# Degeneracy of multiple electron states

1. Jun 2, 2007

### Ahmes

1. The problem statement, all variables and given/known data
A seemingly trivial part of a Homework I've gotten is to find the degeneracy of the ${}^1\! S_0, {}^1\! D_2, {}^3\! P_2, {}^3\! P_1, {}^3\! P_0$ in an $O^{++}$ ion.

2. Relevant equations

3. The attempt at a solution
an $O^{++}$ ion has 4 valance electrons and when $\ell=1$ for example, there are 2x2x2x2x3=48 states all together. I know how to add angular momenta, and technically can add all electrons and the orbital one by one, finding explicitly the states with their Clebsch-Gordan-like coefficients. The thing is that it would take about a week, and I have the feeling that if I just want to find the degeneracy (and not necessarily the states) then it would be much easier.

Any help will be appreciated!