In this paper, by using a perturbation theory, we evaluate the scattering solution to Schrödinger equation under the Newtonian gravitational potential. We find that the scattering amplitude f(θ) depends on the potential U, which is composed of the external part U_ex and the internal part U_in, respectively. The above results are related to the mass density of a rotating Maclaurin spheroid. In the future, we will further analyze the sensitivity of scattering amplitude to the change of average mass density of the spheroid.

中文翻译：

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牛顿近似中标量场的散射

在本文中，我们利用微扰理论，评估了牛顿引力下Schrödinger方程的散射解。我们发现散射幅度f（θ）取决于电势U，电势U分别由外部U _ex和内部U _in组成。以上结果与旋转的Maclaurin球体的质量密度有关。将来，我们将进一步分析散射幅度对球体平均质量密度变化的敏感性。