Pion Effect of Nuclear Matter in a Chiral Sigma Model

We develop a new framework for the study of the nuclear matter based on the linear sigma model.We introduce a completely new viewpoint on the treatment of the nuclear matter with the inclusion of the pion.We extend the relativistic chiral mean field model by using the similar method in the tensor optimized shell model.We also regulate the pion-nucleon interaction by considering the form-factor and short range repulsion effects.We obtain the equation of state of nuclear matter and study the importance of the pion effect.     

Extended Brueckner–Hartree–Fock theory with pionic correlation in finite nuclei

We formulate a nuclear many-body theory with explicit treatment of the strong tensor correlation caused by the pion-exchange interaction. To do this, we have to extend the Hartree–Fock variational model space to include 2-particle 2-hole (2p–2h) states, which are able to handle the tensor correlation and to contain high momentum components originating from its pseudo-scalar nature of the pion. We take the variational principle of the total energy, and obtain equations of motion for the variational parameters as the Hartree–Fock single particle states and 2p–2h states. As for the short range repulsion, we use the unitary correlation operator method (UCOM) to express the short range correlation in the ground state wave function. We then arrive at an extended Hartree–Fock equation with the inclusion of the effect of the pion exchange and short range repulsive interactions. We find this extended Hartree–Fock equation has a structure of the Brueckner theory. Thus, we name the present theoretical framework as an extended Brueckner–Hartree–Fock (EBHF) theory. We compare the EBHF theory with the Feshbach projection method and the Brueckner–Hartree–Fock theory.     

Compound nucleus fission and quasi-fission in reactions of 238U with 16O and 27Al

The thermodynamics of pion-condensed nuclear matter is investigated in a relativistic field theory in the mean field approximation. The conditions of the thermodynamical equilibrium of the system lead to a set of self-consistent equations for the meson field amplitudes and for the wave vector of the pion condensate. It is proved, that in the thermodynamical equilibrium the pressure tensor of isolated, infinite nuclear matter is isotropic at any values of the temperature and chemical potential.     

The role of the form factor and short-range correlation in the relativistic Hartree-Fock model for nuclear matter

The role of the form factor and short-range correlation in nuclear matter is studied within the relativistic Hartree-Fock approximation. We take, first, the mean-field approximation for meson fields and obtain the fluctuation terms of mesons to be used for the Fock energies. We introduce form factors in the meson-nucleon coupling vertices to take into account the finite-size effect of the nucleon. We use further the unitary correlation operator method for the treatment of the short-range correlation. The form factors of the size ( L \Lambda ∼ 1.0 -2.0GeV) of the nucleon-nucleon interaction cut down largely the contribution of the r \rho -meson in the Fock term. The short-range correlation effect is not large but has a significant effect on the pion and r \rho -meson energies in the relativistic Hartree-Fock approximation for nuclear matter.     

格点核子-核子势在核物质中的相对论效应(英文)

利用最新的格点核子-核子势研究了核物质中的相对论效应。通过此格点核子-核子势场,首先我们构建一个包括π介子,σ介子以及ω介子的单玻色子交换势。势场中的介子-核子耦合常数以及截断动量通过拟合格点核力得到的核子-核子散射相移确定。随后采用非常成功的第一性原理多体计算方法Brueckner-Hartree-Fock模型,计算了核物质的基本性质。发现对称核物质的状态方程以及饱和性质在非相对论框架和相对论框架中有很明显的区别。在格点核力中,该相对论效应对核物质的结合能提供吸引的贡献。这与采用传统的核力计算得到的结果是相反的。The relativistic effect in nuclear matter is investigated with the latest lattice nucleon-nucleon (NN) potential. A one-boson-exchange potential (OBEP) including three mesons, pion, σ meson and ω meson was constructed based on the lattice NN potential. The meson-nucleon coupling constants and cutoff momentums are determined by fitting the phase shifts of NN scattering from lattice NN potential. The properties of nuclear matter with this OBEP from lattice potential are calculated by one very successful ab initio many-body method, Brueckner-Hartree-Fock model. The equations of state and saturation properties of symmetric nuclear matter present very obvious different behaviors in non-relativistic and relativistic frameworks. The relativistic effect plays attractive contributions with the components of S and D waves in lattice NN potential, which is opposite comparing to the relativistic effect from the conventional NN potential.     

The study of the binding energy of nuclear matter in the relativistic σ− ω− π model with Δ isobar degree of freedom

The relativistic σ?ω?π model is proposed and used to calculate the binding energy of relativistic nuclear matter. By coupling Δ isobar to the σ meson, the zero-point fluctuation energy of the Δ isobar in the one loop approximation is derived. We calculate the effective mass of nucleon and Δ isobar, exchange and correlation energies, pressure and incompressibility of nuclear matter. The density dependence correction to σNN ωNN coupling constants is a very important mechanism to saturate the binding energy. The pion propagator is nuclear matter is constructed by the relativistic particle-hole, delta-hole and short-range correlation. The pion dispersion relation is calculated we find it’s very sensitive to the effective mass of nucleon and Δ isobar.     

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism

The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.     

Relativistic Particle-Hole and Delta-Hole Excitations for Pion Propagator in Nuclear Matter

The relativistic particle-hole and delta-hole polarization insertions for pion propagator are calculated by using particle-hole-antiparticle representation of nucleon and delta propagators in nuclear matter. The short-range correlations between nucleon-nucleon, nucleon-delta and delta-delta are included via Landau-Migdal parameter g' in the random phase approximation. We calculate the dispersion relations for pions and find out that the damped pion condensation is removed by the short-range correlation and there is a long gap in the dispersion relation.     

The Lorentz-Lorenz correction

The Ericson-Ericson Lorentz-Lorenz correction in the propagation of pions in matter is derived in a relativistic theory for general pion frequency and wave vector, in terms of the nucleon-nucleon pair correlation function. The relation to the electromagnetic Lorentz-Lorenz correction is described. It is shown that ρ-meson exchange between nucleons can be expected to give contributions to the Lorentz-Lorenz correction comparable to those from π-mesons. The precise magnitude of the ρ-contributions depends sensitively on the detailed behaviour of the two-body correlation function, since the range of the interaction through ρ-exchange is comparable to that of the repulsive correlations.     

Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.     

核物质中π分子引起的粒子－空穴和△－空穴激发

以π介子为例给出了正确计算核物质中粒子－空穴激发的相对论方法，指出了它与通常计算方法的区别及通常计算方法中所作近似的不合理性．并与非相对论的粒子－空穴激发的色散关系进行了比较．我们还用这一方法计算并给出了△－空穴激发的表达式．     

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.     

From the NN interaction to nuclear structure and reactions

We present a novel approach for the treatment of realistic nucleon-nucleon interactions in nuclear many-body systems. A unitary correlation operator is used to explicitly introduce short-range central and tensor correlations in many-body states. The correlated interaction is used as an effective interaction in nuclear structure calculations. Results for Lithium isotopes including proton and neutron distributions, radii as well as magnetic moments and quadrupole moments are shown. Molecular resonances in the ¹⁶O?¹⁶O system are given as a first application in reaction theory.     

Study of the Binding Energy of Relativistic Nuclear Matter in the Relativistic σ-ω-π Model

A relativistic σ-ω-π model is proposed to calculate the binding energy of relativistic nuclear matter. We put emphasis on the relativistic particle-hole, delta-hole excitation of pion propagator in nuclear matter. The renormalization of the nucleon self-energy in nuclear matter is made for the pseudo-vector πNN and πNΔ couplings by introducing corresponding form factor and by dispersion relation. We find that the density dependence correction to meson-NN coupling constants is very important to saturate the binding energy of nuclear matter. The density dependence correction to πNN and πNΔ coupling constants has the effect of softening the EOS of nuclear matter.     

Electroweak measurements of neutron densities in CREX and PREX at JLab,USA

We analyze microscopic many-body calculations of the nuclear symmetry energy and its density dependence. The calculations are performed in the framework of the Brueckner-Hartree-Fock and the self-consistent Green’s functions methods. Within Brueckner-Hartree-Fock, the Hellmann-Feynman theorem gives access to the kinetic energy contribution as well as the contributions of the different components of the nucleon-nucleon interaction. The tensor component gives the largest contribution to the symmetry energy. The decomposition of the symmetry energy in a kinetic part and a potential energy part provides physical insight on the correlated nature of the system, indicating that neutron matter is less correlated than symmetric nuclear matter. Within the self-consistent Green’s function approach, we compute the momentum distributions and we identify the effects of the high momentum components in the symmetry energy. The results are obtained for the realistic interaction Argonne V18 potential, supplemented by the Urbana IX three-body force in the Brueckner-Hartree-Fock calculations.     

Quasi-stationary nonlinear waves in nuclear matter close to pion condensation

The nuclear hydrodynamic model is extended to include the fluctuating spin-isospin density and its interaction with the nuclear matter density. Using the TDHF equations, it is shown that the dynamics of these densities interacting with the pion field can be expressed in terms of the generalized pressures derivable from the generalized nuclear matter equation of state. A phenomenological Skyrme interaction model is used to obtain these pressures. A theory of pion-like spin-isospin quasi-stationary nonlinear waves is formulated from the generalized hydroequations describing the dynamics of a coupled pion nuclear matter system. In the lowest order of nonlinearity, it is proved that the amplitude of the spin-isospin sound wave satisfies a nonlinear Schrödinger equation. The solution of these equations is the amplitude modulated pion-like solitary waves in nuclear matter. When this matter is near the pion condensate, the speed of these nonlinear waves is much smaller than that of the ordinary sound waves. An implication of the solitary waves excited in such nuclear matter produced in heavy ion collisions is discussed. The characteristic signature of breaking of such waves, produced in a heavy ion central collision, is the emission of a delayed component of correlated nucleons (possibly also with a pion) peaked in the forward direction. It may be that the lighter nuclei³He and³H are produced through such a mechanism.