International Journal of Modern Physics E

We review energies and magnetic moments of p-shell nuclei obtained with the ab initio No-Core Full Configuration (NCFC) approach using the JISP16 realistic nucleon–nucleon interaction. We present calculated ground state energies for all stable p-shell nuclei and selected unstable isotopes, as well as their magnetic moments. We also review excitation energies for narrow resonances of A = 6 to 9 nuclei. We compare our results with experimental data and with other ab initio calculations, where available. We illustrate how the decomposition of total angular momentum into intrinsic spin and orbital components provides insights into the structure of states and relationships among states. We illustrate the challenges of obtaining converged results for radii, quadrupole moments and B(E2) values.

Recent developments in understanding the influence of the nucleus on deep-inelastic structure functions, the EMC effect, are reviewed. A new data base which expresses ratios of structure functions in terms of the Bjorken variable x_A = AQ²/(2M_A q₀) is presented. Information about two-nucleon short-range correlations (SRC) from experiments is also discussed and the remarkable linear relation between SRC and the EMC effect is reviewed. A convolution model that relates the underlying source of the EMC effect to modification of either the mean-field nucleons or SRC nucleons is presented. It is shown that both approaches are equally successful in describing the current EMC data.

One of the most intriguing questions about neutron stars concerns their maximum mass. The answer is intimately related to the properties of matter at densities far beyond that found in heavy atomic nuclei. The current view on the internal constitution of neutron stars and on their maximum mass, both from theoretical and observational studies, are briefly reviewed.

We studied an application of nonextensive thermodynamics to describe the structure function of nucleon, in a model where the usual Fermi–Dirac and Bose–Einstein energy distribution were replaced by the equivalent functions of the q-statistical. The parameters of the model are given by an effective temperature T, the q parameter (from Tsallis statistics), and two chemical potentials given by the corresponding up (u) and down (d) quark normalizations in the nucleon.

We have investigated Uranium ions interaction at energy 14.0 MeV/u incident on a Vanadium target using mica as nuclear track detector. The detector exposure was made from ions beam facility at UNILAC accelerator of GSI Darmstadt, Germany. The etched detector was scanned using an optical microscope. From the total binary tracks data events, elastic track events were separated using angular correlation criterion. The elastic scattering data have been separated from the binary events and used for the determination of quarter-point angle θ_1/4 (grazing angle). Total and partial reaction cross-sections are measured using the statistic of inelastic two-pronged and higher multiplicity tracks. The experimental measured cross-sections are compared with the cross-sections calculated using sharp cut-off model. The theoretical prediction of reaction parameters of interacting heavy ions have also been determined, that are comparable with experimental measured values.

In this work, we have employed Bethe–Salpeter equation (BSE) under Covariant Instantaneous Ansatz (CIA) to study strong decays of first radial excitations, ω(1420) and ρ(1450) of lightest vector mesons, ω(782) and ρ(770) respectively, through the processes: ω(1420)→ρ+π and ρ(1450)→ω+π. The main motivation for this work was our intention to resolve the problems involved in calculations of triangle quark-loop diagrams as pointed out earlier in Ref. 1 which appear in processes such as h→h'+h" and h→h'+γ (attempted recently) in BSE under CIA, which gives rise to complexities in amplitudes making calculations difficult. We explicitly show the mathematical procedure for handling the process, h→h'+h" involving three hadron–quark vertex functions, which is more involved than that for h→h'+γ and leads to decay widths which are in rough agreement with data.

The natural orbitals (NOs) and natural occupation numbers (NON) of various N = Z, sp and sd shell nuclei are calculated by applying a correlated one-body density matrix (OBDM). The correlated density matrix has been evaluated by considering central correlations of Jastrow type and an approximation named factor cluster expansion. The correlation effects on NOs, NON and the Fermi sea depletion (FSD) are discussed and analyzed. In addition, an approximate expression for the correlated OBDM of the nuclear matter has been used for the evaluation of the relative momentum distribution and FSD. We found that the value of FSD is higher in closed shell nuclei compared to open shell ones and it is lower compared to the case of nuclear matter. This statement could be confirmed by relevant experimental studies.

In this paper, we present the approximate analytical solutions of the Dirac equation for hyperbolical potential within the frame work of spin and pseudospin symmetries limit including the newly proposed generalized tensor interaction (GTI) using the Nikiforov–Uvarov (NU) technique. We obtained the energy eigenvalues and the corresponding eigenfunction using the generalized parametric NU method. The numerical results of our work reveal that the presence of the GTI changes the degeneracy between the spin and pseudospin state doublets.

In this study, the nuclear decay equation is taken under consideration by making use of fractional calculus. In this context, the first-order time derivative is changed to a Caputo fractional derivative hence, the resulting equation is the time fractional nuclear decay equation. The solution of this equation is obtained in terms of Mittag–Leffler function which plays an important role to study the non-Markovian feature of physical processes. As an application of this time fractional formalism, alpha decay half-life values have been calculated for Pb, Po, Rn, Ra, Th and U isotopes. Consequently, the theoretical half-life values have been obtained in consistent with the experimental data. The dependence of the order of fractional derivative μ being a measure of fractality of time, on the nuclear structure has been established. In the investigations carried out, we have arrived to the conclusion that for the μ values which are closed to one, where time becomes homogenous and continuous, the shell closure effects are predominant and that the fractional derivative order μ (i.e., fractality of time) and nuclear structure are closely related to each other.

We explore the consistency of the Quantum Hadro-Dynamics (QHD), namely the Serot and Walecka model, paying attention to its renormalizabilty, the stability of the vacuum and the possible occurrence of a σ-ω condensate. We find that the QHD is not renormalizable as it is usually described, but the true way of formulate it, via the Stueckelberg Lagrangian, alters the formulation of the model in the vacuum but leaves the results in the medium unchanged. Further, we find that the stability of the vacuum imposes a constrain over the parameters of the σ self-interaction while stability against σ condensation at the mean field level imposes a constraint on the coupling constant, namely g_σ<8.828 that is k_F = 207.2 MeV/c, significantly below the standard value of QHD.

The alpha particle preformation and the penetration probability by the Yukawa proximity potential in the even–even nuclei from ¹⁷⁸Pb to ²³⁸U are studied. Using the experimental values of the alpha decay half-lives and the decay energies, we extract the preformation factors and the penetration probabilities. We also calculate the assault frequencies and the decay constants. The obtained results are motivating.

We investigated the approximate solutions of the Dirac equation for the generalized Yukawa types I and II under the framework of pseudospin and spin symmetry limits. We obtained the energy eigenvalues and the corresponding wave functions using the supersymmetry method. Closed form of the energy eigenvalues are obtained for any spin-orbit coupling term κ. We also discuss the energy eigenvalues of the Dirac equation for some well-known potentials such as Yukawa, inversely quadratic Yukawa, new Yukawa, Mie-type and Coulomb potentials which are the special cases of the generalized Yukawa potentials.

A modified phenomenological model is used to calculate nuclear energy levels and describe successfully the backbending of the moment of inertia for the ground state bands in even–even isotopes of Hf and Dy nuclei. The model is a combination of the Myers and Swiatecki model with variable moment inertia (VMI) model. Since the Myers and Swiatecki model has a deviation from experimental energies in which it takes into account pairing effect with constant moment of inertia, in the rotation of nuclei, the Coriolis force acts to de-pair the nucleons pair and align their angular momentum with nuclei total angular momentum, thus Coriolis force increasing and decrease the rotational energy. So, the moment of inertia varies with the angular momentum. Therefore, we modified this model by adding a term to make the moment of inertia vary with angular momentum in the same manner of the VMI model which has a term added to the rotational energy equation. The modified model fits remarkably with the experimental observation and other models in many cases with the use of few parameters especially in rotational nuclei regions similar to Hf and Dy nuclei.