Group theoretical classification of states of a molecular system at definite states of its constituent parts

✍ Scribed by I. G. Kaplan; O. B. Rodimova

• Book ID: 104578867
• Publisher: John Wiley and Sons
• Year: 1976
• Tongue: English
• Weight: 768 KB
• Volume: 10
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560100412

✦ Synopsis

Abstract

A method is developed for determining the allowed states of a many‐particle system at definite states of the subsystems (impurity ion complexes in crystals, nucleon clusters in nuclei, polyatomic molecules). The advantage of the method proposed here over those previously developed is that the present one is independent of the number of particles in the subsystems. Depending on the value of spin S~a~ the subsystems are considered either as bosons or fermions. The representation character expression whose expansion gives all the terms ^2__s__+1^Γ^(α)^ with a definite value of total spin of the system is written as the product of permutation and orbital factors. The orbital factor is defined in terms of characters of the local point group representations. Some alternative ways of calculating the permutation factor are discussed: a) with the use of tables of reduction of the unitary transformation group U~2~S~a~+1 in a three‐dimensional rotation group; b) through the plethysm coefficients; and c) in terms of 3__n__j‐symbols of three‐dimensional rotation group. Some examples of application of the method to various systems are presented.