Equation of state for pion-condensed neutron matter at finite temperature

The equation of state for neutron matter in the presence of a pion condensate is investigated at finite, but small temperature within the σ model. It is found that a transition of van der Waals type takes place at low temperature for sufficiently strong effective p-wave interaction, which disappears however beyond a critical temperature T_c. Within a wide variety of model assumptions, an upper limit of about 50 MeV is found for T_c.     

Relation between nuclear matter and nuclear potential in inelastic alpha—nucleus scattering

Inelastic transition form factors for alpha—nucleus collective excitations are derived from deformed matter distributions by averaging an effective alpha nucleus interaction over the nucleons in the nucleus. The method is an extension of the procedure of calculating the real part of elastic alpha—nucleus potentials from nuclear matter distributions. Numerical examples for the nuclei of ⁴²Ca and ¹⁴²Nd are given. The resulting inelastic form factors depend on the multipolarity of the inelastic excitation and differ from those conventionally derived from a deformed optical potential.     

Non-central effective forces between nucleons in nuclear matter

The non-central components of the Sprung-Banerjee effective interaction are derived from a nuclear matter calculation based on the Reid potential. The strength of the spin-orbit force is about 10% smaller than empirical values used in recent Hartree-Fock calculations using density-dependent interactions.     

Competition between ferromagnetic and antiferromagnetic spin ordering in nuclear matter

The possibility of ferromagnetic and antiferromagnetic phase transitions in symmetric nuclear matter is analyzed in Fermi liquid theory with the Skyrme effective interaction. The density dependence of the ferromagnetic and antiferromagnetic parameters of spin polarization at zero temperature is obtained for SkM* and SGII effective potentials. In the density region where both solutions of self-consistency equations exist, the ferromagnetic spin state is preferable over the antiferromagnetic spin state.     

Analytical relations between nuclear symmetry energy and single-nucleon potentials in isospin asymmetric nuclear matter

Using the Hugenholtz-Van Hove theorem, we derive general expressions for the quadratic and quartic symmetry energies in terms of the isoscalar and isovector parts of single-nucleon potentials in isospin asymmetric nuclear matter. These expressions are useful for gaining deeper insights into the microscopic origins of the uncertainties in our knowledge on nuclear symmetry energies especially at supra-saturation densities. As examples, the formalism is applied to two model single-nucleon potentials that are widely used in transport model simulations of heavy-ion reactions.     

A simple relation between bulk and surface properties of nuclear matter

Starting from a previously derived relation between the derivatives of the bulk nucleon energy e(n_c) and the surface tension σ(n_c) with respect to the central density n_c we obtain a simple model-independent relation between the values of n_c, σ(n_c), the surface parameter t and the bulk modulus K_∞ at saturation. This relation is checked for values obtained in ETF calculations. K_∞=230 MeV is calculated from the well-known experimental values of n₀, σ₀ and t₀.     

Rotating nuclear matter

Rotating nuclear matter is defined as the system of infinitely many nucleons in a rotating frame neglecting the electrostatic interaction and centrifugal single-nucleon potential. We study the ground state of this system as a function of the densities of neutrons and protons. In the limit where the angular velocity is much smaller than the Fermi energy, the structure of the single-nucleon density corresponds to anisotropic spin distributions at the surfaces of local neutron and proton Fermi spheres. The anisotropy results from the non-central terms in the effective two-nucleon interaction. Contrary to the situation in a system of non-interacting nucleons, the spin asymmetry induced by rotation is a strongly non-linear function of the Fermi momentum. In symmetric nuclear matter at normal density it equals roughly that of the non-interacting system due to mutually cancelling contributions from the spin-orbit and central parts of the effective two-nucleon interaction. The volume contributions to the moments of inertia and single-nucleon Routhian of finite nuclei are calculated, and estimates obtained of certain surface contributions to the moment of inertia.     

Interplay between two- and three-body interaction in light nuclei and nuclear matter

A recent study of different models of three-nucleon interaction (TNI) in ³He, ³H, ⁴He and nuclear matter is extended to study the influence of different choices of the accompanying two-body interaction. A new two-body potential, Argonne υ₁₄, is coupled with both the Tucson and isobar intermediate-state models of two-pion-exchange TNI, with a phenomenological intermediate-range repulsive TNI added to the latter. Variational calculations are carried out for these systems, and compared to the earlier work. We find that a stronger tensor component in the two-body potential, as typified by a larger deuteron D-state percentage, gives more attraction for the TNI, counteracting the saturation effect obtained when only two-body forces are considered.     

Optical potential and nuclear matter

The relation of the parameters of the optical nucleon-nucleus potential to the characteristics of nuclear matter is established. The existing values of the parameters of the optical potential reflect well the binding energy per nucleon and the symmetry energy of nuclear matter. It is shown that the theorem of Hugenholtz and van Hove is not valid for the real part of the optical potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–100, January, 1978.     

On the relation between Brueckner theory and Jastrow theory of nuclear matter

The two- and three-hole-line contributions to the ground state energy as calculated from Brueckner theory are derived from a cluster expansion followed by variation of the trial function. The implications of that derivation both for Brueckner theory and for Jastrow theory are worked out in detail. It is argued that the Jastrow theory is able to give simpler methods to calculate the ground state energy which may be of the same accuracy as current Brueckner calculations. It is shown that the single-particle potential of Brueckner theory is intimately related to a subsidiary condition used in the variation of the trial function. The main steps which have to be taken in a derivation of the general hole-line expansion from Jastrow theory are indicated. It is shown that the hole-line expansion is not a cluster expansion in the sense of Jastrow theory, and an interpretation is given of the “self-consistent choice” of the single-particle potential advocated in Brueckner theory.     

Skyrmion in nuclear matter

The properties of Skyrmions in finite nuclei are considered. The deformation effect is taken into account through the external-field-induced distortion of the profile function of a chiral field. The masses of classical Skyrmions and the distribution of their baryon number versus the Skyrmion position within a nucleus are discussed.     

Superfluid nuclear matter calculations

We present a method to calculate nuclear matter properties in the superfluid phase. The method is based on the use of self-consistent off-shell nucleon propagators in the T-matrix equation. Such a complete treatment of the spectral function is required below and around T_c due to a pseudogap formation in the spectral function. In the superfluid phase we introduce the anomalous self-energy in the fermion propagators and in the T-matrix equation, consistently with the strong coupling BCS equations. The equations for the nucleon spectral function include both a contribution of condensed and scattering pairs. The method is illustrated by numerical calculations. Above T_c pseudogap formation is visible in the spectral function and below T_c a superfluid gap also appears.     

Towards exotic nuclear matter

In this article I would like to describe what I am doing right now. First, introductory remarks on nuclear matter at high densities and/or high temperatures are presented. Then, I report our recent data obtained at the Brookhaven AGS. Finally, I describe briefly our future RHIC experiment, PHENIX.     

Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.     

Semi-infinite matter and the nuclear surface

The surface energy and thickness of semi-infinite nuclear matter are calculated by Swiatecki's variational method. Smooth, effective two-body interactions are used to study the relationship between the characteristics of each interaction and the predicted bulk surface properties. Both local and non-local Gaussian interactions are considered and are adjusted to either saturate infinite nuclear matter or to fit two-nucleon (singlet-even) phase shifts. Purely local potentials are found to give an excessively large surface energy ( ), whereas potentials having some non-locality (even if the non-locality is confined to short distances) reduce the surface energy to a reasonable value of (20–30) . The separate potential and kinetic energy contributions are examined in detail and are used to explain how the character of each interaction affects the surface properties. This model calculation shows that the surface energy is greatly influenced by non-locality. Also, we find that the predicted surface thickness tends to be too large (t ≈ 3.5 fm) for potentials that are adjusted to saturate and too small (t ≈ 1.8 fm) for potentials that are fitted to two-nucleon phase-shifts.     

Abnormal nuclear matter and pion condensation

The possibility of nuclear matter undergoing a combined phase transition into abnormal matter and a pion condensate is investigated. Various lagrangians for the meson (σ and π_i) fields, based on the σ-models, are used in mean-field approximation, and the entire system (mesons + nucleons) is treated fully relativistically. Equilibrium conditions of nuclear matter are obtained with NN repulsion, parametrized by the excluded volume approximation. It turns out that the formation of abnormal matter depends crucially on the choice of the σ-model lagrangian and considerably less on the additional pion condensate.     

Asymmetric nuclear matter and Skyrme potential

The binding energy, symmetry energy, pressure, incompressibility, and the velocity of sound are calculated for asymmetric nuclear matter using Skyrme interaction SkO’. The behavior of these physical quantities is studied for different values of the asymmetry parameter α _τ , the density ρ, and the temperature T. Good agreement is obtained in comparison with previous theoretical estimates and experimental data. The text was submitted by the authors in English.     

The tensor interaction and nuclear matter

The separation method of Moszkowski-Scott has been applied to the calculation of the properties of nuclear matter using two different nucleon-nucleon potentials, both in reasonable agreement with two-body data. Calculations with the potential of Brueckner-Gammel gave $\text{A}\text{E}\text{= ?14.2}\text{Mev}$ at an equilibrium densitty corresponding to k_f = 1.5 f^?1. The difference from the results of B and G may be caused by slow convergence of the series (especially in the triplet-even state where the tensor interaction has a large second order contribution). An important factor in obtaining nuclear saturation is shown to be the weakening of tensor interaction effects by the Fermi sea. Evidence for this may also be seen from the results obtained using a different two nucleon potential which, however, still gives good fits to two body data. The potential chosen has a much weaker tensor component and shows no sign of saturation at normal densities (at k_f = 1.5 f^?1, $\text{A}\text{E}\text{= ?23.4}\text{Mev}$). The difference in the two results appears to be much larger than can be accounted for either by higher order terms or by differences in the phase shift approximation to the reaction matrix.