Multiple Electrons Term Symbols and Russell-Saunders Coupling

5 Multiple Electrons Term Symbols and Russell-Saunders Coupling 

Understanding the momentum combinations of lone electrons in a subshell is straightforward. But what about the majority of atomic systems, neutral or ionized, that have more than one electron in the outermost subshell How do we understand all the possible ways the orbital and spin angular momenta of multiple electrons can interact  

If L is the quantum number indicating the vector sum of the orbital angular momentum of an electronic state, and S represents the vector sum of the spin angular momentum of the electronic state, and J represents the total angular momentum of the electronic state, then the term symbol would be constructed as 

Instead of using the numerical value for L, a letter label is used (just like the s,p, d,f. subshell designations stand for T = 0,1,2,3. in atoms). The following capital letters are used to indicate the value for L  

Such letters are commonly used to refer to various electronic states that is, one hears of S states, P states, and so on. The left superscript is not S but 2S -I- 1 (for 

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A term scheme is a representation of an energy level in an isolated many-electron atom, derived via the Russell-Saunders coupling scheme. In general, a term scheme is written as a collection of many-electron quantum numbers S and L. The value of S is not used directly but is replaced by the spin multiplicity, 2S +1. Similarly, the total angular momentum quantum number, L, is replaced by a letter symbol similar to that used for the single-electron quantum number 1. The term scheme is written States with a multiplicity of 1 are called singlet states, states with a multiplicity of 2 are called doublet states, those with a multiplicity of three are called triplets, those with a multiplicity 4 are called quartets and so on. Hence, S is called singlet S, and is called triplet P. 

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