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首页> 外文期刊>Journal of Experimental and Theoretical Physics >Exact nonrelativistic expressions for the tensor for scattering of light by atoms
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Exact nonrelativistic expressions for the tensor for scattering of light by atoms

机译：张量用于原子散射光的精确非相对论表达式

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Exact nonrelativistic analytical expressions are derived for dipole two-photon transitions between arbitrary multiplets of the hydrogen atom and positive hydrogenlike ions. The result is expressed in terms of a single Gauss hypergeometric function and polynomials whose degrees increase linearly with the number of nodes of the bound states of the quantum system. The cross sections of elastic scattering of light by K- and L-shells of the hydrogen atom are given as an example. It is demonstrated that by expanding the discrete-spectrum wave functions in ultraspherical polynomials it is also possible to obtain analytical expressions of the cross sections of two-photon transitions between states described by the Simons model potential. The basis consisting of Chebyshev polynomials is shown to be the best expansion basis, and the coefficients of such an expansion are given for a broad range of parameters of the problem. Calculation of the polarizability of the 5S-state of the rubidium atom is chosen as an example. Finally, the results are compared with the experimental data and the theoretical results of other researchers.
机译：对于氢原子和正氢样离子的任意多重态之间的偶极两光子跃迁，得出了精确的非相对论的解析表达式。结果用单个高斯超几何函数和多项式表示，这些多项式的阶次随量子系统的束缚态结点的数量线性增加。作为例子，给出了通过氢原子的K-壳和L-壳的光的弹性散射的横截面。证明了通过在超球形多项式中扩展离散频谱波函数，也有可能获得西蒙斯模型势所描述的状态之间的两个光子跃迁的横截面的解析表达式。由切比雪夫多项式组成的基础被证明是最好的扩展基础，并且针对问题的广泛参数给出了这种扩展的系数。以chosen原子的5S态的极化率的计算为例。最后，将结果与其他研究人员的实验数据和理论结果进行比较。

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