International Journal of Modern Physics E

The description of the production of light (anti-)(hyper-)nuclei in a hadron resonance gas, or statistical-thermal model approach, has proven to be rather successful, despite the fact that the binding energies of these compound objects are small compared to the emitting fireball temperature. We summarize some recent developments and findings in this approach.

An overview of a hadron resonance gas (HRG) model that includes van der Waals (vdW) interactions between hadrons is presented. Applications of the excluded volume HRG model to heavy-ion collision data and lattice quantum chromodynamics (QCD) equation of state are discussed. A recently developed quantum vdW HRG model is covered as well. Applications of this model in the context of the QCD critical point are elaborated.

Nuclear masses are of great importance in nuclear physics and astrophysics. Descriptive experimental data on nuclear masses and the prediction of unknown masses based on residual proton–neutron interactions are a focus in nuclear physics. The accuracy of the residual interaction determines the accuracy of the nuclear mass values, so the study of residual interactions is essential. Before we carry out this study, there are many papers using artificial neural networks in nuclear physics. But no one uses BP neural network to study residual interactions. In this paper, we obtained a description and prediction model for residual interactions based on BP neural network. By combining experimental values with residual interactions model, we successfully calculate the nuclear masses of $A\ge 100$. Results demonstrate that the differences between our calculated values and experimental values (AME2003, AME2012 and AME2016) show that the root-mean-squared deviations (RMSDs) are small (comparing with AME2003, the odd-A nuclei RMSD and the even-A nuclei RMSD are 112 and 128keV; comparing with AME2012, the odd-A nuclei RMSD and the even-A nuclei RMSD are 103 and 121keV; comparing with AME2016, the RMSD of odd-A nuclei and even-A nuclei are 106 and 122keV, respectively). In addition, we obtained some predicted masses based on AME2003 and AME2012, the predicted values have good accuracy and compared well with experimental values (AME2012 and AME2016). The results show that the study of residual interactions using the proposed BP neural network method is feasible and accurate. This method is helpful for analyzing and extracting useful information from a large number of experimental values and then providing a reference for discovering physical laws and support for physical experiments.

In this study, we have investigated the $\alpha$-decay chains of even–even superheavy nuclei $Z=120$ in the range of $290\le A\le 304$. The Hartree–Fock–Bogoliubov model is used to calculate the binding energy of these superheavy nuclei. We have included the so-called SkP skyrme function as an effective force and the quadruple deformations. The semi-empirical formulas are used in the reproducing $\alpha$-decay and spontaneous fission half-lives of these superheavy nuclei. By studying the decay chains of the Z = 120 isotopes and comparing them with the half-lives of spontaneous fission, it is predicted that the elements ${}^{278}114$, ${}^{284}114$, ${}^{274}114$, ${}^{282}116$, ${}^{280}116$, ${}^{290}116$,${}^{292}116$, ${}^{284}118$, ${}^{294}118$ and ${}^{292}120$ are more stable than the neighboring isotopes in their parent $\alpha$-decay chain. The corresponding neutron and proton numbers represent magical behavior that is in agreement with the numbers predicted before. In this range, the predicted nuclei are found to have large enough half-lives to synthesize them in a laboratory.

${}^{14}$C is a beta decay isotope, its beta decay is very slow reflecting the stability of this nucleus and emitted from medium and heavy mass nuclei. The ${}^{14}$C result is in excellent agreement with the favored ground-state-to-ground-state transition according to the cluster model of Blendowske et al. We study nuclear structure properties of spin-1/2 heavy nuclei in the relativistic core-cluster model, that its cluster is ${}^{14}$C. According to this model for spin-1/2 heavy nuclei and for obtaining its wave function, we solve the Dirac equation with the new phenomenological potential by parametric Nikiforov–Uvarov method and then calculate the binding energy and charge radius.

Energy levels and electromagnetic transition probabilities of odd-mass ${}^{129-135}\mathrm{\text{Pr}}$ and ${}^{127-133}\mathrm{\text{Ce}}$ isotopes have been calculated using the interacting boson fermion model. The even–even ${}^{128-134}\mathrm{\text{Ce}}$ isotopes have been used as the cores. In the model space, the bosons have angular momentum, $L=0$ ($s$-boson) and $L=2$ ($d$-boson) have been considered, while the nine protons for ${}^{129-135}\mathrm{\text{Pr}}$ and 19–25 neutrons for ${}^{127-133}\mathrm{\text{Ce}}$ are allowed to occupy the $1g_{7/2},2d_{5/2},2d_{3/2},3s_{1/2}$ and $1h_{11/2}$ single particle orbitals. The quasi-particle energies and occupation probabilities have been obtained by solving the BCS equation. According to the model space, the wave function for low-lying states has been investigated. The calculated results are in good agreement with the available experimental data.

It was recognized that the magic numbers of nuclei 2, 20, 28, 50, 82 and 126 are predicted to be more stable than the neighbor nuclei. Later on the researchers predicted that the magic numbers for protons are 114, 122, 124 and 164 and the magic numbers for neutrons are 184, 196, 236 and 318. The predicted second generation magic number for proton and neutron comes in the superheavy nuclei region. The superheavy nuclei with magic number of protons/neutrons are ${}^{298}$114, ${}^{310}$114, ${}^{306}$122, ${}^{318}$122, ${}^{308}$124, ${}^{310}$124, ${}^{310}$126 and ${}^{322}$126. All the possible decay modes have been studied by using three different models such as modified generalized liquid drop model, dynamical cluster model and coulomb-proximity potential model. In the second part of this study, we have made detailed investigations to synthesize the above said nuclei using fusion reactions with modified Woods–Saxon potential model. This study also identifies the most possible projectile target combinations for the synthesis of the predicted magic nuclei in the superheavy nuclei region.

This work emphasized the role of the projectile breakup channel by studying the complete fusion (CF) and incomplete fusion (ICF) dynamics of ${}^{6,7}\mathrm{\text{Li}}+{}^{144,152}\mathrm{\text{Sm}}$ reactions. The theoretical calculations for the chosen reactions have been done by opting for the coupled channel approach and the energy dependent Woods–Saxon potential (EDWSP) model. The below barrier fusion enhancements of the studied reactions are reasonably addressed by the outcomes of the adopted models, which in turn can be attributed to the couplings of nuclear structure degrees of freedom of the collision partners to their relative motion. In contrast, at above barrier energies, the CF cross-section data of the chosen reactions are found to be suppressed significantly when compared with the predictions made by using the present models. Interestingly, the fusion suppression factors of the given reactions can be minimized considerably with respect to the reported value when it is analyzed within the framework of the EDWSP model. For instance, in case of ${}^6\mathrm{\text{Li}}+{}^{144}\mathrm{\text{Sm}}$ (${}^6\mathrm{\text{Li}}+{}^{152}\mathrm{\text{Sm}})$ reaction, the magnitude of fusion suppression factor is minimized up to 7% (13%) relative to the reported value whereas for ${}^7\mathrm{\text{Li}}+{}^{144}\mathrm{\text{Sm}}$ (${}^7\mathrm{\text{Li}}{+}^{152}\mathrm{\text{Sm}})$ reaction, the fusion suppression factor is found to be less by 7% (8%) with reference to the reported value. Such suppression effects can be correlated with the low breakup threshold of alpha breakup channel associated with the loosely bound projectile. The projectiles being weakly bound systems split into two charged fragments and either of the breakup components is absorbed by the target resulting in the reduction of incoming flux going into fusion channel. The flux lost from the CF channel appears in the form of ICF yields. For ${}^6\mathrm{\text{Li}}{+}^{152}\mathrm{\text{Sm}}$, total fusion (TF) cross-sections that are sum of CF and ICF cross-sections are also analyzed in conjunction with the EDWSP model and thus reasonably explained by the model calculations. In order to identify the ICF contribution, the ratio of ICF/TF cross-section data of ${}^6\mathrm{\text{Li}}{+}^{152}\mathrm{\text{Sm}}$ reaction has been examined and thus properly addressed by using the EDWSP model. The presence of ICF component in TF cross-section clearly pointed out the breakup of projectile due to its loosely bound nature prior to the Coulomb barrier. Although ICF data of other systems are not available in the literature, a similar behavior is expected for ICF and TF data for ${}^6\mathrm{\text{Li}}{+}^{144}\mathrm{\text{Sm}}$ and ${}^7\mathrm{\text{Li}}+{}^{144,152}\mathrm{\text{Sm}}$ reactions.

In this paper, the generalized Dirac oscillator with $\kappa$-Poincaré algebra is structured by replacing the momentum operator p with $p-im\omega \beta V(r)r$ in $\kappa$-deformation Dirac equation. The deformed radial equation is derived for this model. Particularly, by solving the deformed radial equation, the wave functions and energy spectra which depend on deformation parameter $𝜀$ have been obtained for these quantum systems with $V(r)$ being a Yukawa-type potential, inverse-square-type singular potential and central fraction power singular potential in two-dimensional space, respectively. The results show that the deformation parameter $𝜀$ can lead to decreasing of energy levels for the above quantum systems. At the same time, the degeneracy of energy spectra has been discussed and the corresponding conditions of degeneracy have been given for each case.

Macedo and Guedes have shown how to solve a system of coupled harmonic oscillators with time-dependent parameters [Int. J. Mod. Phys. 23 (2014) 1450048]. We show that the first transformation they did is not correct. We show how to solve the coupled harmonic oscillators for the cases they treat in their paper, namely, $m_1(t)=m_2(t)=m_0{e}^{\gamma t}$, ${\omega }_1(t)={\omega }_{01}{e}^{-\gamma t/2}$, ${\omega }_2(t)={\omega }_{02}{e}^{-\gamma t/2}$ and $k=k_0$.