中文摘要：

半解析求解平均原子模型方法充分利用了已知精确波函数的解析性质，通过对平均原子模型中势函数的数值拟合，就得到仅含一个数值因子的半解析波函数以及相应的能量本征值．本文列出了等离子体中相对论性平均原子模型的诸方程，特别注意方程求解技术和程序设计中的一些细节．与完全数值解以及其他类似模型得到的数值解进行的比较表明，在较高温度条件下半解析结果的精度是相当高的，求解的效率也很高．此外还对物理模型中某些缺陷进行了分析．

英文摘要：

The semi-analytical method is utilized for solving a relativistic average atom model for high-temperature plasmas. Semi-analytical wave function and the corresponding energy eigenvalue, containing only a numerical factor, are obtained by fitting the potential function in the average atom into hydrogen-like one. The full equations for the model are enumerated, and more attentions are paid upon the detailed procedures including the numerical techniques and computer code design. When the temperature of plasmas is comparatively high, the semi-analytical results agree quite well with those obtained by using a full numerical method for the same model and with those calculated by just a little different physical models, and the result＇ s accuracy and computation efficiency are worthy of note. The drawbacks for this model are also analyzed.