What is the Shell Model Interpretation of Low-Lying Levels of C-13?

[_Andreas]

Homework Statement

The low-lying levels of C-13 are ground state, \frac{1^-}{2}; 3,09 MeV, \frac{1^+}{2}; 3,68 MeV, \frac{3^-}{2}; 3,85 MeV, \frac{5^+}{2}. Interpret these four states according to the shell model.

Homework Equations

Negative parity --> \ell = odd; the valence nucleon must occupy a level with the spectroscopic symbol p, f, h etc.
Positive parity --> \ell = even; the valence nucleon must occupy a level with the spectr. symbol s, d, g etc.

The Attempt at a Solution

In the ground state, the 7th neutron must be in the 1p_{\frac{1}{2}} level. All levels below are filled.

In the first excited state, that is, the \frac{1^+}{2} state, I think the 7th neutron is excited from the 1p_{\frac{1}{2}} level to the 2s_{\frac{1}{2}} level. The remaining neutrons occupy the same levels as in the ground state.

In the \frac{3^-}{2} state, one of the two pairs in the 1p_{\frac{3}{2}} level is broken, and a neutron is excited to the 1p_{\frac{1}{2}} level, where it forms a pair with the former valence neutron. The remaining neutrons occupy the same levels as in the ground state.In the \frac{5^+}{2} state, the single neutron in the 1p_{\frac{1}{2}} level is excited to the 1d_{\frac{5}{2}} level. The remaining neutrons occupy the same levels as in the ground state.

Is this correct? Do I seem to understand the shell-model somewhat?

 

[_Andreas]

Here is a website showing all the possible levels, if that can be of any help: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html

(BTW, the thread title should be "NucleAR shell-model problem". Sorry.)

 

[stunner5000pt]

looks good to me
p.s. this is new to me too

 

[_Andreas]

I hope we're right then. :)