How do we compute the energy of the ground state using nuclear shell model?
But this is obviously not what the OP was asking.1) Excitations energy: The ground state has (per definition) energy 0, the excited states have a positive excitations energy
No, the Strutinsky shell correction is actually quite simple.2) Theoreticians calculate it from first principles, and they are more or less successful doing so. If your question is about theoretical calculations, you would have to dig into a good number of books.
The OP asked about how to calculate it using the shell model, not how to extract it from experimental data.3) Or do you want to know about the "Binding Energy"? if this is the case: here comes the explanation:
a nucleus consists of x protons and y neutrons. The mass of the nucleus is then:
M(nucleus) = x times M(proton) + y times M(neutron) - Q
where M(xxx) is the mass of the particle (usually expressed in MeV), and Q is the "Binding Energy". For example, the He4-nucleus consists of 2 protons and 2 neutrons,and has a Binding energy of ~28 MeV. Protons have a mass of 938.27 MeV and neutrons have a mass of 939.56 MeV. The mass of 4He is then: 2 * (938.27 + 939.56) - 28 = ~3727.6 MeV
(note: "MeV" is an energy unit. if one speaks about "mass" one should more correctly write "MeV/c^2")