# Has many-body tunneling at the level of nuclei been studied?

In a recent paper, the authors stress the difference between single-body tunneling and many-body tunneling (at the atomic level): "In contrast to the well-studied incoherent single-particle tunnelling, our understanding of many-body tunnelling is still in its infancy." https://www.nature.com/articles/nphys3225

When considering tunneling at the nuclear level such as in the case of alpha emission or nuclear fusion, the approach typically employed involves solving the wave equation for a particle that tunnels through a potential barrier. To do that, techniques like the WKB approximation are used (see https://en.wikipedia.org/wiki/Quantum_tunnelling#The_WKB_approximation). However, it seems that the underlying assumption here is that the tunneling process is single-particle tunneling.

In contrast, has there been any treatment of many-body tunneling at the nuclear level?

• A process you might look at: two-proton radioactivity, first observed about a decade ago in nuclei near the proton drip line. – rob Jul 27 '19 at 0:24
• – anna v Jul 27 '19 at 5:02

## 1 Answer

However, it seems that the underlying assumption here is that the tunneling process is single-particle tunneling.

Actually the underlying assumption is that one is working with quantum mechanics, and tunneling has a definable probability of occurring if a single wavefunction for the whole system of particles can be defined. That is why one gets approximations. For example the alpha particle is composed out of four nucleons, but is treated as one quantum mechanical entity.

In contrast, has there been any treatment of many-body tunneling at the nuclear level?

It depends on your definition of "many body". If you mean "individual particles at the same time described by the strong nuclear force" you would just have to multiply the probabilities for each for tunneling, because they would have individual wavefunctions. Otherwise, an alpha particle even though composed by many nucleons, will have one wavefunction to solve for in some approximation. That is because of dimensions, the strong nuclear force,(spill over from QCD interactions between nucleons, a short range force), is of dimensions of fermi, and the nuclear force cannot affect nucleons on atomic lattice distances.

The paper you link is evaluating a quantum mechanical system at the atomic level where single protons are studied to be tunneled between molecules, and the force/potential there is electromagnetic. a long range force.. The two quantum mechanical systems,nuclear and atomic, are not comparable.

• "you would just have to multiply the probabilities for each for tunneling, because they would have individual wavefunctions" -- that is not correct in states of coherence i.e. entanglement. In that case, one can no longer speak of individual wave functions but needs to consider the wave function of the entire quantum system. When I say "many body" I mean many nuclei such as in a lattice that can be coupled. If many nuclei in a lattice are in a coherent state, then the tunneling model that your link points to is too simplistic and not valid because it assumes two nuclei in isolation. – MrFu Jul 28 '19 at 2:40
• I have edited in my answer to this comment – anna v Jul 28 '19 at 3:54