By measuring the energies of the emitted alpha particles, how can we say that they have energies less than the height of the nuclear potential well when they are inside the well? How can we be sure that alpha particles are not momentarily acquiring energies greater than the height of the nuclear potential well and coming out without requiring the mechanism of quantum tunneling?
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asked Jun 13, 2023 at 19:01
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1$\begingroup$ physics.stackexchange.com/questions/10863/… may be relevant. But the point is that we can see how high the Coulomb barrier is by trying to get an alpha from outside into the nucleus - that tells us how high the mountain is. Then, when we see alphas come out with lower energy than that we know they did not go over the top of the potential. $\endgroup$– Jon CusterCommented Jun 13, 2023 at 19:38
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The idea that a nucleus is a bunch of nucleons sharing kinetic energy with a would be alpha particle is entirely classical. In the limit the half life goes to infinity, the nucleus becomes a stationary state: it never changes. That doesn't mean there isn't probability current circulating to make orbital angular momentum, nor that it is static. They whole thing is one multi particle entangle state of position, spin, and isospin wave functions.
If you look at the picture from alpha tunneling:
You can imagine there is some operator that connects the nuclear wave function with the free particle alpha wave function outside the nucleus, after that, all that matter is the the density of final states is non-zero (e.g.: the free alpha has positive energy, but it need not be high enough to so-called go over the barrier), and then there is a finite transition probability per unit time.
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$\begingroup$ But how do you answer the part of ' alpha particles are not momentarily acquiring energies ', like how do you disprove that? $\endgroup$ Commented Jun 14, 2023 at 10:02
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$\begingroup$ @HarshdeepChhabra because that's no how quantum states work, so your question is basically 'how do you disprove it's acting classically'. $\endgroup$– JEBCommented Jun 14, 2023 at 14:43