International Journal of Modern Physics E

The reaction ${}^{13}$C${(\alpha ,n)}^{16}$O is an important astrophysical process producing neutrons for $s$-process nucleosynthesis of nuclei heavier than iron in low-mass AGB stars. The reaction rate of ${}^{13}$C${(\alpha ,n)}^{16}$O at relevant energies is dominated by a ${1/2}^{+}$ state in ${}^{17}$O near the $\alpha$-threshold. The adopted value for the excitation energy of the state is −3keV below the threshold at 6359keV. However, recent investigations have indicated that the state is, instead of a sub-threshold state, an above threshold resonance state. The observation is also corroborated by neutron scattering studies from ${}^{16}$O. The location of the state and its implication on the low energy behavior of the astrophysical $S$-factor are of definite interest. The aim of this work is to ascertain the energy location of ${1/2}^{+}$ state in the excitation spectrum of ${}^{17}$O and to estimate its neutron and $\alpha$-partial widths. Subsequently, we look into the effect of the resultant set of parameters of the state on the $S$-factor and reaction rate at important astrophysical energies. A multilevel, multichannel $R$-matrix analysis has been performed for the existing ${}^{16}$O$(n,n)$, ${}^{13}$C$(\alpha ,n)$, ${}^{13}$C$(\alpha ,\alpha )$ and ${}^{16}$O$(n,\alpha )$ data. The excitation energy of the $1/2+$ state in ${}^{17}$O is found to be at 6371.9keV, about 12.9keV above the threshold. The resulting $S$-factor around the Gamow energy of 190keV $(T_9\sim 0.1)$ is $(1.91\pm 0.27)\times 10^6$$\mathrm{\text{MeV}}\cdot \mathrm{\text{b}}$. Relatively, higher $S$-factor value yields a larger reaction rate for ${}^{13}$C($\alpha ,n$)${}^{16}$O at the required temperature window. Consequently, larger number of neutrons relevant to $S$-process nucleosynthesis will be produced from ${}^{13}$C${(\alpha ,n)}^{16}$O reaction.

In this work, the ground state properties of the platinum isotopic chain, ${}^{160-238}$Pt are studied within the covariant density functional theory. The calculations are carried out for a large number of even–even Pt isotopes by using the density-dependent point-coupling and the density-dependent meson-exchange effective interactions. All ground state properties such as the binding energy, separation energy, two-neutron shell gap, root mean square (rms)-radii for neutrons and protons and quadrupole deformation are discussed and compared with available experimental data, and with the predictions of some nuclear models such as the Relativistic Mean Field (RMF) model with NL3 functional and the Hartree–Fock–Bogoliubov (HFB) method with SLy4 Skyrme force. The shape phase transition for Pt isotopic chain is also studied. Its corresponding total energy curves as well as the potential energy surfaces confirm the transition from prolate to oblate shapes at ${}^{188}$Pt contrary to some studies predictions and in agreement with others. Overall, a good agreement is found between the calculated and experimental results wherever available.

The fusion evaporation residue (ER) cross-sections ${\sigma }_{xn}$ for the decay of compound nucleus (CN) ${}^{252,254,255,256}$No${}^{\ast }$ via 1$n$–4$n$ decay channels, synthesized in ${}^{204,206,207,208}$Pb$+$${}^{48}$Ca reaction, are studied, including deformations ${\beta }_{2i}$ for cold-optimum orientations ${𝜃}_i$ at various ${}^{48}$Ca excitation energies of $E^{\ast }=20$ to 45MeV. For the nuclear interaction potentials, we use the Skyrme energy density functional (SEDF)-based on semi-classical extended Thomas Fermi (ETF) approach under frozen density approximation on our earlier study of fusion ER cross-section for the decay of ${}^{252,254-256}$No${}^{\ast }$, via 1$n$–4$n$ decay channels synthesized in ${}^{204,206-208}$Pb$+$${}^{48}$Ca reaction based on the Dynamical cluster-decay model (DCM) using the pocket formula for nuclear proximity potential in which the above reaction was investigated by using hot-optimum orientations. In this work the above reaction has been investigated in two parts, in the first part, $E^{\ast }<25$MeV is used for cold elongated configurations and in the second part, $E^{\ast }>25$MeV is used for hot compact configurations. The Skyrme forces used here are the old SIII, and new GSkI and KDE0(v1) given for both normal and isospin-rich nuclei, with densities added in frozen density approximation. Interestingly, independent of the Skyrme force used, the DCM gives an excellent fit within one-parameter fitting of $\mathrm{\Delta }R$ to the measured data on fusion ER for cold fusion. Of all the three Pb-isotopes and three $E^{\ast }$ considered, at each $E^{\ast }$, the $\mathrm{\Delta }R$ is largest for compound system with mass numbers 256 and 254, and smallest for 252, which means that the neutrons emission occur earliest for 256, then 255 followed by 254 and finally for 252, in complete agreement with experimental data. The possible fusion–fission (ff) and quasi-fission (qf) mass-regions of fragments on DCM are also predicted. The DCM with Skyrme forces is further used to look for all the possible target-projectile ($t$-$p$) combinations forming the “cold” CN ${}^{254}$No${}^{\ast }$ at the CN excitation energy of $E^{\ast }$ for “optimum cold” configurations. The fusion ER cross-sections, for the proposed new reactions in synthesizing the CN ${}^{254}$No${}^{\ast }$, are also estimated for the future experiments.

The available $R$-matrix parametrization of experimental data on the excitation functions for the elastic and inelastic $p{}^7\mathrm{\text{Be}}$ scattering at the collision energies up to 3.4MeV is used to generate the corresponding partial-wave cross-sections in the states with $J^{\pi }=0^{+}$. Thus, obtained data are fitted using the semi-analytic two-channel Jost matrix with a proper analytic structure and some adjustable parameters. Then the spectral points are sought as zeros of the Jost matrix determinant (which correspond to the $S$-matrix poles) at complex energies. The correct analytic structure makes it possible to calculate the fitted Jost matrix on any sheet of the Riemann surface whose topology involves not only the square-root but also the logarithmic branching caused by the Coulomb interaction. In this way, two overlapping $0^{+}$ resonances at the excitation energies $\sim 1.79$ and $\sim 1.96$MeV have been found.

The inclusive spectrum of the charged particles, $\pi$⁰- and $\eta$-mesons produced in the pp collisions at LHC energies were analyzed by fitting them with exponential functions. It was found the spectra were composed of several p${}_T$ regions, which could be characterized by the length of the regions $L_K^c$ and two free fitting parameters $a_K^c$ and $b_K^c$. The study of the $L_K^c$ dependences of the parameters $a_K^c$ and $b_K^c$ and of the energy dependencies of the $L_K^c$, $a_K^c$ and $b_K^c$ showed that the regions can be classified into two groups depending on the values of the $L_K^c$, $a_K^c$ and $b_K^c$. The values of the $L_K^c$ and $b_K^c$ for the first group don’t depend on colliding energy and the type of the particles (though the values of $a_K^c$ increase linearly with energy) whereas the characteristics in the second group of regions show strong dependencies. It was found that the ratio of the length for the $\eta$-mesons to one for the $\pi$⁰-mesons is approximately equal to the ratio of their mass: $〈L_{\eta }〉:〈L_{{\pi }^0}〉\cong m_{\eta }:m_{{\pi }^0}$. Assuming that the values of the $L_K^c$ are directly proportional to the string tension the result could be considered as evidence in favor of parton string fragmentation dynamics. The increase in the lengths for the $\eta$-mesons’ regions is accompanied by an increase of the values for the parameter $b_k^c$. It can mean that the $\eta$-mesons were produced at smaller values of ${\alpha }_S$ compared with that for $\pi$⁰-mesons. The results show that for the first group of regions the lengths of the regions are $\sim$3–5 times greater than the lengths of neighboring, lower p${}_T$ regions. For the second group of regions the lengths of the regions are $\sim$1–2 times greater than the lengths of neighboring lower p${}_T$ region. In the framework of the string fragmentation and hadronization dynamics, this could mean that the particles in the group $I$ of regions are produced through previous-generation strings decays into $\sim$3–5 strings while those in group $II$ originate from previous-generation strings decays into $\sim$2 strings.

Cutting of the tail of the Woods–Saxon (WS) potential influences the distribution of the poles of the $S$-matrix considerably. A new attempt is made here to correct the tail of the cut-off WS potential in order to bring the positions of the poles closer to the WS potential without cut. New types of strictly finite range potentials are introduced in which the tail of the WS and the generalized Woods–Saxon (GWS) potentials are modified to damp them at their ends. This damping affects the energies of the bound and narrow resonant states weakly. The resonant pole positions in the new potentials were affected more significantly and the new pole positions became closer to that of the GWS potential without cut. However, the cut-off effect cannot be diminished completely. The new potentials belong to the $C^{\infty }$ function class.

The Po isotopes show the presence of coexisting structures having different deformations with increasing neutron number within the macroscopic–microscopic Nilsson–Strutinsky formalism. The model is based on the Lublin Strasbourg Drop (LSD) method for the macroscopic energy calculation. We study the shape evolution in a long chain of polonium isotopes, ${}^{178-200}$Po.

Performing a fit procedure on the hyperon masses, we first determine the free parameters in the Cornell-like hypercentral potential between the constituent quarks of hyperons in their ground state. To this end, using the variational principle, we apply the hyperspherical Hamiltonian including the Cornell-like hypercentral potential and the perturbation potentials due to the spin–spin, spin–isospin and isospin–isospin interactions between constituent quarks. In the following, we compute the hyperon magnetic moments as well as radiative decay widths of spin-3/2 hyperons using the spin-flavor wave function of hyperons. Our analysis shows acceptable consistencies between theoretical results and available experimental data. This leads to reliable wave functions for hyperons at their ground state.

Thermal and rotational behaviors of neutron rich fp-shell isotopes such as ${}_{26}^{56}\mathrm{\text{Fe}}$, ${}_{26}^{58}\mathrm{\text{Fe}}$ and ${}_{26}^{60}\mathrm{\text{Fe}}$ were analyzed microscopically within the framework of statistical theory of hot rotating nuclei (STHRN) for the angular momentum range (0–15)$\hslash$ at excitation energy above 4MeV. Pair-breaking phenomenon and band-crossing phenomenon of Fe isotopes were discussed with and without the inclusion of BCS pairing. The STHRN method with BCS effect was extended to the Fe isotopes to determine the critical temperature $(T_C)$, where the pair-breaking phenomenon takes place and it is found to occur below $T=1.0$MeV. The observation of band-crossing phenomenon above the $T_C$ was explained without considering the effect of BCS pairing. The single particle energy levels were engendered from triaxially deformed Nilsson Hamiltonian. The outcomes of the present investigation on moment of inertia (MOI), back-bending phenomenon, spin cutoff parameter show a strong evidence of band-crossing phenomenon and it eventually led to a shape transition from spherical to noncollective oblate. Moreover, attention on separation energy of protons and neutrons reveals that the neutron pairs are responsible for band-crossing. STHRN method was able to reproduce results in good agreement with experiments and comparable with other theories such as projected shellmodel (PSM) and shellmodel Monte Carlo (SMMC) method.

In this work, we systematically study the $\alpha$ decay half-lives of 170 even–even nuclei with $60\le Z\le 118$ within the two-potential approach while the $\alpha$ decay preformation factor $P_{\alpha }$ is obtained by the cluster-formation model. The calculated results can well reproduce the experimental data. In addition, we extend this model to predict the $\alpha$ decay half-lives of 64 even–even nuclei with $104\le Z\le 128$ whose $\alpha$ decay is energetically allowed or observed but not yet quantified. For comparison, the two famous models i.e., SemFIS proposed by Poenaru et al. [Europhys. Lett. 77 (2007) 62001] and UDL proposed by Qi et al. [Phys. Rev. Lett. 103 (2009) 072501] are used. The predicted results of these models are basically consistent. At the same time, through analyzing the changing trend of $\alpha$ decay energy $Q_{\alpha }$ of $Z=118,120,122,124,126$ and 128 isotopes nuclei with the increasing of neutron number N and that of $\alpha$ decay preformation factor $P_{\alpha }$ of those isotopes even–even nuclei with the increasing of neutron number N, $N=178$ may be a new neutron magic number.

Alpha elastic scattering of $p$-nuclei was studied for calculating optical potentials. Choice of the $\alpha$-optical potentials is important to measure the reaction rates of $p$-process. ${}^{106}\mathrm{\text{Cd}}{(\alpha ,\alpha )}^{106}\mathrm{\text{Cd}}$ and ${}^{113}\mathrm{\text{In}}{(\alpha ,\alpha )}^{113}\mathrm{\text{In}}$ elastic scattering cross-section data were used to determine the potential parameter sets at $E_{\mathrm{\text{lab}}}=16.1\text{–}27$MeV for ${}^{106}\mathrm{\text{Cd}}$ and $E_{\mathrm{\text{CM}}}=15.59$, 18.8MeV for ${}^{113}\mathrm{\text{In}}$ system. A Wood–Saxon potential form factor is used for both real and imaginary parts. The potential parameters extracted in the present study exhibit a satisfactory result with respect to existing global potential parameters.

The method of impulse approximation is used to check the validity of the first-order optical potential for the elastic scattering problem of the neutron on the bound system, namely, ${\mathrm{\text{C}}}^{12}(n.n){\mathrm{\text{C}}}^{12},{\mathrm{\text{Ca}}}^{40}(n,n){\mathrm{\text{Ca}}}^{40}$ and ${\mathrm{\text{Pb}}}^{208}(n,n){\mathrm{\text{Pb}}}^{208}$at incident neutron energies of 155 and 225MeV. The optical potential is derived as the first-order term within the spectator expansion of a nonrelativistic multiple scattering terms using the Lippmann–Schwinger equation. The Modern realistic two-body potential ArgonneV18 in the momentum space was used as input in the Lippmann–Schwinger equation. The obtained results for the elastic differential cross-sections are in a good agreement with the experimental data taken from EXFOR Database for all studied targets at neutron energy above 200MeV. As the neutron energy decreases down to approximately 155MeV, the discrepancies with experimental data appear, which is in accordance with the impulse approximation formalism.

In high energy heavy-ion collisions, the final anisotropic flow coefficients and their corresponding event–plane correlations are considered as the medium evolutional response to the initial geometrical eccentricities and their corresponding participant–plane correlations. We formulate a systematic theoretical analysis to study the hydrodynamical responses concerning higher-order effects in $\mathrm{\text{Pb}}+\mathrm{\text{Pb}}$ collisions at $\sqrt{s_{\mathrm{\text{NN}}}}=2.76$TeV by using Monte Carlo (MC) Glauber model. To further understand the transformations of the initial participant–plane correlation, we construct a new set of events which randomize the directions of the initial participant–planes of the original events. Our results indicate that the final strong event–plane correlations are mainly transformed from the large initial eccentricities, rather than the strong participant–plane correlations. However, the large flow coefficients and the discrepancies between the flow coefficients calculated by the single-shot and event-by-event simulations in peripheral collisions are relevant to those strong initial participant–plane correlations.

A systematic study of the ground state properties of transitional nuclei W, Os and Pt is conducted with the help of Skyrme–Hartree–Fock–Bogoliubov theory. Different Skyrme interactions are employed in the study. Two different bases, harmonic oscillator and transformed harmonic oscillator, are used in our investigation. 2$n$-separation energy, charge radii, neutron and proton rms radii, neutron skin thickness and deformation parameter have been estimated. The results obtained are in good agreement with the available experimental values.