International Journal of Modern Physics E

Magnetic dipole and electric quadrupole moments are calculated for odd-$A$ nuclei in the vicinity of $Z=20$ closure. Also, elastic magnetic electron scattering form factors are calculated for some of these nuclei, for which there are available experimental data. Excitation out of major shell space is taken into account through a microscopic theory which allows particle–hole excitation from the core and model-space orbits to all higher orbits with $n\hslash \omega$ excitations, with $n$ as the number of shells that gives convergence to core-polarization matrix elements. Effective charges are obtained for each isotope. Core polarization (CP) is essential for obtaining a reasonable description of the electric quadrupole moments, but has no effect on the magnetic dipole moments but squeezes the magnetic form factors, and describes the data very well. For nuclei where there are data for large momentum transfer values, Skyrme–Hartree–Fock (SHF) method is used to generate from it a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. Those with high momentum transfer data which give evidence of the structure of the different multipoles, are more well described using SHF formalism than the harmonic oscillator (HO) single-particle matrix elements.

The anharmonicity in the $Z=48$Cd, and $Z=52$Te chain of isotopes, which lie close to magic number $Z=50$, is analyzed from the study of the correlation of the energy levels in the ground band, and some anomalies in the various entities are pointed out. The split of the degeneracy of the phonon triplet and quintuplet is illustrated. Formation of multiple coexisting phonon multiplets, associated with higher lying excited $0^{+}$ and $2^{+}$ states, and intruder states, including 2p4h excitation, with varying deformations, in ${}^{110-118}$Cd is discussed. The interacting boson model (IBM) is applied for $N=62,66$ ${}^{110,114}$Cd. The results of a previous study of $N=66$ isotones in the dynamic pairing plus quadrupole model are cited for Cd and Te. The problem of collectivity as reflected in the quadrupole moments and $B(E2,2_1^{+}-0_1^{+})$ values is analyzed. The enigma of deformation features in spherical ${}^{120-124}$Te, reflected in the transition probability $B(E2,0_1^{+}-2_1^{+})$ is resolved. Charge dependence of $E$2 transitions for vibrational nuclei, in producing enhanced $B(E2,0_1^{+}\to 2_1^{+})$ strengths in Te versus Cd is illustrated.

In this work, a new approach is presented for determining the equation of state for pure neutron matter. This is valid in the temperature- and density-regime where the system behaves like a nonideal gas. Further, the calculations involved are confined to the nonrelativistic and low-energy ($\le$ 150 MeV) regime. The approach is based on evaluating the quantum second virial coefficient $B_q$ of the system, where the input potential is the Reid-93 soft-core potential for $J\le 2$, together with the one-pion-exchange potential (OPEP) for higher $J$. The many-body phase shifts are determined within the framework of a generalized scattering theory, taken here as the Galitskii–Migdal–Feynman formalism. The integral equations involved are solved using a highly-accurate matrix-inversion method. These medium phase shifts are then inserted in the Beth–Uhlenbeck formula to determine $B_q$. Once this coefficient has been calculated, other thermophysical properties of the system can be readily computed according to standard expressions. Specifically, these properties include the equation of state (pressure–temperature–density relations), Helmholtz (free) energy, entropy, mean internal energy, specific heat capacity and chemical potential. Our results are compared, whenever possible, to those of previous calculations. The agreement is, on the whole, fair considering that the available calculations vary considerably among themselves.

A set of global optical potential parameters describing the elastic scattering of ⁶Li projectile on 1p-shell nuclei is obtained by fitting the experimental data of elastic scattering angular distributions for ⁹Be, ${}^{10}$B, ${}^{11}$B, ${}^{12}$C, ${}^{13}$C, ${}^{14}$C, ${}^{15}$N, ${}^{16}$O and ${}^{18}$O targets with incident energies from 4.0,MeV to 210.0,MeV and with ⁶Li and ⁷Li targets from 2.0,MeV to 156.0,MeV. The comparison is performed between the results calculated using the derived optical potential and the existing experimental data. The calculations agree well with the experimental data in the whole energy region except from 20,MeV to 50,MeV at backward angles, where there is an upward trend for the experimental data of angular distributions. Besides, the inelastic scattering contributions of the first excited states are deduced by the present global optical potential. The results are also in good agreement with the experimental data. In order to improve the description of elastic scattering, the inelastic scattering contributions of the first excited states are considered in the calculations between 20 and 50,MeV. A satisfactory fit is obtained between them.

Decay analysis of compound nuclei such as ${}^{96}{\mathrm{\text{Zr}}}^{\ast }$ and ${}^{98}{\mathrm{\text{Ru}}}^{\ast }$ formed in ${}^{48}\mathrm{\text{Ca}}+{}^{48}$Ca and ${}^{34}\mathrm{\text{S}}+{}^{64}$Ni reactions, respectively, is studied using two theoretical frameworks, dynamical cluster-decay model (DCM) and PACE4. To explore the decay dynamics in a relatively lighter mass region $({\mathrm{\text{A}}}_{\mathrm{\text{CN}}}\approx 60)$, two more reactions are picked (i) ${}^{34}\mathrm{\text{S}}+{}^{26}$Mg forming the ${}^{60}{\mathrm{\text{Ni}}}^{\ast }$ compound nucleus, (ii) another one involving the odd mass projectile, ${}^{35}\mathrm{\text{Cl}}+{}^{27}\mathrm{\text{Al}}\to {}^{62}{\mathrm{\text{Zn}}}^{\ast }$. In DCM, the fusion excitation functions are calculated using sticking $(I_S)$ and nonsticking $(I_{\mathrm{\text{NS}}})$ limits of the moment of inertia. For the chosen reactions, fusion cross-sections are equivalent to evaporation residue (ER) cross-sections $({\sigma }_{\mathrm{\text{fus}}}={\sigma }_{\mathrm{\text{ER}}})$ as fission cross-sections are negligible. A lower magnitude of maximum angular momentum $({\ell }_{\mathrm{\text{max}}})$ is obtained via the $I_{\mathrm{\text{NS}}}$ approach in comparison to the $I_S$ approach and the angular momentum obtained via the $I_{\mathrm{\text{NS}}}$ approach is closer to the experimental observations. The structure and magnitude of fragmentation potential and preformation probability $(P_0)$ depend on the choice of moment of inertia and the magnitude of angular momentum involved. Besides this, PACE4 is employed to address the fusion cross-section of chosen reactions. The most probable decay channel is identified using both DCM and PACE4 approaches.

In this work, we obtain new solutions of the Bohr Hamiltonian model appropriate for triaxial nuclei, with screened Kratzer potential in the framework of conformable fractional derivative. The analytical solutions for energy spectra are obtained using the conformable fractional Nikiforov–Uvarov method. We discuss the link between the present model and other relevant related models such as Z(5) model, classical screened Kratzer model and conformable fractional Kratzer model. The effect of the fractional-order parameter is investigated on the variations of the interaction potential. The normalized eigen-energies are calculated as well as normalized B(E2) transitions probabilities at different values of the fractional-order parameter. Our results reproduced well the experimental data for ${}^{126}$Xe, ${}^{128}$Xe, ${}^{130}$Xe, ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt atomic nuclei, and are found to be improved in comparison with other related theoretical models.

Bohr Hamiltonian with inversely quadratic Yukawa plus screened Kratzer potential for the $\beta$-part and a harmonic oscillator for the $\gamma$-part is investigated. The expressions of energies and wave functions are obtained using the parametric Nikiforov–Uvarov method. The obtained results are used to evaluate the normalized eigen energies, the root mean square deviation and $B(E2)$ transition rates of ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt atomic nuclei. The numerical results of our model are compared to those of other relevant theoretical models and experimental data. Furthermore, to test the sensitive signature of triaxiality, we used some indicators such as the staggering effect in the $\gamma$-band. It appears that the results provided by our calculations are in accordance with experimental values and improved in comparison with previous models.

Based on the effective-mass concept, we perform the Faddeev calculations for a low-lying spectrum of 3$\alpha$ states in ${}^{12}$C nucleus. A three-body potential is used to describe the known breaking of the 3$\alpha$-cluster structure in the nucleus. We show that the contribution of the three-body potential to the Hamiltonian can be compensated by increasing/decreasing the $\alpha$-particle free mass. The effective-mass values are adjusted to reproduce the experimental data for the ${}^{12}$C nucleus. The energy dependence of the effective mass and the correlation to a three-body potential are discussed. We show that the coupling between the $0^{+}$ ($2^{+}$) levels forms a specific picture of anti-crossing on the energy/effective-mass plane.

The prediction of properties of the low-energy portion of the hadronic spectrum is a challenging task which, up to day, is still tentatively given due to the nonperturbative nature of quantum chromodynamics (QCD) at low energies. In this paper, we are exploring the validity of the SO(4) scheme, as a representative of the fundamental QCD structure of meson-like states in the region below 2.5 GeV. We have focused our attention on the calculation of the energy and width of meson states of various spin, isospin and parities.

In this paper, we present the charged particles jet cross-section study in $pp$ and $pPb$ collisions at $\sqrt{s_{NN}}=5.02$,TeV using PYTHIA8 (PYTHIA8.186 and PYTHIA8.306) and HIJING 2.0 models, in kinematic range of $5<p_T<100$,GeV/c for $pp$ collisions and $20<p_T<120$,GeV/c for $pPb$ collisions. The jets are reconstructed for $R=0.2$, 0.3, 0.4 and 0.6 for the pseudorapidity interval of $\left|\eta \right|<$ 0.9-R. The jets algorithms: cell jet and slow jet inside PYTHIA8.186 and anti-$k_T$ algorithm using HIJING 2.0 have been used for Monte Carlo simulations. The simulation results are then compared with measurements of the ALICE experiment. It is observed that all models’ predictions are lower than experimental data up to $p_T=20$,GeV/c; after that, the Monte Carlo study of Cell and slow jet satisfies the experimental data. The CR tunes could not explain the ALICE data at high $p_T$ values due to nonperturbative QCD effects. We have also calculated the nuclear modification factor $R_{pPb}$, and no clear suppression has been seen in the case of $pPb$ collisions. The results from the models indicate that the QGP is not formed and that the cold nuclear matter effect exists in pPb collisions.