What is the average transition time for a nucleon between protons and neutrons?

gildomar
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I know that the nucleus can be considered a bunch of particles that constantly transition between protons and neutrons due to exchange. Given that, is it meaningful to talk about the "average" time that a nucleon spends as either a proton or a neutron before switching to the other? Or is that a non sequitor?
 
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That does not make sense, but you can still give a rough typical timescale for processes in the nucleus, corresponding to ##\hbar## divided by the binding energy of a nucleon.
 
I am not sure, but I learned during my undergrad that the neutron is stable in the nucleus because it transforms to proton with pions before having the time to beta decay.
HOWEVER here I learned this is nonsense of an explanation and I even got a red ticket for posting a source... and now that I think of it, it's really nonsense because- then - there would be no beta decays for any nucleus...

But in general the characteristic time for a neutron to proton transisition is supposed to be the characteristic time of nuclear interactions... you can find that "characteristic" time only by seeing how much does it take for a photon to pass through a nucleus (so how much fast is the fastest interaction within the nucleus). That's by taking:
t_{ch} \propto \frac{1 fm}{c}
where 1fm is around the radius of the nucleus...
 
Yeah, sorry about that; it was late and I really misinterpreted something that I had read. I realized how backwards it was after I actually slept on the matter.
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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