分子振转模型中的群理论

分子振转模型中的群理论 GROUP THEORY OF VIBRON MODEL OF MOLECULES 胡承正 Hu Chengzheng 1 first-author Deqartment of puysics Wuhan University Deqartment of puysics Wuhan University Deqartment of puysics, Wuhan University Deqartment of puysics, Wuhan University 本文利用玻色子产生和湮没算符给出了描写双原子分子振动-转动谱的动力学群U（4）及其子群的结构;确定了各个子群的Casimir算子表示式;证明了在最多只考虑二体项作用时系统的哈密顿量可以用这些群的Casimir算子表示,从而对显示两种不同群链所代表的对称性的双原子分子得到和Iachello所给出的结果一致的振动-转动能级公式;最后利用这种代数方法计算了CaO分子A′∑—X′∑跃迁的几个振动谱带,得到的值与实验值一致。这表明CaO分子振动谱结构显示O（4）对称性。 Recently F. Iachello extended IBM method to the study of vibration-rota-tion spectra of molecules. In this paper the spectrum generating group appro priate to diatomic molecules and its subgroups are further examined in terms of four specific creation （annihilation） operators which are composed of one scalar operator σ + （σ）and three components of a vector operator π μ + （π μ ）（μ=0, ±1）, The explicit forms of the Casimir operators of the subgroups U（3）, O（4）and O（3） are obtained, It has been shown that the most general Hamilto-nian consisting at most of mutual action of two bodies can be expressed in terms of those Casimir operators, Two kinds of subgroup chains corresponding to different dynamical symmetry of diatomic molecules are discussed, The re-sults thus obtained are in agreement with F, Iaehello′s works, Finally, the vi-brational bands of the A′∑-X′∑ transition of CaO have been calculated by using algebraic techniques, The calculated values are in agreement with the experimental. U（4）群 各子群的Casimir算子 哈密顿量 振动-转动能级公式 U（4）groap Casimir operators of the subgroups Hamiltonian formula of vibration rotation spectra 1988-04-01 2021-04-01 4