy. The disappearance of the shell fluctuations in the potential energy surface of a rare earth nucleus around T ～ 3 MeV is demonstrated.     

Mass splittings of nuclear isotopes in chiral solition approach

The differences in the masses of isotopes with atomic numbers between ～10 and ～30 can be described within the chiral soliton model in satisfactory agreement with data. The rescaling of the model is necessary for this purpose—a decrease in the Skyrme constant by ～30%, providing the “nuclear variant” of the model. The asymmetric term in the Weizsäcker-Bethe-Bacher mass formula for nuclei can be obtained as the isospin-dependent quantum correction to the nucleus energy. Some predictions of the binding energies of neutron-rich isotopes are made in this way from, e.g., ¹⁶Be, ¹⁹B to ³¹Ne or ³²Na. The neutron-rich nuclides with high values of isospin are unstable relative to decay owing to strong interactions. The SK4 (Skyrme) variant of the model, as well as the SK6 variant (sixth-order term in the derivatives of the chiral field in the Lagrangian as soliton stabilizer), is considered; the rational-map approximation is used to describe multi-Skyrmions.     

Extended skyrmion model from quark flavour dynamics

From the effective chiral meson lagrangian derived recently from Nambu-Jona-Lasinio type of quark flavour dynamics, an extended skyrmion model is extracted. This model contains besides the usual Skyrme term further fourth-order derivative terms of the chiral field and in addition the ω meson field. It is shown that the net effect of all fourth-order derivative terms is to destabilize the soliton and to provide the desired medium-range attraction of the nucleon-nucleon interaction, which is responsible for nuclear binding but missing in the original Skyrme model. The soliton is stabilized by the coupling to the ω meson which produces a short-range repulsion. The corresponding equation of state of skyrmion matter is constructed and found to be in qualitative agreement with the equation of state of nuclear matter obtained from effective density-dependent forces.     

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.     

Statistical spectroscopy for nuclei in the fp shell

Nuclei in the fp shell have been studied using the spectral averaging method. This was attempted with a view to provide a rather simple alternative to detailed microscopic calculations. We have considered a decomposition of the overall spectroscopic space (m particles in the fp shell) in terms of a spherical j-orbit, isospin, configuration-isospin and SU(4) isospin subspaces. Centroid energies and widths of these subspaces are evaluated and used to determine binding energies, low-energy spectra and fractional occupancy of j-orbits. We have also examined the extent of Wigner SU(4) symmetry mixing for nuclei in this shell. The ratio of binding energies of isobars suggested by Franzini and Radicati to test the validity of SU(4) symmetry is also evaluated from the calculated binding energies. Comparisons are made with microscopic calculations like the shell model and Hartree-Fock where available. We find that the distribution method is able to determine ground-state energies and spectra of nuclei very well despite the fact that the vector spaces are quite large. The SU(4) symmetry in the ground-state region of these nuclei is strongly mixed largely due to the single particle spin-orbit coupling.     

Systematics of quadrupolar correlation energies

We calculate correlation energies associated with the quadrupole shape degrees of freedom with a view to improving the self-consistent mean-field theory of nuclear binding energies. Systematic results are presented for 605 even-even nuclei from mass number 16 to the heaviest whose mass has been measured, using the Skyrme SLy4 interaction and the generator coordinate method. Correlation energies range from 0.5 to 6.0 MeV, and their inclusion improves two qualitative deficiencies of the mean-field theory, namely, the exaggerated shell effect at neutron magic numbers and the failure of mean-field theory to describe mutually enhanced magicity. For the mass table as a whole, the quadrupolar correlations improve binding energies, separation energies, and separation energy differences by 20%30%.     

Self-consistent mean-field description of nuclear structure and dynamics—a status report

This contribution deals with the predictive power of the Skyrme-Hartree-Fock model. First, we discuss the phenomenological adjustment of the Skyrme energy-functional and the choice of proper fit data. Then, we check the reliability in extrapolations to other observables and nuclei, using two strategies: first, comparison with data for observables not included in the fit, and second, an estimate of the extrapolation error by virtue of the least-squares fitting techniques. Test cases will be energies of extremely neutron rich Sn isotopes as well as energies, giant resonances, and fission properties of super-heavy elements.     

热核上的isovector巨多极共振

将有限温度自洽半经典sumrule方法应用于研究热核上的isovector巨多极共振。用扩展Skyrme力计算了isovector巨单极共振(GMR),巨偶极共振(GDR)和巨四极共振(GQR)的平均激发能量的温度效应。 关键词：     

Core polarization effects on transition densities in medium-heavy nuclei

We propose a microscopic model to study the core-polarization effects of giant resonances on the transition densities of open-shell nuclei. We use the Hartree-Fock-RPA method for the calculation of the single-particle wave functions and the response function of the giant resonances. Particle-vibration coupling is applied to take into account the core polarization effect on the valence many-body wave functions. We apply our model to the quadrupole transitions in the several medium-heavy nuclei. Valence many-body wave functions are calculated with the generalized seniority scheme and with the shell model. Results for the proton and neutron effective charges and the Coulomb form factors for the N = 82 isotones and for ¹¹⁶Sn and ¹¹⁰Pd are presented and discussed. The effective coupling hamiltonian is determined by the Skyrme interaction SGII which is used also in the HF and RPA calculations. The calculated core polarization charges show some state dependences. The average theoretical values are δe_p = 0.4–0.5 and δe_n = 0.6–0.7 compared to typical empirical values of δe_p = 0.6 and δe_n = 1.2.