Hartree-Fock calculations of surface-symmetry properties with finite-range forces

Complete Hartree-Fock calculations on asymmetric semi-infinite nuclear matter have been performed with a family of finite-range Gogny-type forces. For one of these forces all the computed values of the droplet-model symmetry coefficients J, L, M and Q are in good agreement with recent mass-formula fits.     

Surface incompressibility of semi-infinite nuclear matter via constrained Hartree-Fock calculations

With a view to calculating the incompressibility \(\ddot \sigma \) of the nuclear surface, we develop a constrained Hartree-Fock treatment of semi-infinite nuclear matter. Our approach leads first to a proof of the “ \(\dot \sigma = 0\) ” theorem of Myers and Swiatecki, and then to a corroboration of a simple expression for \(\ddot \sigma \) , previously obtained in an intuitive way by Stocker. This expression is used to calculate \(\ddot \sigma \) for theS3, SkM and Gogny forces. The results are significantly different from those of a scaled HF calculation, but in very good agreement with the values of \(\ddot \sigma \) that are implied by RPA calculations of the breathing mode in various finite nuclei.     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Lowest-order and hyper-netted-chain calculations of nuclear matter

Employing two model central interactions the binding energy of nuclear matter is calculated within the framework of the Jastrow variational approach using different types of constrains and including all the contributions from hypernetted-chain diagrams.     

Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.     

Jastrow-type calculations for nuclear matter with the normalization condition

Results are given of constrained Jastrow calculations for the energy per particle and the density of nuclear matter using the test potentials IY and OMY-6, as well as several others, and various correlation functions involving parameters. The constraint chiefly employed is the normalization condition in first order, a condition naturally entering the Jastrow formalism. The energy in the minimization is approximated by the first two and in some cases by the first three terms of its FIY cluster expansion. In addition to the three-body terms in the FIY expansion, the corresponding terms of the AHT expansion are also calculated for comparison. From the computations which were performed it seems that, at least in some cases, the normalization condition constitutes a quite satisfactory constraint, leading to reliable results, when used in low order calculations. In addition, conclusions are drawn as to the sensitivity of the results to the constraint, correlation function and minimized energy expression.     

Microscopic calculation of a pairing gap in semi-infinite nuclear matter

The pairing gap in semi-infinite nuclear matter has been calculated microscopically by solving the gap equation for a nonlocal interaction with the aid of the method proposed by V.A. Khodel, A.V. Khodel, and J.W. Clark [Nucl. Phys. A 598, 390 (1996)] for the case of infinite nuclear matter. The calculation employs the effective pairing interaction obtained previously for semi-infinite geometry on the basis of the separable 3×3 representation of the Paris nucleon-nucleon potential. The gap found in this way changes sharply in the surface region, where it has a pronounced maximum. The dependence of the surface effect on the chemical potential of nuclear matter has been investigated.     

Constrained variational calculations on nuclear matter with state dependent correlations

Constrained variational calculations on the binding energy of nuclear matter have been performed employing three potentials with differing mixtures of central and tensor components. We present numerical results on the energy expectation value in two- and three-body cluster approximation as function of the separation distance at which the central and tensor correlations heal smoothly.     

Variational calculations of realistic models of nuclear matter

We report variational calculations of nuclear matter with a semi-realistic Reid v₁₂ model, and a realistic v₁₄ model of the two-nucleon interaction operator. The v₁₄ model fits the available nucleon-nucleon scattering data up to 425 MeV lab energy, and has relatively weak L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions in addition to the standard central, tensor and ($\text{L}\text{·}\text{S}$). The L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions are treated semiperturbatively; their contribution reduces the overbinding of nuclear matter. However, the equilibrium k_F = 1.7 fm^?1 and E₀ = ?17.5 MeV obtained with the v₁₄ model are both higher than their empirical values k_F = 1.33 fm^? and E₀ = ?16 MeV. We assume that the difference between the calculated and empirical E(ρ) is entirely due to three-nucleon interactions (TNI). The TNI contributions are phenomenologically added to the nuclear matter energy, and their parameters are adjusted to obtain the correct equilibrium energy, density and compressibility. The required TNI contributions appear to be of reasonable magnitude.     

Quantum Monte Carlo calculations of symmetric nuclear matter

We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon-nucleon interactions by means of auxiliary field diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and represents an important step forward towards a quantitative understanding of problems in nuclear structure and astrophysics.     

A remark on the saturation of nuclear forces in nuclear matter

The paper deals with the problem of saturation in nuclear matter, when the two-nucleon interaction is described by the soft core potentials acting in a limited number of orbital states. The potentials used belong to the class of the realistic potentials.     

Soft-core correlations and three body forces in nuclear matter

We show that, when nucleon-nucleon correlations are taken into account using correlation functions derived. from the Reid soft core potential, the contribution of three body forces to the binding energy of nuclear matter is enhanced. The two pion exchange three body forces contributes 6 MeV attraction.     

Constrained semi-infinite nuclear matter and droplet model theorems on nuclei surface structure

Using a completely general constrained energy-density method, we prove two theorems, describing the surface structure of asymmetric semi-infinite nuclear matter, earlier demonstrated only in the droplet model (DM) context by Myers and Swiatecki. As a consequence a well-known relation between neutron skin-thickness and the surface stiffness coefficientQ is shown to have a much wider validity than in the DM context. Moreover we exhibit a microscopic reason for a relation, (earlier quoted as unexpected), between DM surface coefficients and the volume-symmetry coefficientJ.     

Variational calculations of ν8 models of nuclear matter

We report variational calculations of ν8 models of nuclear matter which contain central, spin, isospin, tensor and spin-orbit potentials. These semi-realistic models can explain the nucleon-nucleon scattering in 1S0, 3S1?3D1, 1P1 and 3P2?3F2 states up to ～ 300 MeV. The variational wave function has two-body central, spin, isospin, tensor and spin-orbit correlations. The terms in the cluster expansion of the energy expectation value, that do not contain the spin-orbit correlations are summed by chain summation techniques developed for the ν6 models. Of the terms containing spin-orbit correlations, the two-body and three-body-separable ones are calculated, and the magnitude of the rest is estimated. Results for three phase-equivalent ν8 models, which differ significantly in the strength of tensor and spin-orbit potentials, are reported. They suggest that simple ν8 models may not be able to simultaneously explain the binding energy and density of nuclear matter.     

Nucleon sigma term and quark condensate in nuclear matter

We study the bound-nucleon sigma term and the quark condensate in nuclear matter. In the quark-meson coupling (QMC) model the nuclear correction to the sigma term is small and negative, i.e., it decelerates the decrease of the quark condensate in nuclear matter. However, the quark condensate in nuclear matter is controlled primarily by the scalar-isoscalar σ field. Compared to the leading term, it moderates the decrease more than that of the nuclear sigma term alone at densities around and larger than the normal nuclear-matter density.     

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin–orbit terms from the spin–isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin–orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.     

Some nuclear matter calculations: (II). Insertions in hole and particle lines

Brueckner-Goldstone diagrams that represent insertions in the particle and hole lines of the basic two-body ladder diagram are calculated with the Reid soft-core potential. The bubble insertions in particle lines are calculated exactly, off the energy shell, for small excitations (≦ 2k_F), and contribute 1.5 MeV to the binding energy of nuclear matter. Comparisons are made with the approximations used by Brueckner and Gammel (BG) and by Bethe, Brandow and Petschek (BBP). The BG method is found to be fairly accurate for the treatment of small excitations. The BBP method, used in Dahlblom's three-body work, underestimates the binding by 0.7 MeV. The third-order insertion in hole lines contributes 1.8 MeV to the binding energy, when the reaction matrix is calculated with the bubble insertions in particle lines. Without these bubble insertions the contribution is 1.0 MeV. The difference is due to the slower healing when bubble insertions in particle lines are included as the gap between hole and particle energies then decreases. Inclusion of other higher-order diagrams reduces the contribution from the third-order insertion from 1.8 to 1.2 MeV. Day estimated this contribution to be 0.6 MeV. Bethe, using Dahlblom's and Day's results concludes that the Reid soft core gives 15.4 MeV binding. Our calculations suggest that this could be increased to 16.7–17.3 MeV.     

Model nuclear matter calculations in several Brueckner and Green's function theories

Model nuclear matter calculations are performed using two versions of the Brueckner theory (standard lowest order theory and a version with self-consistent “physical” onshell insertions in particle lines) and three Green's function theories (Λ ₀₀,Λ ₁₀ and Galitskii's ladder approximation). Ground state properties are derived using a strongs-wave nonlocal separable nucleon-nucleon potential. We investigate the differences between the results obtained using different theories, stemming from different treatment of the exclusion principle and of dispersive effects of the medium. The effect of the off-shell self-consistency in theΛ ₁₀ theory is found to be important.