International Journal of Modern Physics E

As one promising approach for producing nuclei beyond the $\beta$-stability line, the multinucleon transfer (MNT) process has been extensively investigated in past decades. An overview of the theoretical progress on production of isotopes in MNT process is presented. The dinuclear system model, one hybrid approach (GRAZING+DNS model), the improved quantum molecule dynamic model, and the model based on the Langevin equations are summarized. The nucleon transfer mechanisms, such as effects of quasi-elastic and deep inelastic collisions, energy dissipation, $N/Z$ equilibration, and shell structure in collisions of two complex nuclei are discussed. We present the progress on production of the exotic nuclei near the neutron-drip line, the neutron-rich isotopes near $N=126$, and the transuranium nuclei.

The study of compound nucleus characteristics through fission fragment properties is a powerful tool to understand the fission mechanism of excited nuclei formed in heavy-ion-induced reactions. In this work, angular anisotropies of fission fragments from fissioning nuclei ${}^{211,212}Rn$, ${}^{213,215}Fr$, ${}^{220}Ra$, ${}^{221}Ac$, ${}^{223,224}Th$ and ${}^{225,227}Pa$ with normal behaviors in angular anisotropy have been analyzed. In this way, the quadrupole deformation parameter of the compound nucleus is calculated by comparison between the experimental data of angular anisotropy and those predicted by the standard saddle-point statistical model. Then the rotational energy, the fission barrier height, and the effective moment of inertia of the compound nucleus are obtained through the calculated quadrupole deformation parameters. It is observed that the quadrupole deformation parameter decreases with increasing the mean square angular momentum. The obtained results illustrate that the rotational energy and the effective moment of inertia increase almost linearly with increasing the mean square angular momentum, while the fission barrier height decreases as expected. However, the calculated values of fission barrier height overestimate the rotating finite-range model predictions. Also, the calculated values of effective moment of inertia represent a nearly linear trend despite those predicted by the rotating finite-range model. In order to discuss the physical ideas underlying the effect of angular momentum on the fission properties, the interaction potential energy during the capture process is studied for the lightest and heaviest reaction systems.

More than 100 excited states of the Calcium-40 nucleus, with isospin 0, are classified into rotational–vibrational bands of an intrinsic tetrahedral structure. Almost all observed states below 8MeV can be accommodated, as well as many high-spin states above 8MeV. The bands have some similarity to those classifying states of Oxygen-16, but the A-mode vibrational frequency is lower relative to the E-mode and F-mode frequencies than in Oxygen-16. Previously identified rotational bands up to spin 16 and energy above 20MeV are unified here into a smaller number of tetrahedral bands.

The properties of cold interacting Fermi gases in terms of scattering length are investigated. The scattering length is calculated by exact solution of Schrödinger equation. A Cosine hyperbolic potential with variable strength is employed in this study. The different interaction regimes are provided by choosing different strength of potential, which are characterized by an inverse of S-wave scattering length and Fermi wave number. The energy per particle for ³He system is calculated within the lowest order constrained variational (LOCV) method. It is found that the bound bosonic pairs as well as bound molecules are formed at positive scattering length, only by considering two-body interactions.

A detailed study of the centrality dependence of pseudo-rapidity distribution has been carried out for ${}^{16}$O-emulsion interactions at 4.5AGeV/c and ${}^{22}$Ne-emulsion interactions at 4.1AGeV/c using nuclear emulsion track detector. Depending on the values of the total charges or sum of the charges of noninteracting projectile fragments, event samples were classified into four centrality classes. Maximum pseudo-rapidity density, average pseudo-rapidity values, moments of pseudo-rapidity distribution along with skewness and kurtosis of the distributions have been investigated for different centrality classes.

The study of higher-order moments of a distribution and its cumulants constitute a sensitive tool to investigate the correlations between the particle produced in high-energy interactions. In our previous work, we have used the Tsallis $q$ statistics, NBD, Gamma and shifted Gamma distributions to describe the multiplicity distributions in ${\pi }^{-}$-nucleus and $p$-nucleus fixed target interactions at various energies ranging from $P_{\mathrm{\text{Lab}}}=27$GeV to 800GeV. In this study, we have extended our analysis by calculating the moments using the Tsallis model at these fixed target experiment data. By using the Tsallis model, we have also calculated the average charged multiplicity and its dependence on energy. It is found that the average charged multiplicity and moments predicted by the Tsallis statistics are in much agreement with the experimental values and indicates the success of the Tsallis model on data from visual detectors. The study of moments also illustrates that KNO scaling hypothesis holds good at these energies.

A possible mechanism for the formation of heavy-mass elements in supernovae is the rapid neutron-capture-mechanism ($r$-process). It depends upon the electron-fraction $Y_e$, a quantity which is determined by beta-decay-rates. In this paper, we focus on the calculation of electroweak decay-rates in presence of massive neutrinos. The resulting expressions are then used to calculate nuclear reactions entering the rapid-neutron capture. We fix the astrophysical parameters to the case of a core-collapse supernova. The neutrino sector includes a mass scheme and mixing angles for active neutrinos, and also by including the mixing between active and sterile neutrinos. The results of the calculations show that the predicted abundances of heavy-mass nuclei are indeed affected by the neutrino mixing.

As is well known, the single level seniority model of pairing has been solved exactly, since long using angular momentum algebra. It is shown that it can also be solved using the Dyson equation of standard many-body theory. The formalism shows some interesting many-body aspects.