Single-particle and two-particle quantum numbers

Consider now the single-particle orbits of the \( 1s0d \) shell. For a \( 0d \) state we have the quantum numbers \( l=2 \), \( m_l=-2,-1,0,1,2 \), \( s+1/2 \), \( m_s=\pm 1/2 \), \( n=0 \) (the number of nodes of the wave function). This means that we have positive parity and $$ j=\frac{3}{2}=l-s\hspace{1cm} m_j=-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2}. $$ and $$ j=\frac{5}{2}=l+s\hspace{1cm} m_j=-\frac{5}{2},-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2}. $$