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.     

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.     

Separabelized Skyrme interaction and characteristics of giant dipole resonances

The accuracy of eliminating the spurious state from the E1-transition strength distribution is studied within the random phase approximation with separabelized Skyrme forces.     

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.     

Effect of large neutron excess on the dipole response in the region of the giant dipole resonance

The evolution of the dipole response in nuclei with strong neutron excess is studied in the Hartree-Fock plus random phase approximation with Skyrme forces. We find that the neutron excess increases the fragmentation of the isovector giant dipole resonance, while pushing the centroid of the distribution to lower energies beyond the mass dependence predicted by the collective models. The radial separation of proton and neutron densities associated with a large neutron excess leads to non-vanishing isoscalar transition densities to the GDR states, which are therefore predicted to be excited also by isoscalar nuclear probes. The evolution of the isoscalar compression dipole mode as a function of the neutron excess is finally studied. We find that the large neutron excess leads to a strong concentration of the strength associated with the isoscalar dipole operator ∑_ir_i³Y₁₀, that mainly originates from uncorrelated excitations of the neutrons of the skin.     

Roles of tensor and isoscalar pairing interactions in β-decay calculations for possible r-process waiting point nuclei with N ~ 82 and 126

In this study, we adopt the self-consistent Hartree-Fock-Bogoliubov (HFB) theory with the proton-neutron quasi-particle random phase approximation (pnQRPA) based on the Skyrme force for calculation of the β^? decay half-lives for nuclei with N ~ 82 and 126 on possible r-process paths. In the calculations, the Skyrme interaction (e.g., SKO') is adopted, and the tensor interaction is added self-consistently in both HFB and QRPA calculations. We systematically study how the half-life is changed by varying the strength of the triplet-even (TE) and triplet-odd (TO) components as well as the IS pairing. We find that a variation in strength of the IS pairing of approximately 20% does not produce a substantial effect on β-decay rates with or without the tensor force, while a strength variation of the TO tensor force considerably affects the change in the β-decay half-lives for the very neutron rich N ~ 82 and 126 isotonic chains. In addition, with the inclusion of the tensor force, the GT decay becomes dominant for very neutron-rich nuclei.     

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.     

Excitation of pygmy dipole resonance in neutron-rich nuclei via Coulomb and nuclear fields

We study the nature of the low-lying dipole strength in neutron-rich nuclei, often associated with the pygmy dipole resonance. The states are described within the Hartree-Fock plus RPA formalism, using different parametrizations of the Skyrme interaction. We show how the information from combined reaction processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.     

Deuteron under strong magnetic fields: Skyrme model study

We explore the deuteron under strong magnetic fields in Skyrme models. The effects of the derivative dependent sextic term in the Skyrme Lagrangian are investigated, and the rational map approximation is used to describe the deuteron. The influences of strong magnetic fields on the electric charge distribution and mass of the deuteron are discussed.     

Effect of tensor nucleon-nucleon forces on the nucleon-nucleus optical potential

In the approximation of unpolarized nuclear matter, the optical potential for nucleon-nucleus scattering is calculated on the basis of the effective Skyrme interaction with allowance for tensor nucleon-nucleon forces. It is shown that the tensor Skyrme forces make a significant contribution to the imaginary part of the optical potential. The effect of tensor nucleon-nucleon forces on the radial distribution of the imaginary part of the optical potential is investigated by considering the example of elastic neutron scattering by ⁴⁰Ca nuclei at scattering energies of about a few tens of MeV.     

Radiative strength function and the pygmy dipole resonance in <Superscript>208</Superscript>Pb and <Superscript>70</Superscript>Ni

The pygmy-resonance parameters and the E1 strength function are derived for ²⁰⁸Pb using a fully self-consistent microscopic formalism recently developed for magic nuclei, which takes into account quasiparticle phonon interactions (or coupling to phonons) in addition to the random phase approximation. For the radiative strength function of ²⁰⁸Pb at energies above 5 MeV, the experimental data of the Oslo group are adequately described by our predictions, whereby the important role of coupling to phonons is confirmed. By comparing the measurements based on the (³He, ³He′γ) and (γ, γ′) reactions, we discuss the physical properties of the radiative strength function measured for ²⁰⁸Pb. For the neutron-rich ⁷⁰Ni nucleus, predictions for the radiative strength function and the pygmy resonance are obtained using a partially self-consistent approach, which invokes the Skyrme forces in deriving the mean field, effective nucleon–nucleon interaction, and phonon characteristics.     

The Two-Nucleon Stripping Process with Skyrme Type Potential

Theory of two-nucleon stripping reactions is reconsidered. The nucleon-nucleon interactions are taken as Skyrme type potentials. Differential cross-sections for two-nucleon stripping reactions are calculated using DWBA approximation with different Skyrme type potentials of different parameters. The angular distributions for different two-nucleon stripping reactions (t, p) with incident triton on the different targets of ³¹P, ⁴⁰Ca, ⁹⁶Zr, ¹¹⁸Sn and ²⁰⁶Pb are calculated giving good agreement with the experimental data. Better values are extracted for the spectroscopic factors.     

Skyrme Sphalerons of an O(3)-σ Model and the Calculation of Transition Rates at Finite Temperature

The reduced O(3)-σ model with an O(3)-σ→ O(2) symmetry breaking potential is considered with an additional Skyrmionic term, i.e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motion which, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the flucuation path integrals which is therefore evaluated using a measuremodified Fourier-Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme-less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.     

Electric dipole strength distribution below the <Emphasis Type="Italic">E</Emphasis>1 giant resonance in <Emphasis Type="Italic">N</Emphasis> = 82 nuclei

In this study quasiparticle random-phase approximation with the translational invariant Hamiltonian using deformed mean field potential has been conducted to describe electric dipole excitations in ¹³⁶Xe, ¹³⁸Ba, ¹⁴⁰Ce, ¹⁴²Nd, ¹⁴⁴Sm and ¹⁴⁶Gd isotones. The distribution of the calculated E1 strength shows a resonance like structure at energies between 6–8 MeV exhausting up to 1% of the isovector electric dipole Energy Weighted Sum Rule and in some aspects nicely confirms the experimental data. It has been shown that the main part of E1 strength, observed below the threshold in these nuclei may be interpreted as main fragments of the Pygmy Dipole resonance. The agreement between calculated mean excitation energies as well as summed B(E1) value of the 1⁻ excitations and the available experimental data is quite good. The calculations indicate the presence of a few prominent positive parity 1⁺ States in heavy N = 82 isotones in the energy interval 6–8 MeV which shows not all dipole excitations were of electric character in this energy range.     

On the collective modes of infinite nuclear matter

In this paper we study the longitudinal collective vibrations of infinite nuclear matter in the long wavelength limit. We present an alternative method for solving the Landau equations which allows analytical expressions for the response function, the odd sum rules and the strength of the modes. We solve the theory for a selection of Skyrme interactions and we also consider the properties of the ground state of the system specifically associated with the four collective states which exist in nuclear matter. The relationship between the quantum mechanical response function and the corresponding classical hydrodynamical quantity is explored and the approximate results obtained through sum rules are compared with the exact solutions of the RPA equations. Finally the Landau parameters obtained with the Skyrme forces are tested against the antisymmetry property of the forward particle-hole scattering amplitude on the Fermi surface and the enhancement factor in the photonuclear dipole sum rule.     

Thermodynamic properties of superconducting nuclear matter

Phase diagrams of superconducting nuclear matter are calculated by solving a set of finite temperature gap equations, using several Skyrme effective interactions. Our results indicate that nuclear matter may have a superconducting phase in a small region with density near one half of the normal nuclear matter density and temperature k_BT ≲ 1.4 MeV. Our calculation is based on a finite temperature Green's function method with an abnormal pair cutoff approximation. The same approximation is employed in deriving the internal energy, entropy and chemical potential of superconducting nuclear matter. In this way, its equation of state is obtained, and compared with that of normal nuclear matter. The energy gap of superconducting nuclear matter is found to depend rather sensitively on both density and temperature. This dependence is analysed in terms of the Skyrme interaction parameters. The correlation effect on chemical potential is found to be important at high density, and its inclusion is essential in determining the equation of state of superconducting nuclear matter.     

原子核Gamow-Teller共振和β衰变寿命的超越平均场描述

原子核的β衰变是决定宇宙中从铁到铀重元素合成的关键核过程之一。原子核β衰变的主导核跃迁是Gamow-Teller(GT)跃迁,因此,研究原子核β衰变寿命的关键是准确描述原子核的GT跃迁。描述原子核GT跃迁和β衰变寿命最常用的理论模型之一为无规相位近似(RPA)模型。然而,由于该模型仅考虑了一粒子一空穴激发组态,因此无法给出GT共振宽度,并容易高估β衰变寿命。为了克服上述困难,基于Skyrme密度泛函,发展了包含粒子振动耦合效应的无规相位近似(RPA+PVC)模型。相比于RPA模型,该模型在组态空间进一步考虑了一粒子一空穴和声子的耦合组态,从而包含了超越平均场的多体关联效应。为了推广至开壳原子核的研究,进一步考虑了对关联效应,发展了包含准粒子振动耦合效应的准粒子无规相位近似(QRPA+QPVC)模型。基于上述模型,研究了幻数原子核和超流原子核的GT跃迁、β衰变和β+/电子俘获。研究发现,采用同一组Skyrme相互作用参数SkM*,上述模型能够重现实验测量的GT共振宽度和跃迁强度分布,部分解释实验观测的GT跃迁强度压低问题,并同时改进对β衰变寿命的描述。该文针对上述最新研究进展进行了综述,并对将来的发展方向给出展望。     

Generator coordinate calculations of giant resonances with the Skyrme interaction

The Skyrme interaction is shown to lead to significant simplifications in generator coordinate calculations. As an illustration, giant resonances are calculated using pure oscillator wave functions. We present results for monopole, dipole and quadrupole isoscalar and isovector modes using two different Skyrme forces, SIII and SIV. A good agreement with available experimental data is obtained.     

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.