International Journal of Modern Physics E

Photonuclear reactions are important tools in the understanding of the nucleus. These reactions are also interesting for realizing the element creation processes in stellar environment. The use of bremsstrahlung photons generated from clinic linear accelerator is practical for performing these type of reactions. In this study, the bremsstrahlung photons with endpoint energy of 18MeV have been used for activating gallium target material. After irradiation, the transition energies and half-lives associated with the decay of ${}^{68}\mathrm{\text{Ga}}$, ${}^{70}\mathrm{\text{Ga}}$ and ${}^{72}\mathrm{\text{Ga}}$ isotopes have been determined The values obtained for half-life of ${}^{68}\mathrm{\text{Ga}}$, ${}^{70}\mathrm{\text{Ga}}$ and ${}^{72}\mathrm{\text{Ga}}$ isotopes are $67.5\pm 0.9$min, $21.1\pm 0.9$min and $13.8\pm 0.4$h, respectively. It has been seen that the values are consistent with the present literature values. In addition, the new measurements of gamma-ray energies for transition energies have been obtained comparable to the literature values with good uncertainties.

The phenomenological formula for ground state binding energy derived earlier [G. Gangopadhyay, Int. J. Mod. Phys. E 20 (2011) 179] has been modified. The parameters have been obtained by fitting the latest available tabulation of experimental values. The major modifications include a new term for pairing and introduction of a new neutron magic number at N = 160. The new formula reduced the root mean square deviation to 363keV, a substantial improvement over the previous version of the formula.

Fission barrier of the heavy nucleus ${}^{250}$Cf is analyzed in a multi-dimensional deformation space. This space includes two quadrupole (${\epsilon }_2,\gamma$) and three hexadecapole deformation (${\epsilon }_{40},{\epsilon }_{42},{\epsilon }_{44}$) parameters. The analysis is performed within an unpaired macroscopic–microscopic approach. Special attention is given to the effects of the axial and non-axial hexadecapole deformation shapes. It is found that the inclusion of the nonaxial hexadecapole shapes does not change the fission barrier heights, so it should be sufficient to minimize the energy in only one degree of freedom in the hexadecapole space ${\epsilon }_4$. The role of hexadecapole deformation parameters is also discussed on the Lublin–Strasbourg drop (LSD) macroscopic and the Strutinsky shell energies.

In this paper, we have investigated the positive-parity states in the odd-mass transitional ${}^{123-135}$Xe isotopes within the framework of the interacting boson–fermion model. Two solvable extended transitional Hamiltonians which are based on SU(1,1) algebra are employed to provide an investigation of quantum phase transition (QPT) between the spherical and deformed gamma — unstable shapes along the chain of Xe isotopes. The low-states energy spectra and B(E2) values for these nuclei have been calculated and compared with the experimental data. The predicted excitation energies and B(E2) transition rates of the odd isotopes are found to agree well with the experimental data. We have also analyzed the critical behavior of even–odd Xe isotopes via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces and special isotopes which are the best candidates for the critical point are identified.

We extend the previous study of dilepton production using [S. Somorendro Singh and Y. Kumar, Can. J. Phys. 92 (2014) 31] based on a simple quasiparticle model of quark–gluon plasma (QGP). In this model, finite value of quark mass uses temperature dependent chemical potential the so-called Temperature Dependent Chemical Potential Quark Mass (TDCPQM). We calculate dilepton production in the relevant range of mass region. It is observed that the production rate is marginally enhanced from the earlier work. This is due to the effect of TDCPQM and its effect is highly significant in the production of dilepton.

In this paper, we have taken the effect of small size of nucleus and static fluctuations into account in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity calculations of ${}^{45}$Ti nucleus. Thermodynamic quantities of ${}^{45}$Ti have been extracted within the BCS model with the inclusion of the average value of the pairing gap square, extracted by the modified Ginzburg–Landau (MGL) method for small systems. Calculated values of the excitation energy and entropy within the MGL+BCS method improve the extracted results within the usual BCS model and show a smooth behavior around the critical temperature with a very good agreement with the semi-empirical values. The result of using MGL+BCS method for the heat capacity of ${}^{45}$Ti is compared with the corresponding semi-empirical values and the calculated values within the BCS, static path approximation (SPA) and Modified Pairing gap BCS (MPBCS) which is a method that was proposed in our previous publications. Both MGL+BCS and MPBCS avoid the discontinuity of the heat capacity curve, which is observed in the usual BCS method, and lead to an S-shaped curve with a good agreement with the semi-empirical results.

The parametric resonance was studied in chiral phase transitions when the momentum distribution is described by a Tsallis distribution. A Tsallis distribution has two parameters, the temperature $T$ and the entropic index $q$. The amplification was estimated in two cases: (1) expansionless case and (2) one-dimensional (1D) expansion case. In an expansionless case, the temperature $T$ is constant, and the amplified modes as a function of $T$ were calculated for various $q$. In 1D expansion case, the temperature $T$ decreases as a function of the proper time, and the amplification as a function of the transverse momentum was calculated for various $q$. In the expansionless case, the following facts were found: (1) the larger the value $q$ is, the softer the amplified modes are for the first and second resonance bands, (2) the amplified mode of the first resonance band decreases and vanishes, as the temperature $T$ increases and (3) the amplified mode of the second resonance band decreases and approaches to zero, as the temperature $T$ increases. In 1D expansion case, the following facts were found: (1) the soft mode is amplified, (2) the amplification is extremely strong around the amplified mode of the first resonance band at $T=0$ and (3) the magnitude of the amplification as a function of transverse momentum oscillates around the amplified mode of the first resonance band at $T=0$.

We propose to study the thermal properties of the odd isotopes of Tin: ${}^{117,119,121}$Sn. To this end, one used two methods to evaluate the properties of these elements. The first theoretical consideration uses a simple prescription to perform the calculation of these properties based on those of even–even neighboring isotopes, assuming the quasi-particle entropy extensivity. The even–even elements are treated as part of the Modified Lipkin–Nogami (MLN) method that allows to take into account the quantal and statistical fluctuations. The second theoretical approach consists of the generalization of the MLN formalism in the case of odd systems, by using the blocking technique. Then, this approach is applied to evaluate the thermal properties of the considered elements. The obtained results by both theoretical approaches are compared to the experimental data. The latter are deduced from the experimental level density within the canonical ensemble. It appears that the assumption of quasi-particle entropy extensivity at low excitation energy allows a simple and an effective treatment of thermal properties of odd nuclei. Indeed, this approach allows to give a good reproduction of experimental data in the particular in the region where the pairing transition occurs.

The ground state magnetic moments and the low-lying magnetic dipole (Ml) transitions from the ground to excited states in heavy deformed odd-mass ${}^{181}$Ta have been microscopically investigated on the basis of the quasiparticle-phonon nuclear model (QPNM). The problem of the spurious state mixing in M1 excitations is overcome by a restoration method allowing a self-consistent determination of the separable effective restoration forces. Due to the self-consistency of the method, these effective forces contain no arbitrary parameters. The results of calculations are compared with the available experimental data, the agreement being reasonably satisfactory.

We study the effect of multi-phonon excitations on large-angle quasi-elastic scattering of massive systems using the full order coupled-channels formalism. We especially investigate the role of triple phonon excitations of the target and projectile nuclei on the quasi-elastic scattering cross-section as well as the barrier distribution for ${}^{54}$Cr, ${}^{56}$Fe, ${}^{64}$Ni and ${}^{70}$Zn + ${}^{208}$Pb systems. It is shown that the calculations taken into account, the triple octupole phonon excitations of the target and triple quadrupole phonon excitations of the projectile for these systems can explain the experimental data of the quasi-elastic cross-section and the quasi-elastic barrier distribution. These results indicate that the coupled-channels formalism is still valid even for the very heavy mass systems.

The experimental binding energies of single-particle and single-hole neutron states belonging to neutron shells that extend from $N$ = 126–184 and 82–126, respectively, have been reproduced by solving the Schrödinger equation with a potential that has two components: the generalized Woods–Saxon (GWS) potential and the spin-orbit (SO) coupling term. The GWS potential contains the traditional WS potential plus a term (SU) whose intensity reaches a maximum in the nuclear surface. Our results indicate the existence of an explicit relationship between the strength of the SU potential and the orbital angular momentum quantum number $\ell$ of the state. This dependence has been used to make reasonable predictions for the excitation energy centroids of states located inside and outside the neutron shells investigated. Comparisons are made with results reported in previous investigations.

Systematic calculations on $\alpha$-decay half-lives of Bi isotopes are performed by using the generalized liquid drop model (GLDM) and several sets of Royer’s analytic formulas. In calculations, the $\alpha$ transitions include the ones of (i) ground state (g.s.) to g.s., (ii) g.s. to isomeric state (i.s.), (iii) i.s. to g.s., (iv) i.s. to i.s. According to the comparison between the calculated half-lives and the experimental data, it is found that the experimental half-lives are reproduced well by the GLDM with the cluster-like mode. This indicates that the nuclear structure details play important roles in the $\alpha$-decay half-lives. In addition, it is found that the experimental half-lives are not reproduced well by these analytic formulas because the parameters are obtained by fitting the experimental half-lives of g.s. to g.s. transitions. To give better predictions on $\alpha$-decay half-lives, the parameters in these formulas should be refitted by including the experimental $\alpha$-transition of (ii)–(iv) mentioned above.

In the preceeding paper, introducing $isospin$-dependent density operators and defining exact momenta (collective variables), we could get an exact canonically momenta approach to a one-dimensional (1D) neutron–proton (NP) system. In this paper, we attempt at a velocity operator approach to a 3D NP system. Following Sunakawa, after introducing momentum density operators, we define velocity operators, denoting classical fluid velocities. We derive a collective Hamiltonian in terms of the collective variables.

We show that strangeness suppression in hadronic and nuclear collisions is fully determined by the initial energy density of the collision. The suppression factor ${\gamma }_s(s)$, with $\sqrt{s}$ denoting the collision energy, can be expressed as a universal function of the initial energy density ${ϵ}_0(s)$, and the resulting pattern is in excellent agreement with data from $p$–$p$, $p$–Pb, Cu–Cu, Au–Au and Pb–Pb data over a wide range of energies and for different centralities.

In this paper, we calculate the mass spectrum, weak decay constants, two photon decay widths, and two-gluon decay widths of ground ($1S$) and radially excited ($2S,3S,\dots$) states of pseudoscalar charmoniuum and bottomonium such as ${\eta }_c$ and ${\eta }_b$, as well as the mass spectrum and leptonic decay constants of ground state ($1S$), excited ($2S,1D,3S,2D,4S,\dots ,5D$) states of vector charmonium and bottomonium such as $J/\psi$, and $\mathrm{{\rm Y}}$, using the formulation of Bethe–Salpeter equation under covariant instantaneous ansatz (CIA). Our results are in good agreement with data (where ever available) and other models. In this framework, from the beginning, we employ a $4\times 4$ representation for two-body ($q\overline{q}$) BS amplitude for calculating both the mass spectra as well as the transition amplitudes. However, the price we have to pay is to solve a coupled set of equations for both pseudoscalar and vector quarkonia, which we have explicitly shown get decoupled in the heavy-quark approximation, leading to mass spectral equation with analytical solutions for both masses, as well as eigenfunctions for all the above states, in an approximate harmonic oscillator basis. The analytical forms of eigenfunctions for ground and excited states so obtained are used to evaluate the decay constants and decay widths for different processes.

Phenomenological analysis of breakup of oxygen nuclei on fragments with the charges one and seven in collisions with protons at 3.25$A$GeV/$c$ was conducted using the Monte Carlo model of isotropic phase space. For the first time, the contributions of mechanism of diffractive breakup of oxygen nucleus and that of quasi-elastic knocking out of one of the protons of oxygen nucleus by a proton target into channel of formation of proton fragment and ${}^{15}$N nucleus with conservation of recoil proton in final state were determined. Cross-section of diffractive breakup of oxygen ${}^{16}$O nucleus on ${}^{15}$N nucleus and proton fragment and that of diffractive breakup of ${}^{16}$O nucleus on nuclei ${}^{14}$N and ²H were estimated for the first time in ${}^{16}$O$p$ collisions at 3.25$A$GeV/$c$.