解束缚电子占据概率方程组的多时标微扰论数值方法

本文利用多时标微扰论,对束缚电子占据概率方程组提出一种数值解法。它适用于高Z介质的低能级电子状态的计算。在适当的物理假设下,方法将P_n满足的刚性常微分方程组变为n_e和P_n满足的微分代数方程组。文中给出了计算公式和数值试验并与Gear方法作了比较。

THE NUMERICAL METHOD FOR SOLVING THE RATE EQUATIONS OF ELECTRON'S AVERAGE OCCUPATION PROBABILITIES BY USING MULTIPLE-TIME-SCALE PERTURBATION THEORY

This paper presents the numerical method for solving the rate equations of electron's average occupation probabilities by using multiple-time-scale perturbation theory.It is especially suitable for lower levels of elements, Since in that case the transition between neighbouring bound energy levels could be considered as fast, the others as slow. Under some reasonable physical assumptions the method leads to the analytic expressions for P_n as functions of the number of free electron, n_s.As a result, in stead of solvingstrong stitff ordinary ditferential equations of (dp_n)/(dt), we just need solving thedifferential equation for n_e and the algebraical equations for P_n. Therefore the problem is much simplified with avoiding the computation of Jacobi iaverse matrix which generally appears is the implicit schemes.