A common way to name states in atomic physics is to use spectroscopic notation. It is essentially a standard way to write down the angular momementum quantum numbers of a state. The general form is , where is the principal quantum number and will often be omitted, is the total spin quantum number ( is the number of spin states), refers to the orbital angular momentum quantum number but is written as for , and is the total angular momentum quantum number.
A quick example is the single electron states, as we find in Hydrogen. These are:
For atoms with more than one electron, the total spin state has more possibilities and perhaps several ways to make a state with the same quantum numbers.
Jim Branson 2013-04-22