over spin meaning in English

上旋球

In the course of these derivation , the orbital integrations and the summations over spin are completed and are presented 3j , 6j , 9j symbols and the radial matrix elements . these derivations are strict and no approximate are introduced . the derivations for the orbit - orbit interaction , the spin - spin interaction and spin - other - orbit interaction , which are fairly complicated , have not been given in the previous literatures
这部分推导工作是严格的，没有引进任何近似，其中轨道-轨道相互作用、自旋-自旋相互作用和自旋-其它轨道相互作用能的理论计算式的推导过程比较复杂，在以前的文献中没有给出这些相互作用能的具体推导过程。
In a word , a new method that theoretically calculates the relativistic corrections and the fine structure of the energy levels in two - electron atom , including the atomic hamiltonian expressed by spherical tensors , the calculation of the angular matrix elements and the summations over spin of the various interactions in the atomic hamiltonian , and the approximate calculation of the radial matrix elements , has been provided in this thesis
总之，本文为双电子原子能级的相对论修正和精细结构的理论计算提供了一种新的方法，包括原子哈密顿算符的球张量表示方法、原子哈密顿中各种相互作用项的角向矩阵元和自旋求和的计算方法，以及径向矩阵元的近似计算方法