系统研究氢原子Stark能谱的数值方法Ⅱ──准稳态及其线型

SYSTEMATIC NUMERICAL METHOD FOR STUDYING STARK SPECTRUM OF HYDROGEN ATOM -QUASI-STABLE STATE AND ITS PROFILE

本文通过标度变换，引入ｔ参量，将抛物坐标下分离变量后，稳定外电场下氢原子的Ｓｃｈｒｏｄｉｎｇｅｒ方程消除了耦合，大大地简化了计算。由“有效动能”曲线给出“准稳态”存在的判据。利用波函数渐近表达式的周期性性质，可求出任意ｍ值的氢原子能级随电场变化的解。本文以ｎ＝６时２１条Ｓｔａｒｋ分裂谱的Ｅ～Ｆ曲线为例，说明这种系统计算法的简便。最后通过连接出射波函数与其渐近形式，计算出散射振幅，分析了ＤＣＳｔａｒｋ能谱的非对称共振线形，并与有关实验及理论结果进行了比较。

Through scaling transformation of parameter t, the Schrodinger equations of hydrogen atom in DC electric field were decoupled in parabolic coordinate and the numerical calculation were dramatically simplified. The threshold for qusi-stable states is given by the effective kinetic energy. The DC stark energy of H of arbitary m and F can be obtained using the periodic property of the asymptotic expression of the wave function (WF). As an example, all the 21 stalk levels of n=6 stated are presented. The scattering amplitude is obtained by matching the out going WF and the asymptotic form, then the asymmetric DC stark profile can be achieved.