# Chemical potential for nucleons

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.

• Wouldn't a (useful) chemical potential imply that the number of nucleons isn't constant? – ACuriousMind Nov 13 '14 at 13:08
• like equation 2 here? helsinki.fi/~hkurkisu/cosmology/Cosmo7.pdf – DavePhD Nov 13 '14 at 15:28
• I think the answer is "yes", chemical potential can be defined for nucleons in the nuclei, see "For nuclear matter at low density and high temperature, the chemical potentials scale with density. The formation of nuclei breaks the scaling behavior, i.e., the bound nucleons have much smaller chemical potentials." in arxiv.org/pdf/1101.3715.pdf, but hopefully someone can give a more proper answer. – DavePhD Nov 13 '14 at 15:40
• Please check the question again, as I have try to make it more clear hopefully. Notice that I have studied the Big Bang nucleosynthesis some years ago, and as far as I knew, the chemical potentials for protons and neutrons were calculated considering them free (unbound). – Caute Nov 13 '14 at 17:58
• @user60565 Isn't the chemical potential the same as binding energy per nucleon at low temperature (meaning not in the millions of degrees), basically around -8.5MeV for the most stable nuclei? – DavePhD Nov 13 '14 at 19:22

## 1 Answer

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)

• Thank you very much for reply to me. What does you mean saying "when the shell structure is lost"? Thanks again – Caute Nov 17 '14 at 18:02
• Due to its quantum nature, the lowest state of nuclei corresponds to nucleons occupying well defined states of specific energies, like electrons in an atom. That is the shell structure, which is very different to the case where all nucleons are in excited states: the energy involved in adding (removing) a nucleon depends on the energy state it will occupy (occupied) and can sometimes be a prohibited process. But when the shell structure is lost, all nucleons have approximately the same energy and it makes more sense to speak of $\mu$ as really an average energy per nucleon exchanged. – rmhleo Nov 18 '14 at 2:04