Scattering‐state solutions to the Dirac spinors with negative‐energy eigenstates in a rotating spheroid

Abstract

AbstractBased on the work of Fu et al. (2020), we derive the rest seven scattering‐state solutions to the Dirac equation when and establish a relation between differential scattering cross‐section, , and stellar matter density, , using the long‐wave approximation. It is found that the sensitivity of average scattering cross‐sections to the change in the stellar matter density is proportional to . We find that the average scattering amplitudes , as well as average scattering cross‐sections , are independent of the masses of particles, , for four scattering states , i = 0, 1, 2 and 3, while and depend on , for the rest four scattering states, , i = 0, 1, 2 and 3. By measuring the scattering cross‐section, we can determine the density of the ellipsoid and obtain its gravitational properties. This work will be useful in understanding the properties of anti‐Dirac spinors and the physical effects in a rotating spheroid.