What is the expression for the single-particle energy of an orbital of a nucleus? Consider the level $p_{3/2}$. In the case of atomic physics, we know the energy of the orbital is
$$E_{J=\frac{3}{2}}=\dfrac{a}{2}\left\{ J\left( J+1\right) -L\left( L+1\right) -S\left( S+1\right) \right\} \hbar ^{2}$$
But in nuclear physics, what is the expression for energy?
 A: The term "orbital" comes from the word "orbit", found in the original semi classical Bohr model. It describes the quantum mechanical space distribution for measuring  an electron at (x,y,z,t) for a given nucleus  given by the  probability distribution calculated with the wavefunction. Even for the simple hydrogen atom, the  energy of the state needs corrections not given by simple formulae because of the different approach of low L quantum number  electrons than higher L.
When it comes to quantum mechanical models of the nuclei, where the strong nuclear  force with the Coulomb force are involved,simple planetary models cannot  fit the observations of nuclear interactions. Complicated models become necessary . The word "orbital" in  nuclear models, as used in the Shell model

The nuclear shell model is partly analogous to the atomic shell model which describes the arrangement of electrons in an atom, in that a filled shell results in greater stability. When adding nucleons (protons or neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. ,,,


The shells for protons and neutrons are independent of each other. Therefore, "magic nuclei" exist in which one nucleon type or the other is at a magic number, and "doubly magic nuclei", where both are. Due to some variations in orbital filling, the upper magic numbers are 126 and, speculatively, 184 for neutrons but only 114 for protons, playing a role in the search for the so-called island of stability.

"Orbital" is used  in the sense of the organization being similar to the atomic organization, not mathematically. More on the shell model here.
Edit after closure:
It is true that the question has a misunderstanding due to ignorance. I took the trouble to answer it because it seemed to me that the misunderstanding might be common and the answer would be useful in searches, for other people with the same misunderstanding. But closed questions are not open to searches, so if you think on these lines, please vote to reopen. I will delete this edit if the question is reopened.
