Free neutrons are unstable (half-life $\sim 10$ min), but bound neutrons are (for many nuclei, including those which are stable) stable.

Question 1: Are there other properties of the neutron / proton which change depending on whether the nucleon is free or bound, or depending on the precise nucleus the nucleon is part of, or depending on the nucleon's location within its nucleus, etc? For example:

  • magnetic moment?

  • electric dipole / multipole moments? (or charge distribution more generally)

  • analogous "shape variations" related to the strong or weak forces?

  • mass?

Question 2: Are there models of the structure of atomic nuclei which take into account such changes to "internal" properties of the nucleons?

I've only heard of the liquid drop model and the nuclear shell model, and though I haven't studied either in detail I have the impression that these models treat the nucleons as point particles, so that the kind of effects I'm talking about are not considered.

P.S. I could probably use some help with tagging on this question.

  • $\begingroup$ Bound neutrons may be stable. $\endgroup$
    – ProfRob
    Aug 20, 2020 at 7:44
  • $\begingroup$ I see there are votes to close my question for needing more focus. In my experience on other Stack Exchange sites (especially MathOverflow), it's common practice to ask a cluster of closely-related questions, with the understanding that an answer to any single one of these questions would be helpful (and would likely shed light on the others as well). I'd appreciate any more specific advice on how to make my question more suitable for the norms of this community. For instance -- should I not have a "Question 1" and a "Question 2"? Should I not suggest so many possible answers to "Question 1"? $\endgroup$
    – tcamps
    Aug 29, 2020 at 14:59
  • $\begingroup$ @RobJeffries Thanks. I've edited to clarify that bound neutrons are stable in some nuclei but not others. That's what you meant, right? Or did you mean that bound neutrons are not known to be stable, but only have some upper bound on their half-life? $\endgroup$
    – tcamps
    Aug 29, 2020 at 15:05
  • $\begingroup$ I mean that beta decay is a thing. $\endgroup$
    – ProfRob
    Aug 29, 2020 at 15:30
  • $\begingroup$ I would say that nuclei exist in which bound neutrons are stable --- that such nuclei are "typical" is a prejudice shared by those of us who are made of stable matter. $\endgroup$
    – rob
    Aug 29, 2020 at 15:31

1 Answer 1


This is really a comment, but comments that may sound like answers have a way of disappearin.

The basic one is the mass, where bound nucleons have to be assigned a smaller mass, dependent on the nucleon and the isotope, as seen the in binding energy curve.

Thus the neutron cannot decay when bound as a result of the strong conservation rule of energy.

For the other properties, the models I know treat them as intrinsic , and use their value to calculate total nucleus properties due to the distribution of nucleons within a nucleus. For example see this for the magnetic moment.

  • $\begingroup$ Thanks, this is great! I've accepted because it seems unlikely anybody will end up posting anything more definitive. $\endgroup$
    – tcamps
    Aug 21, 2020 at 21:45

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