International Journal of Modern Physics E

The 2016 update of the discovery of nuclide project is presented. Only 12 new nuclides were observed for the first time in 2016. A large number of isotopes are still only published in conference proceedings or internal reports. No changes to earlier assignments were made.

In the framework of an equation of state (EoS) constructed from a momentum and density-dependent finite-range two-body effective interaction, the quantitative magnitudes of the different symmetry elements of infinite nuclear matter are explored. The parameters of this interaction are determined from well-accepted characteristic constants associated with homogeneous nuclear matter. The symmetry energy coefficient $a_2$, its density slope $L_0$, the symmetry incompressibility $K_{\delta }$ as well as the density-dependent incompressibility $K(\rho )$ evaluated with this EoS are seen to be in good harmony with those obtained from other diverse perspectives. The higher order symmetry energy coefficients $a_4,a_6$, etc., are seen to be not very significant in the domain of densities relevant to finite nuclei, but gradually build up at supra-normal densities. The analysis carried out with a Skyrme-inspired energy density functional (EDF) obtained with the same input values for the empirical bulk data associated with nuclear matter yields nearly the same results.

The entanglement of pure states of the $0p$-, $1s0d$- and $1p0f$-shell nucleon pairs has been studied. The von Neumann entropy of the partial density matrix has been employed to quantify the entanglement of the $0p$-, $1s0d$- and $1p0f$-shell nucleon pairs. The Slater decomposition theorem has been used to verify if any pure state of a nucleon pair is an entangled state. Results of calculations have evidenced that a dominant part of the isospin $T=0,1$ proton–neutron states of the $0p$-, $1s0d$- and $1p0f$-shell nucleon pairs, respectively, are strongly entangled. It is shown that the calculated data are a source of valuable information on the spin quantum numbers of the entangled protons from two-proton decay.

We considered the systematics of Alpha-decay (AD) half-life (HL) of super-heavy nuclei (SHN) versus the decay energy and the total $\alpha$-kinetic energy. We have considered a potential model with Yukawa proximity potential and thereby calculated the HLs. Our results compared with experimental data and the empirical estimates. Also, we obtained $\alpha$-preformation factors from the ratio between theoretical and experimental results for a few super heavy nuclei. The results indicate the acceptability of the approach.

We explore the origins and breaking mechanisms of the spin and pseudospin symmetries for the antinucleon spectrum by the use of the similarity renormalization group, which transforms the Dirac Hamiltonian into a diagonal form and decomposes it into several independent components. By comparing the contribution of every component to the spin and pseudospin splittings, it is found that the energy splitting of spin doublets is dominated by the spin-orbit coupling while the pseudospin breaking comes mainly from these contributions of the nonrelativistic term and the dynamical term. In addition, the dependencies of the spin and pseudospin symmetries on the shape of the potential and the quantum numbers of the doublets are clarified.

Calculation of alpha particle preformation probabilities for some alpha emitters is considered in the framework of a recent proposed barrier penetration formula, by two different approximations. The behavior of alpha particle preformation probability with the variation of neutron and proton numbers of parent nuclei for isotopes, in the range $74\le Z\le 122$, and isotones, in the range $124\le N\le 132$, is investigated. The same correlations are then studied for the alpha decay half-life, the barrier assault frequency, barrier height and barrier penetration probability. Strong correlations are found and in a good agreement with experimental expectations.

The results of calculations of differential cross-sections for $\alpha$-${}^{12}$C elastic scattering by the $S$-matrix model are presented for 10 energy values in the energy range 65MeV$\le E_{\alpha }\le$ 386MeV in a wide range of scattering angles. The behavior of various scattering characteristics as functions of the projectile energy is analyzed. It is shown that the chosen parametrization of $S$-matrix allows describing correctly the Fraunhofer oscillations of the cross-sections in the region of small scattering angles and the rainbow scattering pattern in the region of sufficiently large angles.

In this paper, the analytical solutions of the $D$-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any $l$ orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary $l$ states for $D$-dimensional space.

The quasimolecular potential in the sudden approximation is used both near and above the Coulomb barrier (CB) for the ${}^{12}\mathrm{\text{C}}+{}^{16}\mathrm{\text{O}}$ system. It is found that the resonances associated with the dinuclear configuration are well produced in energy above the CB. Near and below the CB where adiabatic potential is appropriate, it was found that the potential can also be used, provided the potential parameters are varied and the range parameter of the Yukawa term is increased. Resonance positions for $L=8,9,10$ and 11 agree with experimental findings. The $L=6$ resonance energy and width very near 9MeV and not at 8.8MeV is also reproduced thus supporting experimental results.

High-spin levels of ${}^{103}$Mo have been reinvestigated by analyzing the high statistics $\gamma$-$\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$-$\gamma$ coincidence data from the spontaneous fission of ${}^{252}$Cf taken with the Gammasphere detector array. Two bands and 30 new transitions have been identified. A potential energy surface calculation has been performed. The calculation confirmed the 3/2${}^{+}$[411] configuration of the ground state band and 5/2${}^{-}$[532] for the 346keV excited band, as assigned in the previous work. The two newly established bands were proposed to be one- and two-phonon $\gamma$ vibrational bands coupling to the 5/2${}^{-}$[532] Nilsson orbital, respectively. Triaxial projected shell model calculations have been applied to explain the level structure and are found in good agreement with experimental data.

The $(\mathrm{\text{p}},\mathrm{\text{2p}})$ reaction on ${}^{40}\mathrm{\text{Ca}}$ at incident proton energy of 300MeV is examined in the formalism of finite-range relativistic distorted-wave impulse approximation (FR-RDWIA). In comparison to conventional t-matrix model of Love–Franey, a new form of nucleon–nucleon t-matrix effective interaction is derived at 300MeV using Reid soft core potentials for isotopic spin one and taking into account the finite-range effects in the $\mathrm{\text{p}}-\mathrm{\text{p}}$ interaction at knockout vertex. In comparison to the conventional finite range nonrelativistic and relativistic formalism, the present formalism with a new version of $\mathrm{\text{p}}-\mathrm{\text{p}}$ t-matrix is effectively reproducing the shape of cross-section energy distributions for ${\mathrm{\text{1d}}}_{3/2}$, ${\mathrm{\text{1d}}}_{5/2}$ and ${\mathrm{\text{2s}}}_{1/2}$ states for asymmetric angle pair of $30^{\circ }$–$55^{\circ }$. Discrepancies between the experimental cross-section data and finite range theoretical calculations at ${\mathrm{\text{E}}}_p=300$MeV are reasonably resolved in the present approach. Without any adjustable parameter of bound state, the obtained spectroscopic factors are in reasonably good agreement with the relativistic and nonrelativistic theoretical predictions by $(\mathrm{\text{p}},\mathrm{\text{2p}})$, $(\mathrm{\text{e}},{\mathrm{\text{e}}}^{\prime }\mathrm{\text{p}})$ and $(\mathrm{\text{d}},{}^3\mathrm{\text{He}})$ analysis.

The electric and magnetic transitions in the ${}^{24}$Mg nucleus are studied based on the calculations of the longitudinal and the transverse electron scattering form factors. The universal sd-shell model Hamiltonian (USDA) is used for calculations. The wave functions of radial single-particle matrix elements are calculated using the Skyrme potential. For the longitudinal form factors, a good agreement is obtained between the calculations and the experimental data. For the transverse form factors, the effective $g$ factors are made as adjustable parameters in order to describe the experimental data.