The Skyrmion Skyrmion interaction and the meson exchange model for the NN potential

The properties of nucleon-nucleon (NN) potentials derived from the Skyrme model are investigated compared to those of typical One-Boson-Exchange (OBE) models, For that purpose the NN as well as the nucleon-antinucleon (N¯N) potentials are evaluated for the isoscalar central channel, the isovector spin channel, and the isovector tensor channel. A comparison of NN and N¯N interactions allows a separation into terms with positive and negativeG-parity and therefore a detailed comparison with the properties of the OBE model. This analysis is performed using the classical Lagrangian of the Skyrme model and considering an extension of this Lagrangian by a term of sixth order, which has recently been proposed. The results indicate that the extended Lagrangian yields an interaction which is quite consistent with the OBE picture. The extended model, however, is much more sensitive to the values of the parameters and the approximations being used for the evaluation of the field for two baryons.     

Effective Interactions in the Delta-Shells Potential

We determine two-body Skyrme force parameters from a nucleon–nucleon interaction as a function of the maximal momentum fitting NN scattering data. We find general agreement with V _{low k} interactions based on high quality potentials.     

The role of iterative isobar processes in nuclear matter and the effective nucleon-nucleon interaction

A calculation is performed using lowest order Brueckner theory in momentum space, with explicit isobar configurations included through the coupled channel mathod. The effective interaction for the¹ S ₀-⁵ D ₀ channel is extracted from this calculation. Two different transition potentials are used — one due to Green and Niskanen (1976), the other, due to Green and co-workers (1978). The nucleon-nucleon (NN) interaction used is the Reid soft core potential, compensated for the inclusion of the explicit isobar channel. The effective interaction shows marked momentum dependence in the intermediate range. The loss of attraction depends on the transition potential one chooses. The correlation function involving the nucleon-isobar intermediate state is anti-correlated to the NN part.     

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N²LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.     

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.     

Stabilization of skyrmions via ϱ-mesons

It is shown that a skyrion can be stabilized by introducing ?-mesons into the chiral SU(2)_L × SU(2)_R lagrangian without higher-derivative terms like the Skyrme term. The ?-mesons are considered as dynamical gauge bosons associated with a hidden local symmetry of the non-linear sigma model. The lagrangian reduces to the Skyrme model in a limit of parameters. The Skyrmion mass M is found to be M = 1058 MeV when the parameters are fixed so as to satisfy the KSRF relation. It is also shown that a solition solution in a model with Ω-meson coupled with the baryonic current is a saddle-point solution.     

The hyperon-nucleon interaction potential in the bound-state soliton model: the ΛN case

We develop the formalism to study the hyperon-nucleon interaction potential within the bound-state approach to the SU(3) Skyrme model. The general framework is illustrated by applying it to the diagonal ΛN potential. The central, spin-spin and tensor components of this interaction are obtained and compared with those derived using alternative schemes.     

Structural considerations for elastic magnetic electron-nucleus scattering

To explain the form factors obtained by magnetic electron scattering on ¹⁷O it is clear that core polarization has to be taken into account. We discuss how this can be done by means of the Hartree-Fock theory. We note that projection from an intrinsic state of definite K gives an incorrect answer for weakly deformed systems such as ¹⁷O and we present an alternative procedure for extracting the moments. Using a purely velocity dependent Skyrme interaction (only t₀ and t₁ are non-zero) a Hartree-Fock calculation is carried out for the seventeen-nucleon system. The calculation leads to a suppression of the M3 form factor. It is emphasized that the suppression arises from the fact that not only is the ¹⁶O core deformed, but that spin-up particles have a different deformation than spin-down particles. This arises from the spin dependence of the interaction and from the Pauli principle. A peculiar feature with the interaction that is used is that the M5 form factor gets enhanced. This is attributed to the repulsive velocity dependent term in the interaction. The origin of the velocity dependence is discussed. The effect of the velocity dependence on the magnetic moment operator is also considered.     

Spin-orbit and Pauli-correlation effects in intermediate-energy proton-nucleus inelastic scattering

The excitation of the 3^? (6.13 MeV) state of ¹⁶O by 0.8 GeV protons is studied using Glauber theory with a spin-orbit NN amplitude. Two previously suggested approaches for handling the z-ordered non-commuting NN profile functions, γ, are compared and found to give nearly identical results for the usual observables. Transitions to certain LM substates which are forbidden in one approach are allowed in the other, but their cross sections are proportional to the fourth power of the strength of the NN spin-orbit amplitude and thus quite small. It is also shown that, in this energy region, an expansion in powers of the strength of the spin-orbit interaction converges rapidly and consequently any convenient ordering of the γ's can be used without serious errors. Using this result an estimate of the effects of Pauli correlations on the cross section and the polarization is given.     

The pd → tπ+ reaction in an isobar model: Angular distributions

Various wave function effects are studied in the differential cross section for the pd → tπ⁺ reaction. These include both S- and D-waves for the deuteron and the triton as well as the production of p-wave and d-wave pions. For the triton a parametrized Faddeev wave function is employed and for the deuteron a wave function of Hulthén or McGee type. The two-body correlations considered are NΔ(⁵S₂, ^5D₂, ⁵P₃) and NN(¹D₂) which are found to be the most important partial waves in the pp → dπ⁺ reaction.     

The Skyrme-TQRPA calculations of electron capture on hot nuclei in pre-supernova environment

We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme–TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, ⁵⁶Fe, the Skyrme–TQRPA approach is applied to analyze thermal effects on the strength function of GT₊ transitions which dominate electron capture at E _e ≤ 30 MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are comparedwith those of the other model calculations.     

Nuclear interface energy at finite temperatures

The thermodynamic properties at finite temperatures of the plane interface between two phases of nuclear matter in equilibrium are examined theoretically, and explored numerically. The microscopic hamiltonian, the Skyrme I′ interaction, is used in the Thomas-Fermi approximation to obtain the finite-temperature extensions of earlier zero-temperature results which used the Hartree-Fock and Thomas-Fermi methods. Approximate analytic fits are given to the χ_i (proton fraction on the dense-matter side) dependence of the critical temperature, and to the T and χ_i dependences of the surface thermodynamic potentials, the density of surface neutrons, the surface entropy and the neutron and proton chemical potentials at phase equilibrium. These fits are an ingredient in a compressible liquid-drop nuclear model, the basis of an equation of state for hot, dense matter needed in certain astrophysical applications.The liquid-drop model is used here to construct an isolated, low-T nucleus, whose properties are compared with the original zero-T Hartree-Fock calculations which lead to the Skyrme I interaction, and with other mass formulae. The low-temperature expansion of the surface energy is compared with that obtained in other calculations. The nuclear level density at the Fermi surface, related to the low-T expansion of the entropy of the whole nucleus, is also discussed.     

The short-range nucleon-nucleon repulsion

The short-range repulsion (0.2–0.4 fm) between nucleons is investigated. The opposing effects of ω-meson exchange and ε-meson (J^p = 0⁺) exchange are investigated, and the relation to Regge behaviour is demonstrated using fixed-s dispersion relations. The energy dependence of the short-range interaction is emphasized, and experimental data on polarization in elastic NN scattering at high energy are used to give the necessary coupling constant.     

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio.     

An isobar model for the pd → tπ+ reaction

The differential cross section for the pd → tπ⁺ reaction is calculated at the three proton laboratory energies 400, 470 and 600 MeV. The triton wave function is taken to be of correlated Gaussian form, and the deuteron is one of the s-wave forms due to Hulthén, McGee and Paris. The pion production is considered to take place from intermediate states based on the five types of two-body correlations NΔ(⁵S₂, ⁵D₂, ⁵D₀) and NN(¹D₂, ¹S₀). The final cross sections are not in good agreement with experiment.     

The phonon-coupling model for Skyrme forces

A short review on the self-consistent RPA based on the energy-density functional of the Skyrme type is given. We also present an extension of the RPA where the coupling of phonons to the single-particle states is considered. Within this approach we present numerical results which are compared with data. The self-consistent approach is compared with the Landau–Migdal theory. Here we derive from the self-consistent ph interaction, the Landau–Migdal parameters as well as their density dependence. In the Appendix a new derivation of the reduced matrix elements of the ph interaction is presented.     

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio.     

Nucleon--nucleon interactions in the double folding model for fusion reactions

Nucleus--nucleus potentials are determined in the framework of double folding model for M3Y--Reid and M3Y--Paris effective nucleon--nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile--spherical target system ¹⁶O+²⁰⁸Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y--Reid and M3Y--Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.