International Journal of Modern Physics E

Gap parameter of Lipkin–Nogami (LN) model is replaced by order parameter of the exact Ginzburg–landau (EGL) theory. Thermodynamic quantities such as energy, entropy and heat capacity for ${}^{96,97}$Mo nuclei are calculated using this modified form of the LN model (MLN). In the LN model, the gap parameter suddenly decreases to zero at critical temperature. This causes singular points in the graph of heat capacity. However, in the MLN method, the order parameter does not become zero at critical temperature and gradually decreases along with the temperature. This causes the singular points, which are predicted in the heat capacity of LN model to be eliminated. Therefore, the heat capacity as a function of temperature becomes continuous and S-shaped, which is qualitatively in agreement with the experimental data.

In this work, a detailed study on the multiplicity characteristics of fast and slow target protons produced in the interactions of 3.3AGeV ${}^{22}\mathrm{\text{Ne}}$ and 3.7AGeV ${}^{24}$Mg projectiles with the heavy emulsion nuclei (AgBr) is performed. The experimental data of the multiplicity distributions (MDs) of gray (fast protons) and black (slow protons) particles are fitted with the negative binomial and Gaussian distributions indicating a reasonable consensus with each. The validity of scaling hypothesis of MDs of gray and black particles is verified by studying two types of scaling functions, Koba–Nielson–Olsen (KNO) scaling and Hegyi scaling. The experimental data are displayed by a simplified universal function in each scaling. An examination of the relationship between the entropy and the average multiplicity is performed. The measurements of the higher-order moments (mean, variance, skewedness and kurtosis) of MDs of proton target fragments are measured. The second Muller moments are calculated as well to investigate the correlation among the fast and slow target protons.

The lattice QCD data of pressure and the energy density have been used to extract the hadronic radius parameter of the excluded volume hadron resonance gas (EVHRG) model. The equation of state can be described well with the extracted radius parameter $R_h=0.15$ fm. Specific heat is also calculated in the EVHRG model. Further, two new universal descriptions of chemical freeze-out parameters have been introduced based on pressure and specific heat, respectively. It is shown that the chemical freeze-out parameters obtained at various $\sqrt{s_{NN}}$ in ideal hadron resonance gas (HRG) model approximately correspond to $P/T^4=0.88$ and $C_V/T^3=47$, respectively. These two quantities are important to describe the thermodynamic properties of the hadronic matter created in heavy-ion collision experiment. The sensitivity of universal chemical freeze-out lines on repulsive interaction is also studied. It has been observed that the behaviors of chemical freeze-out lines for $P/T^4$ and $C_V/T^3$ in EVHRG model remain similar to ideal HRG model for the best fit value of hadronic radii.

Nuclear radial distance is a prerequisite for generating any alpha-decay half-life formula by taking a suitable effective potential. We study the emission process of alpha particles from an isolated quasi-bound state generated by an effective potential to a scattering state. The effective potential is expressed in terms of Frahn form of potential which is exactly solvable and an analytical expression for half-life is obtained in terms of Coulomb function, wave function and the potential. We then derive a closed-form expression for the decay half-life in terms of the parameters of the potential, Q-value of the system, mass and proton numbers of the nuclei valid for alpha-decay as well as proton-decay. From the nature of variations of half-life as a function of radial distance, we trace the radial independence region where decay time is almost constant. Finally, by overviewing our results and picking that particular radial distance, we predict the half-lives of a series of nuclei by using the closed-form expression. We also predict the half-lives of isotopes of nuclei with $Z=119$ and 120.

We analyze the relation between the symmetry energy coefficient $a_{\mathrm{\text{sym}}}(A)$ of finite nuclei with mass number $A$ in the semi-empirical mass formula. The nuclear matter symmetry energy $E_{\mathrm{\text{sym}}}({\rho }_A)$ at reference density ${\rho }_A$ in the subsaturation density region can be determined by the symmetry energy $E_{\mathrm{\text{sym}}}({\rho }_0)$ and its density slope $L$ at the saturation density ${\rho }_0$. From this relation, the neutron skin thickness ‘$S$’ in finite nuclei with droplet model are correlated to the various symmetry energy parameters. A prominent role of the bulk symmetry energy $E_{\mathrm{\text{sym}}}({\rho }_0)$ to the so-called surface stiffness coefficient $Q$ is observed in deriving the size of the neutron skin. Two types of neutron skins are distinguished: the “surface” and the “bulk”. The linear dependence of the neutron skin thickness for different stable nuclei ($40\le A\le 238$) on the slope $L$ of the symmetry energy as well as on the relative neutron excess $I=\frac{N-Z}{A}$ is observed. Though the value of the surface width is found to be limited within 0.1fm, its contribution should not be neglected to measure neutron skin thickness.

A systematic investigation of collective properties in the nuclei of an $\alpha$-decay chain from ${}^{216}$Po to ${}^{272}$Cn has been performed in the total-Routhian-surface calculations. The empirical indicator $P$-factor, energy ratio $R_{4/2}=E_{4_1^{+}}/E_{2_1^{+}}$, and the energies of the first excited state $E_{2_1^{+}}$ exhibit a hint about nuclear deformation or shape transition in these nuclei. The calculated results of ground state equilibrium deformations are compared with the previous study and available experimental data, showing a general agreement. In addition, the upbending behaviors in moments of inertia have been reproduced by the present work. It is found that the similar alignment of a neutron $j_{15/2}$ pair is mainly responsible for the upbending in the heavier nuclei. The gentle increasing angular momentums reveal the delayed alignment to certain high spins. Furthermore, taking the near proton drip-line nucleus ${}^{272}$Cn as an example, we briefly discussed the influence of the modification of Woods–Saxon potential parameters (e.g., the strength of the spin-orbit potential $\lambda$ and the nuclear surface diffuseness $a$) on the moment of inertia. This may imply the role of the slight parameter modifications is negligible due to almost unchanged deformation and pairing interactions at ground state.

New transitions in neutron rich ${}^{96}$Y have been identified by analyzing the high statistics $\gamma$-$\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$-$\gamma$ coincidence data from the spontaneous fission of ${}^{252}$Cf at the Gammasphere detector array. Shell model calculations were performed and are found in good agreement with experimental data. The ground state is nearly spherical but a new excited band has large deformation.

Nucleon–nucleus (NA) optical potentials are microscopically generated from a fully self-consistent framework of the particle-vibration coupling (PVC), in which the nucleon–nucleon (NN) effective interaction of the Skyrme type is consistently used to describe the Hartree–Fock (HF) mean-field, the small amplitude collective motions of the target, and the particle-collective states coupling. For the first time, a systematic calculation of low-energy NA elastic scattering off a series of doubly closed-shell nuclei is carried out without ad hoc adjusted parameters. Angular distributions obtained using the present optical potentials are in good agreement with the experimental data. This will be a major step forward in the applications of the Skyrme energy-density-functional theory to build up the global microscopic optical potentials, which are expected to be a powerful tool for the study of unstable (exotic) nuclei at low-incident nucleon energies.

The present work is aimed at considering the recent forms of Bohr Hamiltonian, which are namely the hybrid model and the model combining the X(3) and E(5) symmetries, in the presence of the $\beta$-dependent Morse potential. The energy spectra and the transition rates of each model have been obtained. Some nuclei, the isotopes of Ru, Pd, Xe and ${}^{134}$Ba, have been fitted by using the three-parameter solution of the combined Hamiltonian with the Morse potential. Also, a few nuclei have been fitted by using the four-parameter solution of the hybrid model. In order to evaluate our results, in addition to reporting the root mean square (rms), we compare our data for each nucleus with the corresponding results of other references.

Gap equations at finite temperature are established in the isovector plus isoscalar pairing case $(T=1+T=0)$ using a path integral approach. Expressions of the various statistical quantities, i.e., the energy, the entropy and the heat capacity are then deduced. It is shown that they do generalize the ones obtained in the pure isovector ($T=1$) pairing case, as well as those obtained within the conventional finite temperature Bardeen–Cooper–Schrieffer (FTBCS) theory in the pairing between like-particles case. A numerical study is then performed using the schematic one-level model.

It is shown that the isoscalar n–p gap parameter ${\mathrm{\Delta }}_{np}^{T=0}$ behaves as a function of the temperature, like its homologues ${\mathrm{\Delta }}_{pp}$ and ${\mathrm{\Delta }}_{nn}$ in the conventional FTBCS approach. As for the three other gap parameters, i.e., ${\mathrm{\Delta }}_{np}^{T=1}$, ${\mathrm{\Delta }}_{pp}$ and ${\mathrm{\Delta }}_{nn}$, their behaviors are clearly modified when the isoscalar pairing is taken into account. In particular, one observes a shift of the values of the critical temperatures.

Dealing with the statistical quantities, the inclusion of the isoscalar pairing, in addition to the isovector one, leads to a lowering of the energy as well as a change of the shapes of the curves of the energy, the entropy and the heat capacity as a function of the temperature.