氢原子Rydberg态抗磁谱的高阶B-spline基组计算

Calculation of diamagnetic spectrum of Rydberg hydrogen atom using B-spline basis sets

在球坐标下采用基组展开方法计算了均匀磁场中的氢原子高Rydberg态能谱和振子强度谱.径向和角向均采用高阶B样条基组.径向采用B样条基组能很好地描述束缚态与连续态的耦合;角向采用B样条基组有效地减少了基组维数,计算效率得到大幅度提高.用上述方法计算了磁场中氢原子Rydberg态-40cm-1到零场电离阈的高精度抗磁谱并与已有理论和实验结果作了比较.该方法适用于低于离化阈的所有能区的精确谱计算并易于推广到非氢原子、交叉场中的原子以及高于离化阈的正能区光谱的计算.

The energy spectrum and oscillator strength of hydrogen atom in static magnetic field have been calculated using basis set method. Both the radial and angular wave-functions are expanded in terms of B-spline functions. The resultant size of Hamiltonian matrix is reduced considerably, which enables the calculations to be carried out in personal computer. Diamagnetic spectrum of Rydberg hydrogen atom from - 40cm^- 1 to the field free ionization threshold was obtained with high accuracy. The results have been compared with those of most accurate ones in the literature. The method presented in this paper can be extended easily to the region with positive energy and to the cases of non-hydrogen atoms and the crossed field problem.