Comparison between different proximity potentials and the double-folding model for spherical–deformed interacting nuclei

The Coulomb barrier parameters have been calculated for a spherical–deformed interacting pair of nuclei using 14 different versions of the proximity approaches and a simple analytical formula for the Coulomb part of the heavy ion potential. The results of these proximity versions have been compared with more accurate results obtained from the double-folding model (DFM). We have considered the interacting pair 48Ca + 238Pu as an example and assumed the presence of the quadrupole, octupole, and hexadecapole deformation parameters for 238Pu. The orientation angle dependence of the Coulomb barrier parameters has been computed for different sets of deformation parameters. We found that the proximity types named Prox77, BW Prox91, AW Prox95, Bass Prox77, and Bass Prox80 are the best ones of the available 14 versions of the proximity approaches for calculating the nuclear part of the interaction potential for a spherical–deformed pair of nuclei.

Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior

We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant [Formula: see text]. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localized energy density is integrable in time. For the unchanged part, we study both the full Maxwell equation and the Fackerell–Ipser equation for one component. To treat the Fackerell–Ipser equation, we use a Fourier transform in [Formula: see text]. For the Fackerell–Ipser equation, we prove a refined Morawetz estimate that controls 3/2 derivatives with no loss near the orbiting null geodesics.

EXACT SOLUTION OF THE DIRAC EQUATION FOR A SINGULAR CENTRAL POWER POTENTIAL

We compute an exact solution of the Dirac equation for a certain power law potential that consists of two parts: a scalar and a vector, where the latter contains a Coulomb term. We obtain energies that turn out to depend only on the strength of the Coulomb part of the potential, but not on the remaining power law part. We show that our ansatz also yields a bound state solution for the lowest excited state. This work is an extension of Franklins result.7

Über die Ladungsträgererzeugung in Lösungen, die Stickstoff-Heterocyclen enthalten

In preceeding papers a model for the generation of charge carriers in organic liquids was developed. The activation energy of the dc-conductivity specific for one compound was said to be the sum of a resonance and a COULOMB part: E1 = E+½3 ET (the factor ½ is due to bimolecular recombination) . Measurements with aza-compounds show that E1 is decreasing linearily with increasing calculated π-electron-density at the N-atom. This fact argues for electrons to be the majority chargecarriers. E′ is the energy necessary to localize one electron at the N-atom for a short time, ET is the further separation-energy. With charge-transfer-complexes formed by acridine with aromatic hydrocarbons, E′ increases proportional to the electron-affinity of the hydrocarbons. For energetic reasons it can be assumed that the separated electron moves as a solvatised one through the liquid. An extrapolation shows that the proposed model holds for unsubstituted aromatic hydrocarbons too, but not for aliphatic ones. This is confirmed by experiments. Furthermore, arguments will be developed to distinguish between the conductivity specific for one compound and the conductivity due to impurities. In certain cases the impurity concentration can be estimated from the σ(1/T) curve.