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 , \sigma , and stellar matter density , \mu .
It is found that the sensitivity of \sigma to the change in \mu is proportional to the density \mu .
Because of weak gravitational field and 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 can not be used to study neutron stars and black holes .
In particular , our results are suitable for white dwarfs , which have average densities of about 10 ^ { 5 } -10 ^ { 6 } g cm ^ { -3 } , corresponding to a range of mass of about 0.21 - 0.61 M _ { \bigodot } and a range of radius of about 6000 - 10000 km .