根据热平衡状态下的麦克斯韦速度分布函数,得到了三维空间中两原子间相对运动速度的分布函数。以四能级理论模型为基础,将此分布函数考虑到激光感生碰撞截面的计算之中,直接积分态振幅的运动方程,对弱场和强场两种情况下Eu-Sr系统中的一个激光感生碰撞过程进行了数值计算,得到了特定温度下系统的激光感生碰撞截面的谱线线型。将该数值计算的结果与以前的理论工作进行了比较,分析了两原子间相对运动速度分布对激光感生碰撞过程的影响。分析表明,两原子之间相对运动速度的统计分布虽然不影响激光感生碰撞截面的谱线线型,但对碰撞截面的峰值大小有一定的影响。结论与前人的理论预言相吻合,证明了数值计算的正确性。

The distribution function of relative velocity between two colliding atoms in three-dimensional space is obtained based on Maxwell velocity distribution function under thermal equilibrium condition. Considering this distribution function in the computation of laser-induced collision cross section, one laser-induced collisional energy transfer (LICET) process in Eu-Sr system both in weak and strong field is numerically calculated by integrating the motion equation based on the four-level model, and profiles of laser-induced collision cross section at given temperature are obtained. Impacts of relative velocity distribution on laser-induced collision process are analyzed by comparing the presenting numerical results with the former theoretical research. It is shown that although statistical distribution of relative velocity between two atoms has no impacts on the line shape of LICET spectrum, it has certain impacts on the peak value of collision cross section. The conclusions we came to in this paper are consistent with the theoretical predictions of former investigation, showing the validity of our numerical calculations.