Spectroscopic Notation

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 \bgroup\color{black}$N^{2s+1}L_j$\egroup, where \bgroup\color{black}$N$\egroup is the principal quantum number and will often be omitted, \bgroup\color{black}$s$\egroup is the total spin quantum number ( \bgroup\color{black}$(2s+1)$\egroup is the number of spin states), \bgroup\color{black}$L$\egroup refers to the orbital angular momentum quantum number \bgroup\color{black}$\ell$\egroup but is written as \bgroup\color{black}$S, P, D, F, \dots$\egroup for \bgroup\color{black}$\ell=0,1,2,3,\dots$\egroup, and \bgroup\color{black}$j$\egroup is the total angular momentum quantum number.

A quick example is the single electron states, as we find in Hydrogen. These are:

1\;^2S_{1\over 2}  2\;^2S_{1\over 2}  2\;^2P_{3\over 2} \...
...D_{3\over 2}  4\;^2F_{7\over 2}  4\;^2F_{5\over 2}  \dots

All of these have the pre-superscript 2 because they are all spin one-half. There are two \bgroup\color{black}$j$\egroup values for each \bgroup\color{black}$\ell$\egroup.

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