_Andreas
Apr6-07, 03:22 PM
1. The problem statement, all variables and given/known data
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.
2. Relevant 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.
3. 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?
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.
2. Relevant 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.
3. 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?