Speaker
Description
Based on our previous work of Fu et al.\,(2020), we derive the rest seven scattering-state ($\chi^{(0)}, \phi^{(1)}, \chi^{(1)}, \phi^{(2)}$, $\chi^{(2)},\phi^{(3)}$ and $\chi^{(3)}$) solutions to the Dirac equation when $E=-im \pm ik \approx -im$, and establish a relation between differential scattering cross-section, $\sigma_{i*} (p,\theta,\varphi)$, and stellar matter density, $\mu$, using the long-wave approximation. It is found that the sensitivity of average scattering cross-sections $\bar{\sigma}_{i}(p,\theta)$ to the change
in $\mu$ is proportional to $\mu^{2}$. We find that the average scattering amplitudes $\bar{f}_{i}(p,\theta)$, as well as average scattering cross-sections $\bar{\sigma}_{i}(p,\theta)$, are independent of the mass of particles, $m$, for four scattering-states\,$\chi^{(i)}$, $i$=0,1, 2 and 3, while $\bar{f}_{i}(p,\theta)$ and $\bar{\sigma}_{i*}(p,\theta)$ depend on $m$, for the rest four scattering states,$\phi^{(i)}$, $i$=0,1, 2 and 3.
This work will be useful in understanding the properties of anti-Dirac spinors and the physical effects in a rotating spheroid.
