International Journal of Modern Physics E

Cross-sections for ${}^{40}$Ca + $\alpha$ at low energies have been calculated from two different models and three different $\alpha$-nucleus potentials. The first model determines the cross-sections from the barrier transmission in a real nuclear potential. Second, cross-sections are derived within the optical model (OM) using a complex nuclear potential. The excitation functions from barrier transmission are smooth, whereas the excitation functions from the OM show a significant sensitivity to the chosen imaginary potential. Cross-sections far below the Coulomb barrier are lower from barrier transmission than from the OM. This difference is explained by additional absorption in the tail of the imaginary part of the potential in the OM. At higher energies, the calculations from the two models and all $\alpha$-nucleus potentials converge. Finally, in contradiction to another recent study where a double-folding potential failed in a WKB calculation, the applicability of double-folding potentials for ${}^{40}$Ca + $\alpha$ at low energies is clearly confirmed in the present analysis for the simple barrier transmission model and for the full OM calculation.

We systematically investigate the scaling property of mesons (pions and kaons) and baryons (protons, $\mathrm{\Lambda }$, $\mathrm{\Xi }$ and $\mathrm{\Omega }$) transverse momentum ($p_{\mathrm{\text{T}}}$) spectra at different centrality classes (0–5$\%$, 5–10$\%$, 10–20$\%$, 20–40$\%$, 40–60$\%$, 60–80$\%$ and 80–100$\%$) in proton-lead collisions with center of mass energy per nucleon pair 5.02TeV. In the low $p_{\mathrm{\text{T}}}$ region with $p_{\mathrm{\text{T}}}\le 3.9(3.1,2.5,2.7,2.4\mathrm{\text{and}}2.8)$GeV/c, a universal scaling independent of the centrality is observed in the pion (kaon, proton, $\mathrm{\Lambda }$, $\mathrm{\Xi }$ and $\mathrm{\Omega }$) spectra when a dilatation, $p_{\mathrm{\text{T}}}\to p_{\mathrm{\text{T}}}/K$, is applied. Here, $K$ is a scaling parameter depending on the centrality class. We find that the rates at which ln$K$ changes with the logarithmic value of the average value of the number of participating nucleons, ln$〈N_{\mathrm{\text{part}}}〉$, are stronger for baryons than those for mesons. In the high $p_{\mathrm{\text{T}}}$ region, there is a deviation from the scaling. The more peripheral the collisions are, the more obvious the violation of the scaling is. In the framework of the color string percolation (CSP) model, we show that mesons and baryons are generated from the decay of clusters formed by strings overlapping in the transverse plane with the same size dispersion but with different mean size. The mean size of clusters for baryons is smaller than that of mesons. For the same hadrons at different centrality classes, the mean size of clusters decreases with the increase of centrality. The fragmentation functions for cluster decay are different for different hadrons, while they are universal for the same hadrons at different centrality classes. The universal scaling of the meson and baryon spectra in the low $p_{\mathrm{\text{T}}}$ region can be quantitatively understood with the CSP model at the same time.

Applying the microscopic nuclear physics ideas for fusion reactions to macroscopic galactic systems, we study the evolution of the compact binary galaxy in mass asymmetry (transfer) coordinate. The conditions for the formation of stable symmetric binary galaxy are analyzed. The role of symmetrization of asymmetric binary galaxy in the transformation of gravitational energy into internal energy of galaxies accompanied by the release of a large amount of energy during the symmetrization process is revealed.

We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial relationships between the operator invariants, or equivalently, between eigenvalues of those invariants.

The magnetic moments of $\mathrm{\Lambda }$-hypernuclei are the most interesting observables which provide a highly sensitive probe of lambda in the hypernuclei structure and also supply direct information on hyperon–nucleon interactions. In this work, in a relativistic approach we analytically determine the magnetic moment of several $\mathrm{\Lambda }$-hypernuclei such as ${}_{\mathrm{\Lambda }}^{13}\mathrm{\text{C}}$, ${}_{\mathrm{\Lambda }}^{17}\mathrm{\text{O}}$ and ${}_{\mathrm{\Lambda }}^{41}\mathrm{\text{Ca}}$ in their ground and excited states, i.e., the $1s_{1/2}$, $1p_{3/2}$ and $1p_{1/2}$ states. For our analysis, we consider the central potential of Wood–Saxon and the spin-orbital potential and determine the wave function of hypernuclei. Then, we compute the Dirac, the anomalous and the total magnetic moments of the ground and excited states of $\mathrm{\Lambda }$-hypernuclei.

We generalize the Bogoliubov quark-meson coupling (QMC) model to also include hyperons. The hyperon-$\sigma$-meson couplings are fixed by the model and the hyperon-$\omega$-meson couplings are fitted to the hyperon potentials in symmetric nuclear matter. The present model predicts neutron stars with masses above 2$M_{\odot }$ and the radius of a 1.4$M_{\odot }$ star $\sim$14km. In the most massive stars, bags overlap at the core of the star, and this may be interpreted as a transition to deconfined quark matter.

The relativistic kinetic theory approach has been employed to estimate for a hot mixture constituting of nucleons and pions, four transport coefficients that characterize heat flow and diffusion. Medium effects on the cross-section for binary collisions ($\pi \pi ,\pi N$) have been taken into consideration by incorporating self-energy corrections to modify the $\rho$ and $\sigma$ meson propagators for $\pi \pi$ interaction and the $\mathrm{\Delta }$ propagator for $\pi N$ interaction. The temperature dependence of the various coefficients has been studied for several values of the baryon chemical potential.

We show some interesting properties of tridiagonal and pentadiagonal matrices in the weak coupling limits. In the former case of this limit, the ground state wave function amplitudes are identical to the Taylor expansion coefficients of the exponential function e${}^{(-\frac{v}{e})}$. With regards to transition rates, a dip in the pentadiagonal case which is not present in the tridiagonal case is explained. An intimate connection between energy denominators and exponential behavior is demonstrated.