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.     

Off lattice simulations of cluster-cluster aggregation in dimensions 2–6

Cluster-cluster aggregation has been simulated in dimensions two to six using both linear and brownian cluster trajectories. Relatively efficient off lattice algorithms have allowed large clusters to be generated and values for the fractal dimensionalities of the aggregates have been obtained without finite concentration effects. The values for the fractal dimensionality are in good aggreement with lattice model simulations for euclidean dimensionalities 2–4. The effective dimensionality (D_β) obtained from the dependence of the radius of gyration on cluster size increases with increasing cluster size for all of our models (particularly for d ≥ 4). For clusters in the accessible size range (up to 10³-10⁴) D_β is slightly larger for cluster-cluster aggregation via linear trajectories than for brownian trajectories. For cluster-cluster aggregation via brownian trajectories, the limiting (large cluster size) fractal dimensionality is estimated to be 1.46 ± 0.04 for d=2,1.82 ± 0.10 for d = 3, 2.10 ± 0.15 for d = 4, 2.35 ± 0.15 for d = 4, 2.65 ± 0.25 for d = 6. For cluster- cluster aggregation via linear trajectories, the limiting fractal dimensionality is estimated to be 1.55 ± 0.04 for d = 2, 1.91 ± 0.10 for d = 3≥ 2.5 ± 0.06 for d = 5 and ≥2.64 ± 0.05 for d = 6.     

Constraints on neutron skin thickness and symmetry energy of 208Pb through Skyrme forces and cluster model

We used the cluster structure properties of the 212Po to estimate the neutron skin thickness of 208Pb.For this purpose,we considered two important components:(a)alpha decay is a low energy phenomenon;therefore,one can expect that the mean-field,which can explain the ground state properties of 212Po,does not change during the alpha decay process.(b)212Po has a high alpha cluster-like structure,two protons and two neutrons outside its core nucleus with a double magic closed-shell,and the cluster model is a powerful formalism for the estimation of alpha decay preformation factor of such nuclei.The slope of the symmetry energy of 208Pb is estimated to be 75±25 MeV within the selected same mean-fields and Skyrme forces,which can simultaneously satisfy the ground-state properties of parent and daughter nuclei,as their neutron skin thicknesses are consistent with experimental data.     

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory

The role of tensor force on the collision dynamics of ¹⁶O+¹⁶O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25%, while the calculation with tensor force T11 has good agreement with experimental cross section.     

A study of π±9Be cross sections,and determination of the π 9Be coupling constant

We calculate the total cross sections for π ⁹Be scattering in the Glauber model for two different nuclear models, a single-nucleon model and a cluster model. The cluster model gives much smaller cross sections than the single-nucleon model. Applying forward dispersion relations to the antisymmetric π ⁹Be amplitude, we determine the π ⁹Be coupling constant as (f²)_eff=0.04±0.01.     

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.     

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.     

MICROSCOPIC OPTICAL POTENTIAL CALCULATIONS OF FINITE NUCLEI WITH EXTENDED SKYRME FORCES

Microscopic optical potential calculations in the Hartree-Fock (HF) approximation with Extended Skyrme forces are investigated. The HF equation is derived from the variation principle and the potential formula of spherical nuclei is obtained by two different ways. Then the calculations for symmetric nuclei ¹⁶O, ⁴⁰Ca and asymmetric nucleus ⁹⁰Zr with eight sets of Skyrme force parameters are presented. Our results show that the potential from and variating tendency with incident energy are reasonable and there apparently appears a "wine-bottle-bottom" shape in the intermediate energy region. Furthermore, our calculations reflect shell effects clearly.     

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.     

On the use of Skyrme forces in self-consistent RPA calculations

Self-consistent random-phase (RPA) calculations including the continuum are presented using Skyrme forces. The density-dependent interpretation of the interaction is favoured as it does not violate the spin stability. A possible density dependence of the momentum-dependent S- and P-interaction is taken into account, which allows one to vary the incompressibility K and the effective mass $\text{m}{}^1\text{/m}$ independently. It is shown by analytic relations that these two quantities are the only degrees of freedom left in the parameterization of this Skyrme force,if the ground-state properties shall be reproduced, except for a still open degree of freedom in the spin exchange parameterization. The Landau parameters are discussed as a function of these degrees of freedom in order to find the best possible particle-hole interaction. Continuum calculations of the 1^?, 2 ⁺ and 3^? states in ¹⁶O are presented and compared with-discretized continuum calculations. It is found that the existing Skyrme forces do not show enough attraction and in addition cause relatively large isospin impurities, in ¹⁶O as well as in ²⁰⁸Pb. The influence of large configuration spaces is discussed. A systematic search for an interaction with a stronger particle-hole interaction is presented which seems to favour interactions with a high effective mass, but a low compression modulus.     

Calculation of the static and dynamic triaxial shapes of 24Mg

The Skyrme interaction is used in a Hartree-Fock calculation of ²⁴Mg with triaxial symmetry. A transition between axial and triaxial shapes is studied as a function of the spin-orbit strength. The effect of the other components of the interaction on the shape of ²⁴Mg is examined. Constrained Hartree-Fock calculations of the energy surface and the cranking mass parameter are used for the calculation of the intrinsic γ-vibration. The main result of the dynamical calculation is that despite the different equilibrium shapes obtained with the two forces SIII and SV, the triaxiality obtained by considering the zero-point γ-oscillation is essentially the same for both forces.     

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.     

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.     

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.     

Nuclear-matter incompressibility from fits of generalized Skyrme force to breathing-mode energies

In an attempt to extend the range of values of K_v, the incompressibility of symmetric nuclear matter, for which fits to the measured breathing-mode energies are possible, we investigate generalized Skyrme-type forces with a term that is both density- and momentum-dependent. Acceptable fits are found to be possible only for values of K_v in the range 215±15 MeV. For higher values fits are impossible, while for lower values fits are achieved only by introducing an unphysical collapse of nuclear matter. Thus our generalization of the Skyrme force does not permit a significantly wider range of values of K_v than that already given by force SkM¹. However, with a view to having a more reliable estimate of the compressional properties of the highly neutron-rich nuclear matter that comprises the core of collapsed stars, we present a new version of this latter force giving a much better fit to the masses of neutron-rich nuclei. Comparison with force SkM¹ also shows that the value of K_v extracted from the breathing-mode energies is essentially independent of the choice of effective mass. By providing a counter-example, we show that K_v cannot be extracted from masses and charge distributions alone. As for the third-order coefficient K′, we cannot be more precise than to say that it lies in the interval 700 ± 500 MeV.     

Towards a Skyrme–Hartree–Fock–Bogolyubov Mass Formula

In this work, we explain our astrophysical motivations for deriving a mass formula based on HFB calculations with a Skyrme interaction. We give an overview of existing mass formulae and present briefly the last HF+BCS mass formula [1]. The Skyrme force MSk7 [1] is considered in the study of shell effects at N=82, in the neutron-rich region far from stability, within the HFB and HF+BCS theories, and compared with results obtained using the forces SkP^δ and SkP^δρ [2]. This revised version was published online in July 2006 with corrections to the Cover Date.     

Describing of the properties of quadrupole states in a 94Mo nucleus with skyrme interaction

The influence of coupling between simple and complex configurations on the probabilities of E2 and M1 transitions between vibrational quadrupole states is investigated. The finite rank separable approximation for the Skyrme effective forces is used. Properties of the low-energy spectrum for quadrupole excitations in ⁹⁴Mo nucleus are considered.     

Nuclear monopole polarization in muonic 208Pb

Nuclear polarization effects due to the presence of a muon in an atomic orbit are described in a self-consistent way. Within this framework the monopole part of the polarization energy is calculated by solving Hartree-Fock equations for the combined muon-nucleus system. The nuclear part is described by using the density dependent forces of both Skyrme and Moszkowski. The muon is assumed for the present to be in the 1s and 2s state, respectively, and is treated relativistically. The monopole part of the energy gain turns out to be -0.943 ± 0.070 keV for the 1s-muon and -0.169 ± 0.070 keV for the 2s-muon. The rms-charge-radii are decreasing by 0.20% and 0.036%, respectively.     

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.