While Gamow's theory successfully describes the radioactive $\alpha$-decay by quantum tunnelling, it leaves a key question unanswered. The theory assumes that the $\alpha$ particles pre-exist inside the nucleus; it does not answer how it is formed inside a nucleus. Is there a theory (or model) that addresses the mechanism and calculates the formation probability of an $\alpha$-particle inside a nucleus in a certain range of energy?
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asked Jun 7 at 3:32
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2 Answers
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I was searching for models describing this and found two:
The alpha particle model of nuclei, which circumvents the issue, more or less like you already said in your question, by just assuming that the alpha particles preexist, i.e., neutrons and protons in a nucleus, whenever possible, are arranged in alpha particles, see https://www.sjsu.edu/faculty/watkins/alphamodule.htm .
Furthermore I also found a newer conference paper: https://www.epj-conferences.org/articles/epjconf/pdf/2020/03/epjconf_enas2020_01001.pdf which discusses a model of post-forming an alpha particle outside the range of the nuclear interaction with the daughter nucleus. This contrasts with the commonly accepted mechanism of first alpha particle pre-formation followed by emission through barrier penetration.
The surprise for me was, that the conference paper questions that the alpha particle is actually formed "inside" the nucleus.
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There are also models that compute the alpha pre-formation probability using only nucleon-nucleon interaction. This is typically done in the framework of energy density functional theory, in which the nuclear many-body problem is solved with nucleons as the relevant degrees of freedom. These are called microscopical approaches.
The idea is the following : starting from a nucleus, how can I deform it (geometrically speaking) such that it would be able to emit an alpha particle in the final state ?
This question can be answered by computing the energy of the deformed nucleus for different deformations (we force the system to exhibit a specific deformation and compute the associated energy). Once we have a full map (called potential energy surface), we can try to find the path that would lead to an alpha particle emission.
Historically, this framework has been used to understand fission, like in here (see fig 11 for instance) : https://iopscience.iop.org/article/10.1088/0034-4885/79/11/116301/ampdf. Then it had been applied to heavy nuclei that emit cluster (a carbon nucleus instead of an alpha for instance), see this paper for instance (fig 3 and 4) : https://arxiv.org/abs/1107.1478. More recently, this has also been applied to alpha decay as discussed here : https://arxiv.org/abs/2003.00967 and https://arxiv.org/abs/2211.14135.
