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- Title
Dirac spinor scattering states with positive‐energy in rotating spheroid models.
- Authors
Gao, Zhi‐Fu; Chen, Ci‐Xing; Wang, Na; Zhao, Xin‐Jun; Wang, Zhao‐Jun
- Abstract
There are many rotating spheroids in the universe, and many astronomers and physicists have used theoretical methods to study the characteristics of stellar gravity since Newton's time. This paper derives the solutions of eight scattering states (ϕ(0),χ(0),ϕ(1),χ(1),ϕ(2)$$ \Big({\phi}^{(0)},{\chi}^{(0)},{\phi}^{(1)},{\chi}^{(1)},{\phi}^{(2)} $$,χ(2),ϕ(3)$$ {\chi}^{(2)},{\phi}^{(3)} $$, andχ(3))$$ {\chi}^{(3)}\Big) $$ for the Dirac equation with positive‐energy E=im$$ E= im $$, and establishes the relationship between the differential scattering cross section σi(p,θ,φ)$$ {\sigma}_i\left(p,\theta, \varphi \right) $$ and the stellar density μ$$ \mu $$. It is found that: (1) For the eight scattering states, their average scattering cross‐sections σi‾$$ \overline{\sigma_i} $$ are proportional to μ2$$ {\mu}^2 $$, and depend on the star's radius, and the higher the stellar density μ$$ \mu $$, the greater the sensitivity of σi‾$$ \overline{\sigma i} $$ to the change of μ$$ \mu $$; (2) For the four scattering states χ(i),i=0,1,2,3$$ {\chi}^{(i)},i=0,1,2,3 $$, their average scattering amplitudes f‾(p,θ)$$ \overline{f}\left(p,\theta \right) $$ and σ‾(p,θ)$$ \overline{\sigma}\left(p,\theta \right) $$ depend on the mass m$$ m $$ of the particles; while for the other four scattering states ϕ(i)$$ {\phi}^{(i)} $$, i=0,1,2,3$$ i=0,1,2,3 $$, then f‾$$ \overline{f} $$ and σ‾$$ \overline{\sigma} $$ are independent of m$$ m $$. This study links the gravitational characteristics of stars with the scattering cross section, creating a new method for studying the gravitational characteristics, which helps to reveal the mystery of the gravity of rotating ellipsoidal stars.
- Subjects
DIRAC equation; DIFFERENTIAL cross sections; QUANTUM field theory; SCATTERING amplitude (Physics); STARS; PHYSICISTS
- Publication
Astronomische Nachrichten, 2024, Vol 345, Issue 2/3, p1
- ISSN
0004-6337
- Publication type
Article
- DOI
10.1002/asna.20240012