International Journal of Modern Physics E

The status of relativistic nuclear many-body calculations of nuclear systems to be built up in terms of protons and neutrons is reviewed. In detail, relativistic effects on several aspects of nuclear matter such as the effective mass, saturation mechanism, and the symmetry energy are considered. This review will especially focus on isospin asymmetric issues, since these aspects are of high interest in astrophysical and nuclear structure studies. Furthermore, from the experimental side these aspects are experiencing an additional boost from a new generation of radioactive beam facilities, e.g., the future GSI facility FAIR in Germany or SPIRAL2 at GANIL/France. Finally, the prospects of studying finite nuclei in microscopic calculations which are based on realistic NN interactions by including relativistic effects in calculations of low momentum interactions are discussed.

The optimal usage of designed fuel pellets is one of the very important parameters in inertial confinement fusion (ICF) systems. In this research, time-dependent dynamical equations for D/D fuel are written by considering impurity of ⁶Li. Then dependency of gain on temperature, density and pellet radius is studied using Runge–Kutta method. The obtained results show that the energy gain will be maximized at the initial temperature 35 keV, density, 5000 g/cm³ and ratio impurity of ⁶Li, 0.05.

Quasimolecular optical potentials used for identical nuclei have been modified for application to different interacting nuclei. This has been applied to the ²⁸Si–¹⁶O system and compared with those results using the Woods–Saxon potential that had been found to reproduce the experimental results. The result indicates that the modification is useful and provides information on nuclear properties and explains the origin of imaginary potential. It has the applicability to a wide range of nuclei.

We discuss some aspects of the approach of the mass parameters by means of the simple cranking model. In particular, it is well known that the numerical application of this formula is often subject to ambiguities or contradictions. It is found that these problems are induced by the presence of two derivatives in the formula. To overcome these problems, we develop here a number of simple arguments which tend to justify the removal of these terms. As soon as this is done, the formula becomes simpler and easier to interpret. In this respect, it is shown how the shell effects affect precisely the mass parameters. A number of numerical tests help us in our conclusions.

The angular distribution data for the elastic scattering of 100–172.5 MeV isoscalar alpha particles from several nuclei between ¹⁶O and ²⁰⁸Pb are studied within the framework of the strong absorption model due to Frahn and Venter. The best fit parameter values of the nuclear interaction are determined. These are then used to analyze the inelastic scattering of alpha particles leading to the excitation of the 2⁺ and 3^- collective states in the target nuclei and the corresponding deformation parameters are extracted. A reasonably good account of both elastic and inelastic scattering is given by the same set of parameter values derived from the analyses of the elastic scattering.

The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson–meson states with the four-quark states is considered. The four-quark amplitudes of the tetraquarks, including u, d, s, and bottom quarks, are constructed. The poles of these amplitudes determine the masses and widths of S-wave bottom tetraquarks.

We investigate the exact solution of the Dirac equation for the Hartmann potential. The radial and polar parts of the Dirac equation are solved by Nikiforov–Uvarov method. The bound state energy eigenvalues and the corresponding two-component spinor wave functions of the Dirac particles are obtained.

The Frahn–Venter and McIntyre models are employed to analyze the experimental data of a set of elastic scattering reactions for heavy ions. The existence of semi-classical phenomena such as Fresnel and Fraunhofer diffraction patterns has been obtained by analyzing the experimental data of a set of elastic scattering reactions ¹²C + ²⁸Si at laboratory energies 24.0, 49.3, 70.0, 83.5, and 186.4 MeV, ¹⁶O + ²⁸Si at laboratory energies 72.0, 141.5, and 215.0 MeV, ¹⁶O + ¹⁶O at laboratory energies 145.0 and 350.0 MeV, ¹⁶O + ¹²C at laboratory energies 128.0 and 168.0 MeV; ¹²C + ¹²C at laboratory energies 89.7, 93.8, 105.0, 112.0, 117.1, 121.6, 126.7, and 158.8 MeV. The theoretical models can reasonably reproduce the general pattern of the data, thus allowing us to extract important parameters from elastic scattering processes. Deviations of some reproduced results from experimental data may be attributed to weak absorption. It is found that interpretation of the diffraction features of the data is model-independent. The values of extracted parameters, from both models, are found comparable to each other and to those of others. The correlation between the total reaction cross-section and the incident laboratory energy for each scattering is discernible and comparable with those of others.

Possibility of occurrence of chaotic behavior in multiparticle production in relativistic nuclear collisions is examined. Erraticity spectrum and entropy index are determined and compared with those of FRITIOF-generated events. The results obtained in the present study reveal existence of erraticity in multiparticle production in relativistic nuclear collisions.

Nonstatistical fluctuations in the density distribution of shower tracks coming out of ³²S–Ag/Br interaction at an incident momentum of 200A GeV/c, have been characterized by using the intermittency and multifractality techniques. A sample of ³²S–Ag/Br nuclear emulsion events has been partitioned into three subsamples with respect to the shower track multiplicity in such a way that one can roughly estimate the average centrality for each subsample. Thereby, the centrality dependence of a set of relevant intermittency and multifractal issues has been investigated.

The properties of neutron stars are investigated by including δ meson field in the modified quark–meson coupling model. It is found that δ meson has opposite effects on hadronic matter with or without hyperons: it softens the EOSs of hadronic matter with hyperons, while it stiffens the EOSs of pure nucleonic matter. Moreover, by replacing the isovector mesons with the contact scalar–isovector interaction, a considerable change of proton fraction is observed. It is shown that the contact scalar–isovector interaction provides an approach to satisfy the constraint of Direct Urca critical star masses. However, the inclusion of δ meson increases the proton fraction, consequently it decreases the M^DU which departs farther from the Direct Urca constraint. Furthermore, the inclusion of δ meson field can increase the maximum mass of neutron star and enlarge the corresponding radius, while these quantities are decreased when the contact scalar–isovector interaction is included.

We have studied the nuclear structure properties of high angular momentum states in N = Z, ⁴⁴Ti, and ⁴⁸Cr nuclei by using Hartree–Fock–Bogoliubov (HFB) method with variation after angular momentum projection (VAP-HFB) technique. Effect of Kuo–Brown "KB" and its modified effective interactions has been studied using four sets of single-particle energies (SPEs) on rotational bands of these nuclei. It is seen that the HFB theory with projected wave functions by employing the VAP method describes well the overall trends of the experimental yrast level spectrum and the transition probabilities in these nuclei. The backbending of the ⁴⁸Cr nucleus has been well reproduced by the present VAP-HFB calculations with the original "KB" effective interaction at J = 12ℏ. The modified effective interaction also gives backbending for ⁴⁸Cr but at J = 10ℏ. The shape change associated with backbending effect in ⁴⁸Cr is due to the large decrease in B(E2↓) values beyond J = 12ℏ state.

In the theory of the Dirac equation and in the standard model, the neutrino is massless. Both these theories use Lorentz invariance. In modern approaches however, spacetime is no longer smooth, and this modifies special relativity. We show how such a modification throws up the mass of the neutrino.