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Energy Levels in Nuclei

The discrete energy states that nucleons occupy within the nucleus, determined by quantum mechanical principles and nuclear forces.
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The statement of the theorem

Consider the Hamiltonian H^\hat{H} for a system of AA nucleons confined within a volume VV. The allowed energy levels EkE_{k} are determined by solving the time-independent Schrödinger equation for the many-body system: \nH^Ψk(r1,…,rA)=EkΨk(r1,…,rA)\hat{H} \Psi_{k}(\mathbf{r}_1, \dots, \mathbf{r}_A) = E_{k} \Psi_{k}(\mathbf{r}_1, \dots, \mathbf{r}_A) \nIn the independent particle model, the single-particle Hamiltonian h^\hat{h} is used, leading to the eigenvalue problem: \n(−ℏ22m∇2+V(r))ψnlj(r,θ,ϕ)=Enljψnlj(r,θ,ϕ)\left( \frac{-\hbar^2}{2m} \nabla^2 + V(r) \right) \psi_{n l j}(r, \theta, \phi) = E_{n l j} \psi_{n l j}(r, \theta, \phi) \nwhere EnljE_{n l j} are the discrete energy levels.