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Nuclei Shell Energy

  1. Nov 6, 2008 #1
    In the nuclei Shell Model I understand the nomenclature for the shell sequence but I don’t know how to calculate the respective energy levels for each shell.

    For example how do you calculate the energy level for
    1g(7/2) or 3d(5/2)

    Pointing me to an online reference will also be helpful. However, I have not learned bra-kets or Hamiltonian math yet.
  2. jcsd
  3. Nov 6, 2008 #2


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    what is Hamiltonian math? :-p

    The energy levels are different for different nuclei, you first take an approriate form of the central potential (V_c), e.g Wood Saxon.

    Then you that the potential includes an [tex]\vec{l}\cdot \vec{s}[/tex] term (spin-orbit coupling), your potential is thus:

    V(r) = V_c(r) + V_{ls} \vec{l}\cdot \vec{s}

    where, of course:

    [tex]V_{ls} = const. \dfrac{1}{r}\dfrac{\partial}{\partial r} [/tex]

    Then you take your nuclei, find the excited levels and their energies, fit to the parameters of the V_c and starts to solve the Schrödinger equation (nummerically), and thus you obtain all the energies.

    This is a VERY sketchy idea how to do it, Nuclear many body physics is quite complicated..
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