International Journal of Modern Physics E

Since Mayer and Jensen employed the single-particle shell model to interpret the magic numbers, various microscopic nuclear models have been developed to study the nuclear force and structure. The configuration–interaction shell model (CISM), performed in truncated model space with the inclusion of the residual interaction, is one widely-used nuclear structure model. In the last decade, CISM has progressed in investigating the cross-shell excitation in exotic light nuclei, the similarity and difference in mirror nuclei, and the isomerism and seniority conservation in medium and heavy nuclei. Additionally, researchers have attempted to construct effective Hamiltonians for nuclei near ${}^{132}$Sn and ${}^{208}$Pb through a unified way in the CISM framework. In parallel, related models, including the nucleon-pair approximation (NPA) approach, the Monte Carlo shell model (MCSM), the projected shell model (PSM), the Gamow shell model (GSM), etc., have also been extensively developed and validated in the last decade. This paper reviews the recent progress in CISM and some related models.

The quarkonium yield productions in the relativistic Heavy-Ion Collisions and their modifications within the Quark–Gluon Plasma (QGP) produced in the collisions have been investigated for more than four decades. Similarly, phenomenological model studies with various themes have been performed to comprehend the features of the QGP medium along with its associated particle production. This paper proposes a model that combines the effects of color screening, gluon-induced dissociation, and recombination on quarkonium production in heavy-ion collisions involving ($\mathrm{\text{Pb}}+\mathrm{\text{Pb}}$ ions) at a center-of-mass energy of $(\sqrt{s_{\mathrm{\text{NN}}}})=5.02$TeV. Unlike the Boltzmann transport rate equations of dissociation and recombination, the rate equations are decoupled and solved individually using a method involving Bateman solution ensuring the dissociation and recombination of heavy quarks within the QGP medium are accounted well.

We present a review of published experimental measurements on anisotropic flow in heavy-ion collisions. Flow coefficients $v_n$ are presented for charged and identified hadrons at various beam energies ranging from $\sqrt{s_{\mathrm{\text{NN}}}}=7.7$GeV to 200GeV at the Relativistic Heavy Ion Collider (RHIC) and $\sqrt{s_{\mathrm{\text{NN}}}}=2760$GeV at the Large Hadron Collider (LHC). We present $v_1$ and its slope $d{v}_1∕dy$ and discuss possible first-order Quantum chromodynamics (QCD) phase transition. $v_1$ of particles containing heavy quarks (Charm quarks) is also discussed to illustrate the effect of the magnetic field produced in relativistic heavy-ion collisions. We also present flow harmonics ($v_2$, $v_3$ and $v_4$) for inclusive charged and identified hadrons. We compare the charged particle $v_n$ coefficients with hydrodynamics to study and constrain initial conditions in the transport models. The results of identified particle $v_2$ from ideal and viscous hydrodynamics are discussed to understand the dynamics and mechanism of particle production in high-energy nuclear collisions.

We calculate four types of initial vorticities in Au$+$Au collisions at energies $\sqrt{S_{\mathrm{\text{NN}}}}=5$–200GeV using a microscopic transport model PACIAE. Our simulation shows the nonmonotonic dependence of the initial vorticities on the collision energies. The energy turning point is around 10–15GeV for different vorticities but not sensitive to impact parameter.

In this work, the role of inelastic processes in the formation of a transient Bose–Einstein condensation (BEC) is investigated based on kinetic theory. We calculate the condensation rate for an overpopulated gluon system which is assumed to be in thermal equilibrium and with the presence of a BEC. The matrix elements of the inelastic processes are chosen as the isotropic one and the gluons are considered to have a finite mass. Our calculations indicate that the inelastic processes can hinder the formation of a BEC since the negatively infinite net condensation rate can destroy any BEC instantly.

The prediction of quantum electrodynamics for elastic electron–proton scattering needs further modifications to agree with experimental data. Two scattering mechanisms that may occur are the forward and backward scattering angles for four-momentum transfer $Q^2=0.2$ up to 0.8 (GeV/$c$)². This is due to two different scattering centers. But the forward scattering is observed only at relatively high values of $Q^2\ge 1$(GeV/$c$)². The modifications related to the electric and magnetic form factors characterize the proton’s internal structure. These form factors’ dependence on $Q^2$ provides good agreement with other analysis methods. The proton’s charge radius, which corresponds to the maximum value of the scattering radius, is $0.81\pm 0.04$fm. The scattered electron is sensitive to proton internal constituents, especially at high values of $Q^2$ in which both scattering radius and photon wavelength decrease.

In this paper, we investigate the masses of the pseudoscalar ($D$($D^0$, $D^{+}$), $\bar{D}$($\overline{D^0}$, $D^{-}$) and vector open charm mesons ($D^{\ast }$($D^{\ast 0}$, $D^{\ast +}$), ${\bar{D}}^{\ast }$(${\bar{D}}^{\ast 0}$, $D^{\ast -}$) as well as the pseudoscalar (${\eta }_c(1S)$, ${\eta }_c(2S)$) and the vector charmonium states ($J∕\psi$, $\psi (2S)$, $\psi (1D)$) in the asymmetric hot strange hadronic medium in the presence of strong magnetic fields. In the magnetized medium, the mass modification of open charm mesons due to their interactions with baryons and the scalar fields ($\sigma$, $\zeta$, and $\delta$) is investigated in a chiral effective model. Moreover, the charged pseudoscalar meson ($D^{\pm }$), as well as the longitudinal component of charged vector meson ($D^{\ast \pm \parallel }$), experience additional positive mass modifications in the magnetic field due to Landau quantization. The effect of the modification of gluon condensates simulated by the medium change of dilaton field $\chi$ on the masses of the charmonia is also calculated in the chiral effective model. The contribution of masses of light quarks is also considered in the modification of gluon condensates. At high temperatures, the magnetically induced modifications of scalar fields significantly reduce the in-medium masses of mesons. The effects of magnetically induced spin mixing between the pseudoscalar and the corresponding vector mesons are incorporated in our study through a phenomenological effective Lagrangian interaction. The spin mixing result in a positive mass shift for the longitudinal component of the vector mesons and a negative mass shift for the pseudoscalar mesons in the presence of the magnetic field. From the obtained in-medium masses of charmonia and open charm mesons, we have also calculated the partial decay widths of $\psi (1D)$ to $D\bar{D}$, using a light quark pair creation model, namely, the ${}^3{P}_0$ model.

Mono-energetic $\gamma$-beams ($\mathrm{\Delta }\sim 10$eV) based on thermal neutron capture, in a nuclear reactor, using the Mn($n,\gamma$) reaction were utilized for generating a fast neutron source from Zinc, via the ${}^{67}$Zn($\gamma ,n$) reaction. One of the incident $\gamma$-lines of the Mn source at $E_{\gamma }=7244$keV, photoexcites by chance a resonance level in ${}^{67}$Zn, with subsequent emission of neutrons at an energy of 191keV. The cross-section for this process was measured and found to be $\sigma (\gamma ,n)=252\pm 41$mb with an intensity of the order of 10⁴n/s. The angular distribution of the 191keV neutron group was also measured.

To study the energy-dependent characteristics of thermodynamic and hydrodynamic parameters, based on the framework of a multi-source thermal model, we analyze the soft transverse momentum ($p_T$) spectra of the charged particles (${\pi }^{-}$, ${\pi }^{+}$, $K^{-}$, $K^{+}$, $\bar{p}$, and p) produced in gold–gold (Au–Au) collisions at the center-of-mass energies $\sqrt{s_{NN}}=7.7$, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200GeV from the STAR Collaboration and in lead–lead (Pb–Pb) collisions at $\sqrt{s_{NN}}=2.76$ and 5.02TeV from the ALICE Collaboration. In the rest framework of emission source, the probability density function obeyed by meson momenta satisfies the Bose–Einstein distribution, and that obeyed by baryon momenta satisfies the Fermi–Dirac distribution. To simulate the $p_T$ of the charged particles, the kinetic freeze-out temperature T and transverse expansion velocity ${\beta }_T$ of emission source are introduced into the relativistic ideal gas model. Our results, based on the Monte Carlo method for numerical calculation, show a good agreement with the experimental data. The excitation functions of thermodynamic parameter T and hydrodynamic parameter ${\beta }_T$ are then obtained from the analyses, which shows an increasing tendency from 7.7GeV to 5.02TeV in collisions with different centralities.

The $〈N_{\mathrm{\text{part}}}〉$ dependencies of the experimental average transverse momentum, $〈p_t〉$, of the charged pions, charged kaons, protons and antiprotons produced at midrapidity ($|y|<0.1$) in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions from the Beam Energy Scan (BES) program at the RHIC (Relativistic Heavy Ion Collider), measured by STAR Collaboration in the ${(s_{nn})}^{1∕2}=7$–39-GeV energy range, have been described quite well with the power-law model function. We have obtained $0<\alpha (\mathrm{\text{pion}})<\alpha (\mathrm{\text{kaon}})<\alpha ((\mathrm{\text{anti}})\mathrm{\text{proton}})<0.2$ inequality at all BES energies, indicating the clear mass ordering (dependence) of the power parameter $\alpha$. On the whole, the exponent parameter $\alpha$ for the charged kaons as well as (anti)protons decreases noticeably with increasing $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collision energy from ${(s_{nn})}^{1∕2}=7.7$GeV to ${(s_{nn})}^{1∕2}=39$GeV. Drastic change observed in the energy ($s_{nn}$) dependence of the parameter $\alpha$ for the charged kaons at ${(s_{nn})}^{1∕2}\approx 39$GeV could possibly indicate a significant change in the mechanism(s) of the charged kaon production in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions at around ${(s_{nn})}^{1∕2}\approx 39$GeV. Significant change in the ${(s_{nn})}^{1∕2}$ dependence of the parameter $\alpha$ for the charged pions observed at around ${(s_{nn})}^{1∕2}\approx 20$GeV is consistent with a possible change in the mechanism(s) of the particle production in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions at around ${(s_{nn})}^{1∕2}\approx 20$GeV, reported earlier by STAR Collaboration. Significant gaps between $\alpha$ (protons) and $\alpha$ (antiprotons) as well as between (${\pi }^{+}$) and $\alpha ({\pi }^{-})$ have been seen in the region ${(s_{nn})}^{1∕2}=7$–20GeV. These gaps diminish and practically disappear with $({\pi }^{+})\approx \alpha ({\pi }^{-})$ and $\alpha$ (protons) $\approx \alpha$ (antiprotons) in the region ${(s_{nn})}^{1∕2}>20$GeV. Altogether, the findings, regarding collision energy dependencies of the parameter $\alpha$ for the studied particle species, could indicate the probable phase transition of a nuclear matter to the mixed phase of QGP and hadrons taking place in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions at around ${(s_{nn})}^{1∕2}\approx 20$GeV. The differences found between parameter $\alpha$ versus ${(s_{nn})}^{1∕2}$ dependencies of the particles and antiparticles have been connected with the ratios of antiparticle and particle yields and differences in the mechanisms of production of particles and antiparticles. It is deduced that the exponent parameter $\alpha$ should be sensitive to the degree of particle (system) thermalization and particle production mechanisms, and its drastic change could be related to the change in the mechanisms of particle production or/and phase transitions in the nuclear/hadronic matter.

In this paper, we calculate the electromagnetic (EM) transition decay widths between two mesons containing different heavy quarks (c and b) for the process; $B_c^{\ast }\to B_c+\gamma$, using the Bethe–Salpeter (BS) framework. The calculated results are found to be in a reasonable agreement with other theoretical models but the experimental data for this problem is not yet available.

In this paper, we get the nuclear mass-density parameter of known mass and known charge radius by using the AME2020 nuclear mass database and the CR2013 nuclear charge radius database. For the nuclei with $N\ge 21$, we obtained an empirical formula of the constant parameter equal to 0 for the difference of nuclear mass-density parameter between two neighboring isotope. That is, the nuclear mass-density parameter of the two neighboring isotopes was equal. By using this empirical formula combined with AME2020 and CR2013 databases, the calculated value of 625 nuclear charge radii was obtained. The root-mean-square deviation (RMSD) of nuclear charge radius that we have successfully obtained is $\sigma =0.011$fm. In addition, one of the corrections is the neutron factor. This correction is the key improvement which reduces the RMSD to 0.0077fm. Considering the neutron shell effect, the different shell ranges were divided into two categories for correction, and the RMSD was reduced to 0.0056fm. Based on the revised empirical formula combined with the AME2020 database, the calculated and predicted values of nuclear charge radius were obtained with high accuracy. Some of these predictions are also very consistent with experimental values measured in recent years. In addition, we use BP neural network to study the difference of nuclear mass-density parameter on the basis of two categories. The RMSDs obtained are 0.0028fm and 0.0038fm, respectively. It can be seen that such a division has a certain degree of reliability and feasibility. These results show that the new relation proposed in this paper has simplicity and reliability, which can be compared with other local nuclear charge radius relations.

In this paper, we systematically studied half-lives of the different decay modes using various theoretical models such as the unified fission model (UFM) and the effective liquid drop model. Beta-decay half-lives were evaluated using semi-empirical formulae available in the literature. We compared half-lives of all the studied decay modes and identified shorter half-lives among the same in ${}^{205-233}$Ac nuclei. We investigated the actinium series which is similar to the thorium series. Among these decay series, alpha-emitting isotopes show great promise for cancer treatment because of their short path length and high-energy transfer of radiation. Furthermore, we predicted the decay chains of the actinium isotopes. All the decay series of actinium ends with the formation of stable nuclei or with longer half-lives. The predicted decay series and new isotopes during the decay process are helpful in the field of medicine and radiotherapy.

We study the impact of the in-medium mass splitting between bosons and anti-bosons on their spectra and elliptic flow. The in-medium mass splitting may cause a separation in the transverse momentum spectra, as well as a division in the elliptic flow between bosons and anti-bosons. The magnitude of this effect becomes greater as the in-medium mass splitting increases. With the increasing rapidity, the splitting effect of the spectra increases and the splitting effect of the elliptic flow decreases. These phenomena may provide a way to differentiate whether the influences on boson and anti-boson in the medium are consistent.

The proxy-SU(3) model is systematically used to obtain the ground state deformation and its evolution with neutron number for several isotopic chains ($Z=28$–34). These outputs are compared with the results of covariant density functional theory (CDFT) as well as the finite-range droplet macroscopic model (FRDM). Even Z results show good agreement with the CDFT results, while the odd Z results show good agreement with FRDM model results.