As an ansatz, suppose we know that when a smaller nucleus is incident upon a larger one with 1 MeV of kinetic energy, there is a nontrivial probability that a neutron will tunnel from the smaller to the larger:
$$ ^{12}C(d,p)^{13}C $$
Even if the energy of the incident particle is less than needed to surmount the Coulomb barrier, the neutron can tunnel from one nucleus to the other with a probability $T,$ the tunneling probability. One way to understand this probability is as a function of separation of the nuclei and time that they spend in proximity to one another.
To simplify the ansatz, then, suppose that rather than having the smaller nucleus approach the larger one against Coulomb repulsion, instead it is simply held at a specific distance $d_1$ for a specific amount of time $t_1$ such that the neutron tunneling probability is $T_1,$ and then after $t_1$ expires the smaller nucleus is instantaneously moved far away.
- With a knowledge of $t_1$ and $d_1,$ is there a straightforward way to obtain the time interval $t_2$ needed for the same interaction to occur with probability $T_1$ at a distance $d_2?$
- If so, is this result a general one, or does it depend upon such details as the resonances of the interacting nuclei?
EDIT: It occurs to me that this thought experiment is quite relevant to muon-catalyzed fusion.
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