abstract

This study explores the elastic scattering of charged hadronic system through a new approximation scheme for the effective potential. The Phase Function Method (PFM) is employed to examine the scattering phase shifts in the \(p\)–He\(^{3}\) system, where a modified Kratzer potential is enhanced by electromagnetic interactions and spin–orbit coupling. A six-parameter potential model is developed and optimized to match the calculated scattering phase shifts, differential cross-sections, and proton analyzing power curves with experimental data for the \(p\)–He\(^{3}\) system. The results show strong consistency with experimental measurements and previous theoretical predictions, affirming the accuracy and utility of the proposed method in analyzing scattering phenomena within this system.

abstract

The evolution equation of the Szekeres metrics allows for solutions with the mass function \(M \lt 0\). They exist in both classes of the Szekeres metrics, have no Big Bang singularity and no origin. In both classes, the conditions for no shell crossings ensure that the mass density \(\rho \) of the dust source in the Einstein equations is negative at all times. Thus, these metrics do not qualify as cosmological models. In the Friedmann limit, the implication \(M \lt 0 \Longrightarrow \rho \lt 0\) is immediate. In the general Szekeres metrics, it follows by tuning conclusions from different equations.

abstract

A nonlinear Lorentz-invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy, and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian limit, but it is not given by the Jüttner distribution commonly employed in relativistic kinetic theory. The nonlinear kinetic diffusion equation on a general Lorentzian manifold is consistent with the contracted Bianchi identities and therefore can be coupled to the Einstein equations of general relativity.