Spectroscopic terms arising from a given electronic configuration

3 Spectroscopic terms arising from a given electronic configuration 

We are now in position to derive the electronic states arising from a given electronic configuration. These states have many names spectroscopic terms (or states), term symbols, and Russell-Saunders terms, in honor of spectroscopists H. N. Russell and F. A. Saunders. Hence, the scheme we use to derive these states is called Russell-Saunders coupling. It is also simply referred to as L-S coupling. 

Each electronic state is defined by three angular momenta total orbital angular momentum vector L, total spin angular momentum vector S, and total angular momentum vector J. These vectors have the following definitions  

In eqs. (2.3.4) and (2.3.5), , and s, are the orbital angular momentum vector and spin angular momentum vector of an individual electron, respectively. For a state defined by quantum numbers L, 5, and J, the magnitudes of the total orbital angular momentum, total spin angular momentum, and total angular momentum vectors of the system are [L(L + 1)]1/2, [5(5 + 1)]1/2, and [J(J + 1)]1/2 a.u., respectively. 

Furthermore, each state is labeled by its L value according to  

---