International Journal of Modern Physics E

By means of $4\pi$ emulsion track detectors, we report the characteristics of the experimental angular distributions of the fast target protons (grey particles) emitted in interactions of ${}^{16}$O with emulsion nuclei at 3.7AGeV. Grey tracks in nuclear emulsion corresponding protons with kinetic energy in the ranges $26<E_{K.E}\le 400$MeV. The angular distributions are compared with those resulting from interactions of other projectiles (${}^{12}$C, ${}^{22}$Ne and ${}^{28}$Si) at nearly the same incident energy. These angular distributions are studied at different target sizes ($N_h$-values) and at various projectile spectator charges ($Q$-values) in the framework of the modified Maxwell– Boltzmann statistical model. The nuclear limiting fragmentation hypothesis is shown to be fulfilled for these target protons angular distributions which are found to be independent of the target size and centrality of collisions. Also, the size of the projectile is found to be ineffective at Dubna energies. The angular distributions of all groups of events possess peaks positioned at $\theta g\sim 60^{\circ }$. The calculated statistical moments of the distributions along with skewness and kurtosis are investigated in addition to the forward-backward asymmetry ratio $(F∕B)$ for the different groups of events.

We present a systematic study of the transverse mass ($m_T-m$) spectra of ${\pi }^0$ and $\eta$ mesons in $Cu+Au$ collisions at $\sqrt{s_{NN}}=200$GeV, $U+U$ collisions at $\sqrt{s_{NN}}=192$GeV, $Pb+Pb$ collisions at $\sqrt{s_{NN}}=2.76$TeV and $p+Pb$ collisions at $\sqrt{s_{NN}}=5.02$TeV. The published data of invariant yields of ${\pi }^0$ and $\eta$ mesons as a function of $p_T$ are taken from PHENIX and from ALICE collaborations in the mid-rapidity region for different centrality cases. The primary object is to check the similar suppression patterns and identical spectral shapes of ${\pi }^0$ and $\eta$ mesons at different center-of-mass energies in different collision systems. We employ $m_T$ scaling approach to study the spectral shapes of $\eta$ meson from the given pion (${\pi }^0$) spectra. For this purpose, we use the modified Hagedorn function as a fit function. We obtain $m_T$ scaled $\frac{\eta }{{\pi }^0}$ ratio to study the spectral shape and suppression pattern of ${\pi }^0$ and $\eta$ mesons. This ratio is useful to obtain the decay contribution of ${\pi }^0$ and $\eta$ mesons in photonic and leptonic channels but also points to the quantitative changes in the dynamics of the heavy ion collisions.

Based on the framework of the modified potential cluster model (MPCM), with orbital states classified using Young diagrams, we consider the possibility of prediction absentee of experimental data for the total cross-sections of the radiative neutron capture on ${}^{11}$B to the first excited state of ${}^{12}$B at 0.95314MeV (2${}^{+}$), to the second excited state of ${}^{12}$B at 1.67365MeV (2⁻), and prediction absentee of experimental data for the total cross-sections to the third and fourth excited states of ${}^{12}$B at 2.6208MeV (1⁻) and 2.723MeV (0${}^{+}$), for a reaction energy of 10meV to 7MeV. We calculate the reaction rate for a temperature range of 0.01–10.0 $T_9$ on the basis of the obtained cross-sections, which take into account resonances up to 5MeV. We then demonstrate that low-lying resonances have a significant impact on the reaction rate of capture. An approximation for the calculated reaction rate is derived based on an analytical formula.

In this paper, the energy, and wavefunctions of the low-lying bound and resonance states of ${}_{\mathrm{\Lambda }}^{61}$Ca and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{62}$Ca are studied. For ${}_{\mathrm{\Lambda }}^{61}$Ca we adopted $\mathrm{\Lambda }{+}^{60}$Ca two-body cluster model while for ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{62}$Ca we adopted $\mathrm{\Lambda }+\mathrm{\Lambda }{+}^{60}$Ca three-body cluster model. Two models of potentials, namely SH: Hulthén type and WS: Woods–Saxon type potentials, each having a spin-orbit coupling term is chosen for the $\mathrm{\Lambda }$-nucleus pair while three-range Gaussian (TRG) Nijmegen hardcore and softcore potential models are chosen for $\mathrm{\Lambda }\mathrm{\Lambda }$ pair. The resulting few-body (two- and three-body) Schrödinger equations are solved numerically to get the bound state energies and wavefunctions. For the three-body calculation, we used hyperspherical coordinates. The formalism of supersymmetric quantum mechanics is applied to construct a one-parameter family of isospectral potential to investigate the resonance states of the $\mathrm{\Lambda }{+}^{60}$Ca (${=}_{\mathrm{\Lambda }}^{61}$Ca) core-$\mathrm{\Lambda }$ two-body system. To study the effect of replacement of the outer core valence nucleon(s) of ${}^{62}$Ca by $\mathrm{\Lambda }$ hyperon(s), two- and three-body cluster model calculations for the bound states of ${}^{61}$Ca and ${}^{62}$Ca are also carried out using the same set of two-body potentials, as used for ${}_{\mathrm{\Lambda }}^{61}$Ca and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{62}$Ca respectively. And a clear enhancement in the one- and two-$\mathrm{\Lambda }$ separation energies and a shrinking of the overall size of the nucleus is indicated. The computed results are compared with some of those found in the literature.

Higher-order approximation based on Taylor expansion over the saddle point is employed to approach the partition function of a hot nucleus in the presence of the like-particle pairing correlations. Analytical expressions have been derived for the correction terms of different thermodynamic quantities such as energy, entropy and heat capacity. Furthermore, the theory has been applied to the schematic and realistic models. It is found that the correction terms are temperature-dependent functions and are more deeply sensitive to the pairing gap in the vicinity of the critical temperature.

The elastic scattering angular distributions and the fusion excitation function data for the reactions induced by the loosely bound projectile ⁹Be on ${}^{27}$Al, ${}^{28}$Si, ${}^{144}$Sm and ${}^{208}$Pb targets at near and above barrier energies have been analyzed with a motive to investigate the importance of breakup couplings within the framework of continuum discretized coupled channels approach. It is found that at energies much higher than Coulomb barrier, the breakup effects are insignificant for light targets while for heavy targets, the breakup effects play a dominant role at these energies. But at energies comparable to the barrier height, the role of breakup becomes crucial for light mass targets also.

Recently, from the study of the absolute $B(E2)$ values for the ($\gamma$–$g$) $E$2 transitions, the different roles of the triaxiality parameter $\gamma =(0^{\circ }\text{–}20^{\circ })$ and $\gamma =(20^{\circ }\text{–}30^{\circ })$ parts were pointed out. Here, the use of the triaxial rotor model expressions for the $B(E$2)s in producing the bell-shaped curve of $B(E2,2_{\gamma }-0_1^{+})$ is illustrated. The variation of certain ($\gamma$–$g$) $B(E2)$ ratios versus $\gamma$ for the states $2_{\gamma }$ and $3_{\gamma }$ are illustrated, reflecting the two regions of $\gamma$. The inter relation of the $\gamma$ and $\beta$ variables is illustrated for the Os isotopes.