中文摘要：

本文较系统地简介了双原子分子振动能谱和离解能的研究历史、现状及若干研究方法，重点介绍了孙卫国等最近建立的研究双原子分子完全振动能谱的代数方法（AM）和计算双原子分子离解能的新物理公式。然后应用AM方法和离解能新公式对一批同核和异核双原子分子，以及双原子分子离子电子态的完全振动能谱和离解能进行了研究。结果表明，AM方法和新建立的离解能解析式相结合的理论方法对研究双原子分子及离子的完全振动能谱和离解能是行之有效的、简单经济的物理方法，为实验技术难以精确测量其高激发振动能级或离解能的双原子分子或离子体系提供了获得精确的完全振动能谱和体系离解能的一种理论新方法。

英文摘要：

A brief review on historical and current status and several research methods of vibrational energy spectra and molecular dissociation energies of diatomic molecular systems has been outlined. An algebraic method （AM） used to study the full vibrational energy spectra of diatomic systems, and a new analytical formula used to calculate accurate molecular dissociation energies are described. The AM method and the new formula are applied to study the full vibrational energy spectra and molecular dissociation energies of some electronic states of some homonuclear and heteronuclear diatomic molecules and some diatomic ions. Studies show that the AM method and the new analytical expression are reliable and economical physical methods for studying full vibrational energy spectra and molecular dissociation energies of diatomic electronic systems theoretically, which are particularly useful for those diatomic systems whose high-lying vibrational energies may not be available. dissociation energy; algebraic method