The use of Three Simple Related Procedures in Determining the Russell-Saunders Terms of Equivalent Electrons

It is difficult to make advances in well-developed traditional fields and as a result such research is often neglected. However, this does not mean that reinterpretations or indeed discoveries in these fields are less important than in novel research subjects. Three novel procedures to determine the Russell-Saunders terms were developed from the spin partitioning approach and the direct microstate product representation. While these procedures are similar to literature methods, they have different origins and resulting formats. In addition these three methods were previously reported independently and as a consequence no connections were recognized. However, our new procedures have reinterpreted these methods using the concept of the direct product of the representations of microstates and as a consequence have unified them into a coherent system. A significant innovation is that this allows the most logical features of these three methods to be combined to create a self-consistent technique. The first two methods simply involve the creation of tables with “multiplication” of microstates, but the third method simplifies the process further by decomposing the direct product representation into a direct sum of irreducible representations and at the same time eliminates the need for tables. A key feature of all three procedures is that they automatically rule out all the unwanted microstates of equivalent electrons.