Do you know if the concept of chemical potential can be properly defined for nucleons in the nuclei? I mean, if I can picture the nuclei like an interacting gas of nucleons, then may I think of a chemical potential for nucleons, similarly to the case of an electron liquid. Of course the nature of the interactions is different for the two cases. My idea is related to the liquid drop model of nuclei.
Yes it has been defined in a coherent way and used many times. You are following a correct reasoning: once you treat a nucleus as an ensemble of nucleons is natural to associate the chemical potential as the energy involved in adding/removing a nucleon from the nucleus. This is generally the case for excitation energies higher than 1 MeV/A when the shell structure is lost A.V. Ignatiuk, Phys. Lett. B 76 (1978) 543.
You will find the use of this concept very often in nuclear astrophysics models of stars where an average description of nuclear behaviour is both relevant useful. The description of the competing processes of absorbing nucleons and releasing them and beta decay is usually described in terms of the behaviour of chemical potential for nucleons in these conditions (ArXiv1,ArXiv2)