abstract

We report on the variation in the \(^{64}\)Ge\((p,\gamma )^{65}\)As reaction rates due to uncertainties of either nuclear mass and level structure of the \(^{65}\)As isotope or non-resonant reaction rates. The change in the reaction rates is from a few factors to one order of magnitude due to the uncertainty of the non-resonant rates, which were calculated using the astrophysical S-factor and the statistical Hauser–Feshbach model. The mass uncertainty of the \(^{65}\)As nucleus (\(\Delta {m} = 85\) keV) results in a variation of a few factors in the reaction rates at \(T_9 = 1\). At present, the estimated effective lifetimes of \(^{64}\)Ge in the rp-process are ranging from 0.5 to 162 ms. The results indicate that the resonance at \(E_x = 1.155\) MeV and the \(Q\)-value of the reaction must be precisely determined to improve the accuracy of rp-process simulations.

abstract

Using a simple equation of state for the quark–gluon plasma (QGP), we expand the hydrodynamic equations around equilibrium configurations. The resulting differential equations describe the propagation of perturbations in the energy density. We derive in detail the nonlinear Schrödinger equation (NLSE) which governs the modulation instability (MI) in the cold quark–gluon plasma.

abstract

The Mathisson–Papapetrou equations are used for investigations of influence of the spin-gravity coupling on a highly relativistic spinning particle in Schwarzschild’s field. It is established that interaction of the particle spin with the gravitomagnetic components of the field, estimated in the proper frame of the particle, causes the large acceleration of the spinning particle relative to geodesic free fall. As a result, the accelerated charged spinning particle can generate intensive electromagnetic radiation when its velocity is highly relativistic. The significant contribution of the highly relativistic spin-gravity coupling to the energy of the spinning particle is analyzed.

abstract

In the present study, we examine Casimir effects of the charged massless scalar field in 1+1 dimensions in the external background potential which includes linear and non-linear electrostatic fields. We calculate the Casimir energy for Dirichlet, Neumann, and mixed boundary conditions using the perturbation theory. We find that the Casimir energy is strengthened in the Neumann boundary condition and is lowered in other cases.

abstract

We show that the connection used by Bordemann, Neumaier and Waldmann to construct the Fedosov standard ordered star product on the cotangent bundle of a Riemannian manifold is obtained by symplectification of the complete lift of the corresponding Levi-Civitá connection, in the sense of Yano and Patterson. In terms of local coordinates, this was already shown earlier by Plebański, Przanowski and Turrubiates. In the final part, we comment on the usefulness of this connection in the context of homological reduction of deformation quantized models.