International Journal of Modern Physics E

The Skyrme model is a low energy effective field theory of strong interactions where nuclei and baryons appear as collective excitations of pionic degrees of freedom. In the last years, there has been a revival of Skyrme’s ideas and new related models, and some of them with BPS bounds (topological lower energy bounds) have been proposed. It is the aim of this paper to review how they can be applied to the study of neutron stars allowing for a description by means of topological solitons. We will focus on different aspects as the equation of state or the mass-radius relation, where we find that high maximal masses are supported.

Aims of this work are: (i) Investigation of the production of some radioisotopes that could be used in nuclear battery technology with neutron-induced reaction processes, (ii) Estimation of the cross-section curves of $(n,\gamma )$ reactions for astrophysical processes in the energy region between 1eV and 1MeV, (iii) Determination of suitable level density models for the $(n,\gamma )$ reaction processes. Additionally, the obtained results were compared with the experimental data and recommended data. Based on the calculated results, to eliminate lack of nuclear data in the literature, we recommend new experiments for some reaction processes to be performed by the experimenters. Moreover, for the $(n,\gamma )$ reaction processes, suitable level density models were proposed.

The experimental results on the multiplicity and probability distribution of the emitted charged pions $(N_{\pi })$ in the interactions of ${}^{84}$Kr${}_{36}$ projectile at around 1GeV per nucleon with nuclear emulsion targets are reported. In this work, we have employed a wounded nucleon model (WNM) to calculate the total number of wounded nucleons $(W)$ and the total number of interactions $(\nu )$. The dependence of average multiplicities of produced relativistic charged particles on the calculated wounded nucleons and total interactions are investigated. The obtained results revealed that the average multiplicity of $〈N_{\pi }〉$ is dependent on the projectile and target mass number. The calculated values of the total number of wounded nucleons and the total numbers of interactions show a strong dependence on the mass of the colliding nuclei. The emission rate of the mean multiplicity of $〈N_s〉$ and $〈N_{\pi }〉$ linearly increases with increasing the total number of wounded nucleons and interactions.

In this paper, analytical solution of the Bohr model with Mie potential for even–even and odd–even nuclei are evaluated in the Bose alone symmetry $[E(5)-\mathrm{\text{Mie}}]$ and a new class of Bose–Fermi dynamical symmetry $[E(5)-\mathrm{\text{Mie}}\otimes U(4)]$, respectively. The excitation energy spectra as well as electromagnetic transition strengths, quadrupole moments and dipole moments are investigated near the critical point of shape phase transition between the spherical and deformed $\gamma$-unstable nuclei. To show our results are compatible with experiment, some examples are tested.

Data on nuclear-level densities extracted from transmission data or gamma energy spectrum store the basic statistical information about nuclei at various temperatures. Generally, this extracted data goes through model fitting using computer codes like CASCADE. However, recently established semiclassical methods involving no adjustable parameters to determine the level density parameter for magic and semi-magic nuclei give a good agreement with the experimental values. One of the popular ways to paramaterize the level density parameter which includes the shell effects and its damping was given by Ignatyuk. This damping factor is usually fitted from the experimental data on nuclear-level density and it comes around 0.05 ${\mathrm{\text{MeV}}}^{-1}$. In this work, we calculate the Ignatyuk damping factor for various nuclei using semiclassical methods.

In previous works we considered schematic Hamiltonians represented by simplified matrices. We defined two transition operators and calculated transition strengths from the ground state to all excited states. In many cases the strengths decreased nearly exponentially with the excitation energy. Now we do the reverse. We start with the highest energy state and calculate the cascade of transitions until the ground state is reached. On a log plot we show the average transition strength as a function of the number of energy intervals that were crossed. We give an analytic proof of exponential behavior for transition strength in the weak coupling limit for the $T_2$ transition operator.

This paper focuses on the emission characteristics of single-, double- and multi-charged projectile fragments in the interaction of ${}^{84}$Kr with nuclear emulsion in peripheral collision at relativistic energy. We have also studied the variation of the average multiplicity of multi-charged projectile fragments with respect to the mass of the projectile beam, which reveals that the average multiplicity of multiple charge fragments increases with an increase in the mass of projectile beam. The results are consistent with other experimental observations.

Partial cross-sections of the $n\alpha$ and $dt$ collisions in the quantum state $J^{\pi }={\frac{3}{2}}^{+}$ near the $dt$-threshold, taken from an available $R$-matrix analysis, are fitted using the semi-analytic multi-channel Jost matrix with proper analytic structure and some adjustable parameters. Then the spectral points are sought as zeros of the Jost matrix determinant (which correspond to the $S$-matrix poles) at complex energies. The correct analytic structure makes it possible to calculate (analytically continue) the fitted Jost matrix on any sheet of the Riemann surface whose topology involves not only the square-root but also the logarithmic branching caused by the Coulomb interaction. As a result of such an analytic continuation, it was found that the previously established ${\frac{3}{2}}^{+}$-resonance (at $\sim 47\mathrm{\text{keV}}$) and its shadow pole (at $\sim 80\mathrm{\text{keV}}$) both are split in overlapping pairs. Apart from studying the properties of a specific nuclear state, it is also proved for a general multi-channel problem that the Coulomb forces change the topology of the Riemann surface as well as destroy the so-called mirror symmetry of the $S$-matrix.

The light elements and their isotopes were produced during standard big bang nucleosynthesis (SBBN) during the first minutes after the creation of the universe. Comparing the calculated abundances of these light species with observed abundances, it appears that all species match very well except for lithium (⁷Li) which is overproduced by the SBBN. This discrepancy is rather challenging for several reasons to be considered on astrophysical and on nuclear physics ground, or by invoking nonstandard assumptions which are the focus of this paper. In particular, we consider a variation of the chemical potentials of the neutrinos and their temperature. In addition, we investigated the effect of dark matter on ⁷Li production. We argue that including nonstandard assumptions can lead to a significant reduction of the ⁷Li abundance compared to that of SBBN. This aspect of lithium production in the early universe may help to resolve the outstanding cosmological lithium problem.

The possibility for the existence of the exotic ${NNN}^{\ast }$ states is explored with the objective of calculating the $N^{\ast }$ momentum distribution inside such nuclei. Even though the latter is an essential ingredient for the analysis of the experimental data on the $pd\to pd{\pi }^0$, $pd\to ppp{\pi }^{-}$ and $pd\to pnn{\pi }^{+}$ reactions aimed at finding an $\eta$-mesic ³He, the data analysis is usually performed by approximating the $N^{\ast }$ momentum distribution by that of a nucleon. Here, we present calculations performed by solving the three-body Faddeev equations to obtain the momentum distribution of the $N^{\ast }$ inside possible ($N^{\ast }$)${}^{+}np$, ($N^{\ast }$)${}^{0}np$ and ($N^{\ast }$)${}^{+}$-$d$ states. The $N^{\ast }$ momentum distributions are found to be much narrower than those of the nucleons and influence the data selection criteria.

A model-independent and $\ell$-dependent four parameter formula has been recently proposed for the studies of one proton and two proton radioactivity. The same form of the formula with different parameter sets worked well for 1p and 2p emission indicating the fact that the similar phenomenological law is able to successfully reproduce both 1p as well as 2p emission half-lives suggesting the identical descriptions of these phenomena. Retaining the same form of the formula, its applicability is studied in this work for calculating the ground state as well as excited state $\alpha$ emission. For this study, we consider 22 odd–odd nuclei, 31 odd–even nuclei, 52 even–odd nuclei, 88 even–even nuclei with the parent nucleus charge numbers in the range of $83\le Z\le 91$, $83\le Z\le 101$, $84\le Z\le 98$, and $88\le Z\le 102$, respectively. For each of these subsets the emission of $\alpha$ with different angular momentum values are considered. The general formula with four different parameter sets is proposed and the obtained results are compared with the experimental data. The study reveals that the general form of the proposed empirical formula is suitable for calculating the half-lives of 1p, 2p and $\alpha$-emission with different $\ell$-values. With very minimal input like $Q$-values, and charge number of the daughter nucleus, this formula can be used as a handy tool for a systematic study as well as to plan new experiments.

The influence of neutrons on charge changing cross-sections (${\sigma }_{\mathrm{\text{cc}}}$) in C isotopes on ${}^{12}$C and proton targets has been investigated in the framework of Glauber model. By comparing the theoretical results and experimental data, it is found out that the influence mainly comes from the projectile neutrons, and the ${\sigma }_{\mathrm{\text{cc}}}$ has a slight change with the increase of the neutron number. Besides, the calculations also illustrate that the influence gets bigger with the reduction of the incident energy.

The elementary (one-particle) $U(d_1+d_2)\supset U(d_1)\otimes U(d_2)$ isoscalar factors, involving two-rowed initial and final irreducible representations (irreps), are obtained. Using the latter, further some of the multiplicity-free $U(d_1+d_2)\supset U(d_1)\otimes U(d_2)$ isoscalar factors, involving the $U(d_1+d_2)$ couplings of the type $[E_1,E_2,\dot{0}]\times [p,\dot{0},-q]\to [E_1^{\prime },E_2^{\prime },\dot{0}]$, are obtained using the building-up procedure. The present results extend the ones obtained earlier for the one-rowed initial and final irreps.