Each single-particle state is labeled by the following quantum numbers:

• Orbital angular momentum \( l \)
• Intrinsic spin \( s \) = 1/2 for protons and neutrons
• Angular momentum \( j = l \pm 1/2 \)
• \( z \)-component \( j_z \) (or \( m \))
• Some labeling of the radial wavefunction, typically \( n \) the number of nodes in the radial wavefunction, but in the case of harmonic oscillator one can also use the principal quantum number \( N \), where the harmonic oscillator energy is \( (N+3/2)\hbar \omega \).

In this format one labels states by \( n(l)_j \), with \( (l) \) replaced by a letter: \( s \) for \( l=0 \), \( p \) for \( l=1 \), \( d \) for \( l=2 \), \( f \) for \( l=3 \), and thenceforth alphabetical.