Nuclear Matter Approach Research Articles

Quasielastic (p, n) reactions described by a microscopic optical model based on the Gogny force

In this work, we want to study quasielastic (p, n) exchange reactions using a semi-microscopic optical model derived from a previous work, Lopez Moraña and Viñas (2021 J. Phys. G48 035104) based on a nuclear matter approach where the real and imaginary parts are given by the first and second order terms, respectively, of the mass operator obtained by a Brueckner–Hartree–Fock calculation using a G-matrix built up with an effective Gogny interaction. The study of these quasielastic reactions is performed within a Distorted Wave Born Approximation to evaluate the wave functions in the entrance and exit channels, which in turn are used to compute the transition matrix elements. This model, which is free of adjustable parameters, provides a reasonably good agreement with the considered experimental data, namely differential cross sections, analyzing powers and total cross sections, of different reactions spanned along the periodic table at several energies.

Nucleon-nucleus optical potential computed with the Gogny interaction

The ability of the Gogny forces of the D1 family to describe the nucleon-nucleus scattering is studied. To this end, we use an optical model (OM) potential built up using a semi-microscopic nuclear matter (NM) approach. The real and imaginary parts of the OM are provided by the first and second-order terms, respectively, of the Taylor expansion of the mass operator calculated within the Brueckner–Hartree–Fock (BHF) method using the reaction G-matrix built up with the effective Gogny force instead of a microscopic interaction. The optical potential in finite nuclei is obtained through the local density approximation (LDA) using the neutron and proton densities provided by a quasi-local Hartree–Fock (HF) calculation with the same Gogny force for the sake of consistency. A reasonable good agreement is found between the theoretical differential cross-sections and the analyzing powers (AP) of the elastic neutron and proton scattering along the periodic table from Ca to Pb calculated with the Gogny forces and the corresponding values predicted by the global phenomenological potential of Koning and Delaroche. To investigate the limits of the approximations used in this work, comparisons with the results of nucleon-nucleus elastic scattering in 40Ca and 48Ca obtained using the nuclear structure model (NSM) are also performed.

Comparison between optical-model potentials in G -matrix folding method and improved local-density approximation method

Microscopic optical-model potentials evaluated by two methods in a nuclear matter approach, namely a $G$-matrix folding method and an improved local-density approximation (LDA) method, are compared. The real parts agree well and show good correspondence to a phenomenological Woods-Saxon potential when second-order contributions are taken into account. On the other hand, the resemblance is not so good in an imaginary part. The reason for the similarity in the real part of the two methods is examined. The improved LDA, which requires less numerical effort, is useful to apply in other cases such as hyperon potentials.

Relativistic density functional for nuclear matter

In the present work, we have mapped the exchange Fock contributions from the Dirac–Hartree–Fock (DHF) approach for nuclear matter onto the direct Hartree terms. This results in the relativistic mean field (RMF) model with the density dependent couplings. The density dependence of the effective coupling constants thus reflects the exchange correlations. The exchange part of an energy density of the linear DHF model in dense matter is evaluated in a parameter-free closed form and, after the rearrangement of the terms, expressed as density functional.

Microscopic description of elastic and direct inelastic nucleon scattering off spherical nuclei

The purpose of this study is to improve the modeling of nucleon direct inelastic scattering to the continuum using a microscopic and parameter-free approach. For the first time, direct elastic scattering, inelastic scattering to discrete excitations and to the continuum are described within a microscopic approach without adjustable parameters. Proton scattering off 90Zr and 208Pb are the reactions used as test case examples of the calculations. The model uses the Melbourne g-matrix and the Random Phase Approximation description of nuclear states, implemented with the Gogny D1S interaction. The relevant optical and transition potentials in a finite nucleus are calculated within a local density approximation. As we use the nuclear matter approach we limit our study to incident energies above 40 MeV. We first checked that this model provides an accurate account of measured cross sections for elastic scattering and inelastic scattering to discrete states. It is then applied to the direct inelastic scattering to the continuum considering all one-phonon excitations predicted within the RPA approach. This accounts for a part of the direct pre-equilibrium emission, often labeled as the one-step direct process in quantum-based approaches. Our approach provides a very accurate description of angular distributions where the one-step process dominates. The impact of collective excitations is shown to be non negligible for energy transfer to the target up to 20 MeV, decreasing as the incident energy increases. For incident energies above 80 MeV, our modeling provides a good account of direct proton emission for an energy transfer to the target up to 30 MeV. However, the proton emission we predict underestimates the measured cross sections for incident energies below 80 MeV. We compare our prediction to those of the phenomenological exciton model to help interpret this result. Directions that may improve our modeling are discussed.

Unruh thermalization, gluon condensation, and freeze-out

The deconfinement transition and the hadronization mechanism at high energy are related to the quark-antiquark string breaking and the corresponding temperature depends on the string tension $\sigma$. In the Unruh scheme of hadron production it turns out $T = \sqrt{\sigma/2\pi}$, with $\sigma \simeq \E$, the vacuum energy density. In heavy ion collisions at lower energy, i.e. large baryonchemical potential, $\mu_B$, the dynamics is dominated by Fermi statistics and baryon repulsion. However one can still consider $\E$ as the relevant physical scale and its evaluation as a function of the baryon density, in a nuclear matter approach, gives dynamical information on the $\mu_B$ dependence of the hadronization temperature and on the value of the critical end point in the $T-\mu_B$ plane.

Role of the saturation properties of hot nuclear matter in the proximity formalism

Temperature dependence of the surface thickness parameter $b$ in the original version of proximity formalism is investigated by including the modification effects of equation of state (EOS) at finite temperature on nuclear potential. Here, this modification is performed using the evaluation of the increasing of total energy in the overlapping region by the EOS extracted from the extended Thomas-Fermi approach for asymmetric nuclear matter at finite temperature. This EOS is also supplemented with the saturation effects of nuclear matter density. Our results show a different temperature dependence for surface thickness $b$ of the excited compound nucleus, which is formed during the fusion process. The original version of Proximity 77 with this new form of $b(T)$ provides a reasonable result for theoretical values of the barrier characteristics and fusion cross section. Our obtained results are also compared with other theoretical approaches.

Comparison between global phenomenological and microscopic optical potentials for proton as projectile below 100 MeV

For 112 target nuclei (52 elements) with proton as projectile, we calculate the reaction cross sections and elastic scattering angular distributions, as well as the χ2 values for 16 kinds of proton optical model potentials: two sets of phenomenological global optical potentials and the microscopic optical potentials proposed by Shen et al for 14 sets of Skyrme force parameters: GS1–6, SBJS, SKM, SGI-II, SKa-b, SG0I-II. We find that for obtaining the proton microscopic optical potential based on the nuclear matter approach with Skyrme force, SGI, SKa and SKb are the three sets of optimal Skyrme force parameters.

A CLASS OF NONLINEAR RELATIVISTIC MODELS FOR NUCLEAR MATTER AND THE BINARY PULSAR J0737-3039A

In this work, we calculate the moment of inertia of the pulsar of the binary system J0737-3039A in the framework of Einstein's gravitational theory combined with a relativistic field theoretical approach for nuclear matter in the slow rotating regime, taking into account that the star's frequency is much smaller than Kepler's frequency. In the description of the EoS for nuclear matter, we consider a generalized class of relativistic multi-baryon Lagrangian density mean field approach which contains adjustable nonlinear couplings of the meson fields with the baryon fields. Upon adjusting the model parameters to describe bulk static properties of ordinary nuclear matter, we determine the EoS of the pulsars. By analyzing the results, dynamical constraints for neutron star models are identified.

Asymmetric colliding nuclear matter approach in heavy ion collisions

The early stage of a heavy ion collision is governed by local non-equilibrium momentum distributions which have been approximated by colliding nuclear matter configurations, i.e., by two Lorentz elongated Fermi ellipsoids. This approach has been extended from the previous assumption of symmetric systems to asymmetric 2-Fermi sphere configurations, i.e., to different densities. This provides a smoother transition from the limiting situation of two interpenetrating currents to an equilibrated system. The model is applied to the dynamical situations of heavy ion collisions at intermediate energies within the framework of relativistic transport (RBUU) calculations. We find that the extended colliding nuclear matter approach is more appropriate to describe collective reaction dynamics in terms of flow observables, in particular, for the elliptic flow at low energies.

Relativistic Hartree-Bogoliubov approach for nuclear matter with nonlinear coupling terms

We investigate the pairing property of nuclear matter with Relativistic Hartree-Bogoliubov(RHB) approach. Recently, the RHB approach has been widely applied to nuclear matter and finite nuclei. We have extended the RHB approach to be able to include non-linear coupling terms of mesons. In this paper we apply it to nuclear matter and observe the effect of non-linear terms on pairing gaps.

The JLM model for nucleon scattering off strongly deformed nuclei up to 200 MeV

In this work we introduce new developments of our nucleon-nucleus optical model potential (OMP) built from the nuclear matter (NM) approach of Jeukenne, Lejeune and Mahaux (JLM). Having selected prescriptions for the local density approximation (LDA) and using nuclear densities obtained from Hartree-Fock-Bogoliubov (HFB) calculations, the normalizations of the potential depth are carefully optimized and given functional forms that represent their variations with projectile energy over a broad mass and energy range for incident protons an neutrons. These OMPs, used in the coupled channel framework, produce good predictions of neutron and proton scattering and reaction measurements available up to 200 MeV for deformed rigid nuclei in the range A=80–240.

Semimicroscopic nucleon-nucleus spherical optical model for nuclei withA>~40at energies up to 200 MeV

A nucleon-nucleus optical model potential (OMP) is built from the nuclear matter (NM) approach of Jeukenne, Lejeune, and Mahaux (JLM). The imaginary component of the on-shell NM mass operator, originally parametrized by these authors as a function of matter density and energy, is given a new representation suitable for energies from 1 to 200 MeV. The JLM model extended in this manner is then applied through an improved local density approximation (LDA) to treat nucleon scattering from closed- and near closed-shell nuclei with masses $40<~A<~209$. For proton, neutron, and charge radial densities, we use those obtained from Hartree-Fock-Bogoliubov calculations based on the finite range, density dependent Gogny force. Several LDA and spin-orbit potential prescriptions are tested to select those which provide the best overall description of elastic scattering and reaction measurements. Over three hundred datasets including differential cross sections, analyzing powers, spin rotation functions, and reaction cross sections are considered in the present analyses. The OMP components include normalization factors which are optimized for each incident energy, probe, and for most target nuclei. We give close forms which represent the energy variation of these factors for the $n+X$ and $p+X$ systems. The global OMPs built in this manner produce a good overall description of the neutron and proton scattering and reaction measurements available up to 200 MeV.

Nuclear and neutron matter calculations with different model spaces

In this work we investigate the so-called model-space Brueckner-Hartree-Fock (MBHF) approach for nuclear matter as well as for neutron matter and the extension of this which includes the particle-particle and hole-hole (PPHH) diagrams. A central ingredient in the model-space approach for nuclear matter is the boundary momentum k M beyond which the single-particle potential energy is set equal to zero. This is also the boundary of the model space within which the PPHH diagrams are calculated. It has been rather uncertain which value should be used for k M . We have carried out model-space nuclear matter and neutron matter calculations with and without PPHH diagrams for various choices of k M and using several modern nucleon-nucleon potentials. Our results exhibit a saturation region where the nuclear and neutron matter energies are quite stable as k M varies. The location of this region may serve to determine an “optimum” choice for k M . However, we find that the strength of the tensor force has a significant influence on the variations of binding energy with k M . The implications for nuclear and neutron matter calculations are discussed.

Microscopic description of nucleon-nucleus scattering based on realistic nucleon-nucleon interactions

Based on the Bonn potential as the realisitic nucleon-nucleon (NN) interaction and the Dirac-Brueckner-Hartree-Fock (DBHF) approach for nuclear matter, we derive the microscopic nucleon-nucleus optical potential at intermediate energies. We calculate observables (differential cross sections, analysing powers, spin rotation functions and total cross sections) in nucleon-nucleus scattering and compare our predictions with experimental data as well as other calculations. Fairly good agreement is found between our microscopic results and experimental data. We also calculate the nucleon mean free path in nuclear medium starting from the bare NN interaction. The microscopic nucleon mean free path is in good agreement with the empirical value.

Microscopic calculation of in-medium proton-proton cross sections.

We derive in-medium proton-proton cross sections in a microscopic model based upon the Bonn nucleon-nucleon potential and the Dirac-Brueckner approach for nuclear matter. We demonstrate the difference between proton-proton and neutron-proton cross sections and point out the need to distinguish carefully between the two cases. We also find substantial differences between our in-medium cross sections and phenomenological parametrizations that are commonly used in heavy-ion reactions.

Momentum-dependent mean field based upon the Dirac-Brueckner approach for nuclear matter.

A momentum-dependent mean field potential, suitable for application in the transport-model description of nucleus-nucleus collisions, is derived in a microscopic way. The derivation is based upon the Bonn meson-exchange model for the nucleon-nucleon interaction and the Dirac-Brueckner approach for nuclear matter. The properties of the microscopic mean field are examined and compared with phenomenological parametrizations which are commonly used in transport-model calculations.

Microscopic nucleon-nucleus optical potentials at intermediate energies

Based on the Bonn potential as the realistic nucleon-nucleon (NN) interaction and the Dirac-Brueckner-Hartree-Fock (DBHF) approach for nuclear matter, we derive the microscopic nucleon-nucleus optical potential at intermediate energies. The present results are compared with those of the Dirac phenomenology, the relativistic impulse approximation and the Walecka model (QHD-I). The bulk properties of the optical potential are also compared with the available empirical data.

Relativistic microscopic description of proton-nucleus scattering at intermediate energies.

We study elastic proton-nucleus scattering at intermediate energies. The nucleon-nucleus optical potential is derived from the Bonn nucleon-nucleon potential and the Dirac-Brueckner approach for nuclear matter. Our calculations, which do not contain any adjustable parameters, yield good agreement with experiment.

Microscopic calculation of in-medium nucleon-nucleon cross sections.

We derive in-medium nucleon-nucleon (NN) cross sections in a microscopic model. Our calculations are based upon the Bonn NN potential and the Dirac-Brueckner approach for nuclear matter. We consider energies up to 300 MeV (in the laboratory frame) and densities up to twice nuclear matter density. Our results deviate substantially from cross section parametrizations that are commonly used in the nuclear medium.