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Nucleus shell-model problem

  1. Apr 6, 2007 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    Negative parity --> [tex]\ell[/tex] = odd; the valence nucleon must occupy a level with the spectroscopic symbol p, f, h etc.
    Positive parity --> [tex]\ell[/tex] = 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 [tex]1p_{\frac{1}{2}}[/tex] level. All levels below are filled.

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

    In the [tex]\frac{3^-}{2}[/tex] state, one of the two pairs in the [tex]1p_{\frac{3}{2}}[/tex] level is broken, and a neutron is excited to the [tex]1p_{\frac{1}{2}}[/tex] 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 [tex]\frac{5^+}{2}[/tex] state, the single neutron in the [tex]1p_{\frac{1}{2}}[/tex] level is excited to the [tex]1d_{\frac{5}{2}}[/tex] 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?
     
    Last edited: Apr 6, 2007
  2. jcsd
  3. Apr 6, 2007 #2
    Last edited: Apr 6, 2007
  4. Apr 6, 2007 #3
    looks good to me
    p.s. this is new to me too
     
    Last edited: Apr 6, 2007
  5. Apr 6, 2007 #4
    I hope we're right then. :)
     
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