The scattering of Dirac spinors in rotating spheroids
The scattering of Dirac spinors in rotating spheroids
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旋转球体中狄拉克旋量的散射
DOI：
10.1140/epjc/s10052-020-8140-2
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发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Wang Na
中科院分区：
文献类型：
--
作者：
Gao Zhi Fu;Chen Ci Xing;Wang Na
宇宙中有很多恒星是旋转的椭球体，研究它们具有非常重要的意义。自牛顿时代以来，许多天文学家和物理学家通过考虑从欧拉流体动力学方程导出的力矩方程来研究恒星的引力特性。在本文中，我们研究了狄拉克方程旋量的散射，特别研究了旋转麦克劳林椭球体极限情况下的散射问题。首先给出旋转椭球星的度量，然后在该度量下写出狄拉克方程，最后推导狄拉克方程的散射解，并建立微分散射截面 和恒星物质密度 之间的关系。发现对变化的敏感性与密度成正比。由于引力场较弱且质量密度恒定，我们的结果是合理的。该结果可以应用于白矮星、主序星、红巨星、超巨星等，只要它们的引力场很弱，可以用牛顿近似来处理，并且假设流体是不可压缩的。请注意，我们将恒星的物质密度视为其平均密度，并且恒星并不被认为是致密的。显然我们的结果不能用于研究中子星和黑洞。特别是，我们的结果适用于白矮星，其平均密度约为–g cm，对应于约质量范围和约公里半径范围。
There are many stars that are rotating spheroids in the Universe, and studying them is of very important significance. Since the times of Newton, many astronomers and physicists have researched gravitational properties of stars by considering the moment equations derived from Eulerian hydrodynamic equations. In this paper we study the scattering of spinors of the Dirac equation, and in particular investigate the scattering issue in the limit case of rotating Maclaurin spheroids. Firstly we give the metric of a rotating ellipsoid star, then write the Dirac equation under this metric, and finally derive the scattering solution to the Dirac equation and establish a relation between differential scattering cross-section,, and stellar matter density,. It is found that the sensitivity ofto the change inis proportional to the density. Because of the weak gravitational field and the constant mass density, our results are reasonable. The results can be applied to white dwarfs, main sequence stars, red giants, supergiant stars and so on, as long as their gravitational fields are so weak that they can be treated in the Newtonan approximations, and the fluid is assumed to be incompressible. Notice that we take the star’s matter density to be its average density and the star is not taken to be compact. Obviously our results cannot be used to study neutron stars and black holes. In particular, our results are suitable for white dwarfs, which have average densities of about–g cm, corresponding to a range of mass of aboutand a range of radius of aboutkm.
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