Isoscalar NN spin-orbit potential from a Skyrme model with scalar mesons

As a first step toward circumventing the difficulty to obtain an attractive isospin-independent NN spin-orbit force from Skyrme-type models involving only pions, we investigate an improved Skyrme Lagrangian that incorporates the scalar-isoscalar meson ε which can be viewed as the cause behind the enhancement of the ππ S-wave. We find that at large distances, the main contribution to the spin-orbit potential comes from the scalar Lagrangian and it is found to be attractive. We briefly discuss how to pursue this work to finally obtain a medium-range attractive interaction.     

Arguments against one-boson-exchange models of nuclear forces and new mechanism for intermediate-and short-range nucleon-nucleon interaction

Arguments against the traditional Yukawa-type approach to NN intermediate-and shortrange interaction due to scalar-isoscalar and heavy-meson exchanges are presented. Instead of the Yukawa mechanism for intermediate-range attraction, some new approach based on the formation of a symmetric six-quark bag in the state |(0s)⁶[6]_X, L=0〉 dressed owing to strong coupling to π, σ, and ρ fields is suggested. This new mechanism offers a strong intermediate-range attraction, which replaces effective σ exchange (or excitation of two isobars in the intermediate state) in traditional force models. A similar mechanism with the production of a vector ρ meson in the intermediate six-quark state is expected to lead to a strong short-range spin-orbit nonlocal interaction in the NN system, which may resolve the long-standing puzzle of the spin-orbit force in baryons and in two-baryon systems. The effective interaction in the NN channel provided by the new mechanism will be enhanced significantly if the partial restoration of chiral symmetry is assumed to occur inside the six-quark symmetric bag. A simple illustrative model is developed that demonstrates clearly how well the suggested new mechanism can reproduce NN data. Strong interrelations have been shown to exist between the proposed microscopic model and one-component Moscow NN potential developed by the authors previously and also with some hybrid models and the one-term separable Tabakin potential. The new implications of the proposed model for nuclear physics are discussed.     

Resonant behaviour in double charge exchange reaction of πmesons on the nuclear photoemulsion

The invariant-mass spectra of the ppπ^- and pp systems produced in the double charge exchange (DCX) of positively charged pions on photoemulsion are analysed. A pronounced peak is observed in the ppπ^- invariant-mass spectrum, while the M_pp spectrum exhibits a strong Migdal-Watson effect of the proton-proton final-state interaction. These findings are in favor of the NN-decoupled NNπ pseudoscalar resonance with T = 0 called d'.     

Charge-constrained coherent pion states produced in nuclear matter

In a recent article, Bloss, Hone and Scalapino have used a simplified model Hamiltonian and Keldysh field theoretic methods to approximately calculate the power radiated as Cherenkov charged pions whose emission is triggered when a fast nucleon traverses nuclear matter. The model used by these authors conserves charge by flipping the isospin state of the fast nucleon alone for each charged pion emitted. Since it is the nuclear matter excited by the fast nucleon which should be largely reponsible for emitting the Cherenkov charged pions, we investigate an alternate model that allows all the disturbed nuclear matter to change its charge state when a charged pion is emitted—as an idealization, the emitting matter is assumed to have an infinite number of charge states, in contrast to the two of the fast nucleon. This modified model is shown to be exactly solvable in terms of charge-constrained coherent pion states; the power radiated as charged pions is found to be approximately twice that calculated by Bloss et al. from their model.     

On induced double-nucleon emission. III. 12C, (π−, NN) and short-range correlations

The reaction channel (π^?, NN) for the absorption of bound negative pions by nuclei is used as a means to study nuclear short range correlations. A three-body partial-wave analysis has been carried out for the final-state scattering which includes a Reid soft-core nucleon-nucleon interaction and an optical potential. This coupled-channel formalism rapidly converges as we eliminate the asymptotic single-nucleon and deuteron interactions. It is found that for ¹²C reasonable agreement with experiment cannot be obtained in this model without modification of the high relative-momentum components of bound shell model pair wave functions.     

Pion interaction in nuclear matter and chiral symmetry restoration

This paper is devoted to the interplay between p-wave, s-wave pion-nucleon/nucleus interaction and in-medium pion-pion interaction with special emphasis on the role of the nuclear pionic scalar density driving a large amount of chiral symmetry restoration. In particular we show that the πNN coupling constant and the Goldberger-Treiman relation are preserved in the nuclear medium under certain conditions. We also discuss the related problem of the in-medium pion-pion strength function.     

Pion superfluidity in nuclear matter

We utilize analogies with theories and properties of both liquid He⁴ and electrons in solids and liquids in constructing a model of nuclear matter in which the presence of stabilized pions is assumed. This model is then used to predict relationships between various thermodynamic parameters of a nuclear matter system, such as that between its “free” pion density and the characteristic transition temperature at which a Bose-Einstein condensation will commence.     

Isovector part of nuclear energy density functional from chiral two- and three-nucleon forces

A recent calculation of the nuclear energy density functional from chiral two- and three-nucleon forces is extended to the isovector terms pertaining to different proton and neutron densities. An improved density-matrix expansion is adapted to the situation of small isospin asymmetries and used to calculate in the Hartree-Fock approximation the density-dependent strength functions associated with the isovector terms. The two-body interaction comprises of long-range multi-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition, the leading-order chiral three-nucleon interaction is employed with its parameters fixed in computations of nuclear few-body systems. With this input one finds for the asymmetry energy of nuclear matter the value A(?? ₀) ? 26.5 MeV, compatible with existing semi-empirical determinations. The strength functions of the isovector surface and spin-orbit coupling terms come out much smaller than those of the analogous isoscalar coupling terms and in the relevant density range one finds agreement with phenomenological Skyrme forces. The specific isospin and density dependences arising from the chiral two- and three-nucleon interactions can be explored and tested in neutron-rich systems.     

Thermodynamic properties of superconducting nuclear matter

Phase diagrams of superconducting nuclear matter are calculated by solving a set of finite temperature gap equations, using several Skyrme effective interactions. Our results indicate that nuclear matter may have a superconducting phase in a small region with density near one half of the normal nuclear matter density and temperature k_BT ≲ 1.4 MeV. Our calculation is based on a finite temperature Green's function method with an abnormal pair cutoff approximation. The same approximation is employed in deriving the internal energy, entropy and chemical potential of superconducting nuclear matter. In this way, its equation of state is obtained, and compared with that of normal nuclear matter. The energy gap of superconducting nuclear matter is found to depend rather sensitively on both density and temperature. This dependence is analysed in terms of the Skyrme interaction parameters. The correlation effect on chemical potential is found to be important at high density, and its inclusion is essential in determining the equation of state of superconducting nuclear matter.     

Effective nuclear interaction: Dirac versus conventional approach

The effective interaction in nuclear matter (G-matrix) is calculated, in the relativistic (Dirac-Brueckner-Hartree-Fock) as well as in the conventional Brueckner-Hartree-Fock approach. Starting point is a nucleon-nucleon potential which, in addition to single-meson exchange, contains delta-isobar box diagrams with ππ- and πϱ-exchange, leading to Pauli blocking and dispersive effects. The implications for nuclear matter binding and Landau parameters are investigated.     

Equation of state of dense nuclear matter

An equation of state for cold nuclear matter for the region of densities ρ_nm−4ρ_nm, where ρ_nm is empirical nuclear-matter density, is constructed. We begin from the detailed calculation of Day and Wiringa for the two-body interactions; these give a saturation density of ∼2ρ_nm. This density is brought down to ρ_nm by the addition of relativistic corrections. Additional binding is obtained from three-body forces. A reasonable picture is obtained with the Day-Wiringa compression modulus for the two-body calculation, but the picture can be further improved by choosing this to be smaller.Our equation of state is similar to that of Friedman and Pandharipande in the region of nuclear matter denstiy ρ_nm, but, due to higher-order terms in the loop correction, is substantially softer at high density. Basically what happens is that the many-body effects saturate with increasing density, leaving only the two-body interactions.With this equation of state, prompt supernova explosions are very powerful when the compression modulus of neutron-rich matter (twice as many neutrons as protons) is ∼150 MeV, which corresponds to K_nm ∼ 190 MeV for symmetric nuclear matter.Analysis shows that hot nuclear matter formed in heavy ion collisions demands a very stiff equation of state. We understand this as arising from the strong velocity dependence in the real part of the optical model potential which follows chiefly from the Lorentz character of the interactions, the vector mean field growing with increasing density and the scalar one decreasing. This gives a substantial repulsive contribution to the energy per particle and produces a stiff effective equation of state for several hundred MeV heavy-ion collisions. With increasing degree of equilibration the magnitude of the repulsive energy decreases since equilibration decreases the effective momentum. Given the strong velocity dependence in the interaction, the hot equation of state can be reconciled with the cool one.     

Low-energy pions in nuclear matter and ππ photoproduction within a BUU transport model

In the present paper we investigate a method to describe low-energy scattering events of pions and nuclei within a Boltzmann-Uehling-Uhlenbeck (BUU) transport model. Implementing different scenarios of medium modifications, we studied the mean-free path of pions in nuclear matter at low momenta and compared pion absorption simulations to data. Pursuing these studies we have shown, that also in a regime of a long pionic wave length the semi-classical BUU model still generates reasonable results. We present results on π-induced events in the regime of 10 MeV≤T _kin ^π ≤130 MeV and photo-induced ππ production at incident beam energies of 400–460 MeV.     

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.     

Accurate nucleon–nucleon potential based upon chiral perturbation theory

We present an accurate nucleon–nucleon (NN) potential based upon chiral effective Lagrangians. The model includes one- and two-pion exchange contributions up to chiral order three. We show that a quantitative fit of the NN D-wave phase shifts requires contact terms (which represent the short range force) of order four. Within this framework, the NN phase shifts below 300 MeV lab. energy and the properties of the deuteron are reproduced with high-precision. This chiral NN potential represents a reliable starting point for testing the chiral effective field theory approach in exact few-nucleon and microscopic nuclear many-body calculations. An important implication of the present work is that the chiral 2π exchange at order four is of crucial interest for future chiral NN potential development.     

Quark condensate in the nuclear matter

We calculate the quark condensate in the nuclear matter, taking into account the single-pion and two-pion exchanges between nucleons. We find the dependence of the averaged value of the quark operator¯qq on the density of the matterρ. At very low density the nonlinear terms are proportional toρ ² and increase the tendency to restoration of the chiral symmetry. At larger values of density the account of interaction inside the matter slower down the restoration of chiral symmetry compared to the gas approximation law. The leading nonlinear term in Fermi momentum power expansion becomes of the orderρ ^4/3 . The value of the condensate at the saturation value of density is obtained. The role of multinucleon effects is analyzed.     

Ring diagrams,Landau parameters,pion condensation and the binding energy of nuclear matter

We calculate all direct π-exchange ring diagrams to arbitrary orders in nuclear matter. Our model incorporates intermediate Δ(1236) resonances, correlations, ρ- as well as π-meson exchange and mesonic form factors. We find that the convergence of the diagram summation is governed by two quantities which have an immediate physical interpretation: the Landau parameter G'₀ and the threshold for pion condensation. The contribution to the energy of nuclear matter from terms of third and higher order is 2 MeV/particle (repulsion) at normal density, with a strong density dependence.     

Ground state properties of nuclear matter

The ground state properties of nuclear matter are calculated in theΛ ₁₁-approximation¹. A nucleon-nucleon interaction of the Yamaguchi-type and thes-wave part ofTabakin's potential have been considered. In both cases too large values for the density of nuclear matter and the binding energy per nucleon are found. The momentum distribution turns out to be very small for momenta larger than the Fermi momentum.