Nuclear Shell Model, how to develop a shell-model code

Shell-model project

Another, slightly more challenging space is the \( (1/2)^4 \) space, that is, with eight single-particle states we have

Index	\( n \)	\( l \)	\( s \)	\( m_s \)
1	0	0	1/2	-1/2
2	0	0	1/2	1/2
3	1	0	1/2	-1/2
4	1	0	1/2	1/2
5	2	0	1/2	-1/2
6	2	0	1/2	1/2
7	3	0	1/2	-1/2
8	3	0	1/2	1/2

For \( N=2 \) there are 16 states with \( M=0 \); for \( N=3 \) there are 24 states with \( M=1/2 \), and for \( N=4 \) there are 36 states with \( M=0 \).