Nuclear Shell Model
I am a PhD Chemist currently self-studying some nuclear physics, but am finding myself a bit confused on some notation in the nuclear shell model. Particularly the spectroscopic notation for the subshells.
I understand arriving at the combinations of quantum numbers as follows:
>1st shell: 2 states (n = 0, j = 1/2).
>2nd shell: 6 states (n = 1, j = 1/2 or 3/2).
>3rd shell: 12 states (n = 2, j = 1/2, 3/2 or 5/2).
>4th shell: 8 states (n = 3, j = 7/2).
>5th shell: 22 states (n = 3, j = 1/2, 3/2 or 5/2; n = 4, j = 9/2).
>6th shell: 32 states (n = 4, j = 1/2, 3/2, 5/2 or 7/2; n = 5, j = 11/2).
>7th shell: 44 states (n = 5, j = 1/2, 3/2, 5/2, 7/2 or 9/2; n = 6, j = 13/2).
>8th shell: 58 states (n = 6, j = 1/2, 3/2, 5/2, 7/2, 9/2 or 11/2; n = 7, j = 15/2).
I also understand the relationship between j and l.
But when it comes to the spectroscopic notation, I am finding that the notation is nlj.
That value n definitely doesn't correspond to the quantum number n above and I am not finding anything on how to arrive at this different value of n.
I have figured out a pattern that seems to work as far as I can tell where this value for this spectroscopic notation value is that it seems to = 1+(n-l)/2.
I found something that indicated it could be related to radial nodes, which seems to go along with the whole n-l situation. But, I am not quite able to explain to myself why that pattern is working.