Calculating Nuclei Shell Energy Levels: No Bra-Ket Math Needed

[bluestar]

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.

 

[malawi_glenn]

what is Hamiltonian math?

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 $$\vec{l}\cdot \vec{s}$$ term (spin-orbit coupling), your potential is thus:

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

where, of course:

$$V_{ls} = const. \dfrac{1}{r}\dfrac{\partial}{\partial r}$$

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..