Microscopic approach to the nucleon-nucleon effective interaction and nucleon-nucleon scattering in symmetric and isospin-asymmetric nuclear matter

After reviewing our microscopic approach to nuclear and neutron-rich matter, we focus on how nucleon-nucleon scattering is impacted by the presence of a dense hadronic medium, with special emphasis on the case where neutron and proton densities are different. We discuss in detail medium and isospin asymmetry effects on the total elastic cross section and the mean free path of a neutron or a proton in isospin-asymmetric nuclear matter. We point out that in-medium cross sections play an important role in heavy-ion simulations aimed at extracting constraints on the symmetry potential. We argue that medium and isospin dependence of microscopic cross sections are the result of a complex balance among various effects, and cannot be simulated with a simple phenomenological model.     

Neutron star models and nuclear forces

Equations of state of cold neutron matter are calculated by the method of unitary transformations for a hard-core and a soft-core potential. Equilibrium configurations are constructed in the Newtonian and the general relativistic theory of gravitation. It is found that Newtonian treatment to a certain extent gives very good results. On the other hand neutron star models are strongly affected by the nuclear forces used in the equation of state.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

The role of nucleon-nucleon short-range correlations in the nuclear structure function in thex > 1 region

By using the Jastrow correlation wave function, the role of nucleon-nucleon short-range correlations in the nuclear structure function in thex > 1 region is reanalyzed. The result shows that, with the proper energy-momentum distribution of nucleons in the nucleus including the effect of nucleon-nucleon short-range correlations, the experimental data of the nuclear structure function in thex > 1 region can not be well explained. It seems that additional components which go beyond the conventional nuclear physics are necessary to describe the effect.     

Spin, iso-spin dependence of nucleon-nucleon effective interaction in nuclear matter calculations

A set of density dependent nucleon-nucleon (N-N) interactions has been examined in nuclear matter calculations by varying spin-isospin contributions. Two sets of potentials have been considered. One having a density dependentσ-function type short range part followed by one term long range Gaussian part while the other having a density dependentσ-function part followed by two Gaussian terms. The strength parameters of the potential have been fitted to the saturation properties of nuclear matter, i.e. binding energy per particle of 15.5 MeV atk _F=1.35 fm⁻¹. Several sets of these two potentials have been generated by varying the strength parameterM of Majorana exchange operatorP _M. It is seen thatM indirectly controls the spin, iso-spin contribution to the interaction potential and thus affects the nuclear matter properties such as compressibility and symmetry energy considerably, while variation of these quantities with the range parameterμ for givenM is moderate at lowM values while at higherM values it is quite large.     

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.     

Effect of confined one-gluon-exchange potential and instanton-induced interaction on nucleon–nucleon interaction

The effect of confined one-gluon-exchange potential and instanton-induced interaction potential in the singlet(~1S_0) and triplet(~3S_1) channels for nucleon–nucleon interaction has been investigated in the framework of the relativistic harmonic model using the resonating group method in the adiabatic limit with the Born–Oppenheimer approximation. The contributions of the different components of the interaction potentials have been analyzed.     

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ( ,) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, does not depend sensitively on the choice of the parameter γ in Skyrme interaction. Received: 5 May 2000 / Accepted: 16 January 2001     

Saturation of nuclear matter and short-range correlations

A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each other. The resulting saturation densities are closer to the empirical result when compared with (continuous choice) Brueckner-Hartree-Fock values. Arguments for the dominance of short-range correlations in determining the nuclear matter saturation density are presented. A further survey of the role of long-range correlations suggests that the inclusion of pionic contributions to ring diagrams in nuclear matter leads to higher saturation densities than empirically observed. A possible resolution of the nuclear matter saturation problem is suggested.     

Determination of the nucleon-nucleon interaction in the ImQMD model by nuclear reactions at the Fermi energy region

The nucleon-nucleon interaction is investigated by using the improved quantum molecular dynamic (ImQMD) model with three sets of parameters IQ1,IQ2 and IQ3,in which the corresponding incompressibility coefficients of nuclear matter are different. The charge distributions of fragments are calculated for various reaction systems at different incident energies. The parameters strongly affect the charge distributions and the fragment multiplicity spectrum below the threshold energy of nuclear multifragmentation. The fragment multiplicity spectrum for ²³⁸U+¹⁹⁷Au at 15 A MeV and the charge distributions for ¹²⁹Xe+¹²⁰Sn at 32 and 45 A MeV,and ¹⁹⁷Au+¹⁹⁷Au at 35 A MeV are reproduced by the ImQMD model with the set of parameter IQ3. It is found that: 1) The charge distribution of the fragments and the fragment multiplicity spectrum are good observables for testing the model and the parameters. 2) The Fermi energy region is a sensitive energy region for studying nucleon-nucleon interaction.     

Determination of the nucleon-nucleon interaction in the ImQMD model by nuclear reactions at the Fermi energy region

The nucleon-nucleon interaction is investigated by using the improved quantum molecular dynamic （ImQMD） model with three sets of parameters IQ1, IQ2 and IQ3, in which the corresponding incompressibility coefficients of nuclear matter are different. The charge distributions of fragments are calculated for various reaction systems at different incident energies. The parameters strongly affect the charge distributions and the fragment multiplicity spectrum below the threshold energy of nuclear multifragmentation. The fragment multiplicity spectrum for 238U＋197Au at 15 A MeV and the charge distributions for 129Xe＋12~Sn at 32 and 45 A MeV, and 197Au＋197Au at 35 A MeV are reproduced by the ImQMD model with the set of parameter IQ3. It is found that： 1） The charge distribution of the fragments and the fragment multiplicity spectrum are good observables for testing the model and the parameters. 2） The Fermi energy region is a sensitive energy region for studying nucleon-nucleon interaction.     

Charge density: A probe for the nuclear interaction in microscopic transport models

The transport properties of the ³⁶Ar +⁵⁸Ni system at measured with the INDRA array, are studied within the BNV kinetic equation. A general protocol of comparison between the N-body experimental fragment information and the one-body distribution function is developed using global variables, with a special focus on charge density. This procedure avoids any definition of sources and any use of an afterburner in the simulation. We shall discuss the feasibility of such an approach and the distortions induced by the finite detection efficiency and the completeness requirements of the data selection. The sensitivity of the different global observables to the macroscopic parameters of the effective nuclear interaction will be studied in detail.Received: 21 January 2003, Published online: 5 August 2003PACS: 25.70.-z Low and intermediate energy heavy-ion reactions - 24.10.-i Nuclear reaction models and methodsN. Le Neindre: Permanent address: Institut de Physique Nuclaire, IN2P3-CNRS, F-91406 Orsay cedex, France.     

Phase transitions for two-dimensional models with isotropic short-range interactions and continuous symmetries

Using the powerful method of reflection-positivity and chess-board estimates, we prove the existence of phase transition for certain class of isotropic short-range interactions with continuous symmetry, provided that the dimension of the lattice is at least two, and the temperature is low enough.     

Calculations of the triton binding energy for Reid's soft-core nucleon-nucleon interaction

The triton energy E_T has been calculated variationally for Reid's soft-core potential. The $\text{L}\text{·}\text{S}\text{-}\text{term}$ and the ¹D₂, ³D₂ states contribute - 2 MeV and +0.2 MeV resp. The odd-state contribution is negligibly small. Our results are compared with those of other authors.     

Energy dependence of effective nucleon-nucleon interaction and position of the nucleon drip line

A semimicroscopic version of the self-consistent theory of finite Fermi systems is proposed. In this approach, the standard theory of finite Fermi systems is supplemented with relations that involve the external values of the invariant components of the Landau-Migdal amplitude and which follow from microscopic theory. The Landau-Migdal amplitude at the nuclear surface is expressed in terms of the off-shell T matrix for free nucleon-nucleon scattering at the energy E equal to the doubled chemical potential of the nucleus being considered. The strong energy dependence of the free T matrix at low E changes the properties of nuclei in the vicinity of the nucleon drip line. It is shown that, upon taking into account the energy dependence of the effective interaction, the neutron drip line is shifted considerably toward greater neutron-excess values. This effect is illustrated by considering the example of the tin-isotope chain.     

Asymptotic symmetry breakdown and restoration in a statistical system of particles with a short-range vector interaction,and cosmological models

A relativistic statistical system of particles interactine via a massive Prock vector field on a Schwarzschild gravitational field background, is considered. It is shown that in the case of attraction of like charges, an asymptotic breakdown of the discrete symmetry is possible at large r, and its restoration at rr. Isotropic cosmological models are constructed both for the case of attracting and repulsing charges.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp, 42–48, September. 1982.     

P-odd effects observed in neutron-induced reactions and isospin structure of weak nucleon-nucleon interaction

It is shown that, by introducing a resonance phase for two opposite-parity quasistationary states of the same spin, the observed sign dependence of P-odd effects in neutron-induced reactions can be matched with theoretical predictions. The proposed approach makes it possible to deduce information about the isospin structure of weak nucleon-nucleon interaction.     

A study of short-range correlation effects on nuclear spatial and momentum distribution

The relation between the nuclear spatial and momentum densities is studied by means of their integral representations in terms of uniform distributions. Examples of this approach are given for the harmonic oscillator model of⁴He and¹⁶O, with and without Jastrow correlations, and for the single-particle potential model of⁴⁰Ca.