# Coulomb barrier and proton evaporation

Why is it that neutrons evaporate from nuclei more easily than protons do?

Intuitively, since protons are electrostatically repelled (in addition to whatever nuclear forces they have in common with neutrons), one would expect protons to be ejected more readily than neutrons. (Maybe this is even what does happen for small nuclei, but apparently not large nuclei.)

It seems to be said in common parlance that the Coulomb force/barrier acts to contain the protons. Which is counter-intuitive.

On the other hand, at least some textbooks acknowledge the coulomb force trying to push protons away from others in the nucleus, and so they infer that the nuclear force (e.g., residual strong force) must act more strongly on protons than what it does on neutrons. (At least in big nuclei, "beta stable nuclei", nuclei with an excess of neutrons..) So how does this nuclear force distinguish between protons and neutrons?

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–  Ben Crowell Apr 29 '13 at 23:51

## 2 Answers

Your intuition about the charge repulsion and strong force acting on Protons more is less important that you think. The strong nuclear force is a few orders of magnitude greater than electromagnetism so coulomb repulsion just doesn't contribute much.

What matters most is the nuclear binding energy to separate a proton from the nucleus. If the resulting system is below the proton separation energy it's possible for the proton to tunnel out. See Proton emission and Proton drip line for more information about this. It does happen but remember Neutron emission is also rare. $\beta^+$ and $\beta^-$ and Alpha emission are much more common.

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Isn't the binding energy of an alpha particle less than for a proton? I mean, this is how fusion in stars work. So given the choice, a nucleus would rather throw off an alpha particle, and that does happen more often than neutrons so in a fully circumspect view I think the nuclei emissions make complete sense. –  Alan Rominger Apr 30 '13 at 0:51
@AlanSE: That's not quite right. See this question: physics.stackexchange.com/questions/61699/… –  Ben Crowell Apr 30 '13 at 0:53
@BenCrowell There are 3 relevant parts to the picture I see here. There's the Q value, there's the more-or-less the Coulomb quantum tunneling barrier which favors lower charges (which I missed above), and there's a sort of anthropic principle. If a nucleus found it energetically favorable to decay by neutron emission then it likely would have already done so. Because we're interested in nuclei that actually exist, we want to know about decays that have half-lives on the order of 10 billion years or so. To explain that final point probably requires more research than I've done. –  Alan Rominger Apr 30 '13 at 1:19
@AlanSE: It doesn't have anything to do with the anthropic principle. The anthropic principle would be relevant if we were discussing what nuclei would exist under some alternative laws of physics, in a different part of the string-theory landscape, in a different cosmological epoch, etc. –  Ben Crowell Apr 30 '13 at 13:24
@BenCrowell I think that's too specific of a definition for that word, there are simple anthropic observations, which are entirely different than the anthropic principle. But maybe I'm the one over extending the scope of the word. What would you call the observation? –  Alan Rominger Apr 30 '13 at 16:25

"Why is it that neutrons evaporate from nuclei more easily than protons do?"

This is not true in general. In depends strongly on where the nucleus is relative to the neutron drip line and the proton drip line. It also depends on Z and on how excited the nucleus is.

A cold nucleus that's beyond the neutron drip line will emit a neutron in a very short time, on the order of the time required for a neutron to travel a distance equal to the diameter of the nucleus. A cold nucleus that's beyond the proton drip line will typically decay by proton emission, but the time scale will be much longer, because the proton has to tunnel out through the Coulomb barrier.

It's counterintuitive but true that although the electrical force between protons is repulsive, the existence of the electrical potential barrier does reduce the rate of proton emission. This question goes into that: Tunneling of alpha particles

"at least some textbooks [...] infer that the nuclear force [...] must act more strongly on protons than what it does on neutrons. [...] So how does this nuclear force distinguish between protons and neutrons?"

No, this is wrong, and textbooks don't say this. What breaks the symmetry (isospin symmetry) between neutrons and protons is the electromagnetic interaction, not any isospin violation by the strong force.

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