I think this is a great question because not too long ago we struggled with the opposite question: How can electron-based molecules exist at all? (Funny that now I have to differentiate it from antiproton-based molecules...) The old model of atoms where electrons 'orbited' classically/astronomically interpret the electron as literally circling around the nucleus, and because a moving charge radiates energy electromagnetically it should shed it's orbital energy until it reaches the nucleus. This was a big conundrum way back before we settled on quantum mechanics, which solves this by recognizing that electrons 'orbit' is more like an acoustic standing wave and that there are a small number/quanta of available states that the electron can possibly exist in. Electron orbitals are not continuous or near-continuous, they are very much discrete, and there is some minimum activation energy required to shift between the various orbital states.

This quora answer actually looks like a reasonable description of the issue past physicists faced: https://www.quora.com/Why-do-electrons-in-an-atom-keep-a-dis...

So I'd guess that the reason why the antiproton's orbit decays is because its orbital energy levels are "continuous enough" that its orbital energy can decay smoothly down to zero. Maybe this is related to the fact that the electron is relatively massless compared to the antiproton.

I think it's cool that we found a state of matter where the old model of atomic orbital motion that we interpreted as a paradox might be a physically accurate description in this circumstance.

It doesn't. The ground state orbital of the antiproton is in principle stable, just like the electron orbitals in a regular atom. The difference is that antiprotons can annihilate with protons from the helium nucleus when they get too close. This is why the experiments observe orbitals with high quantum numbers where the overlap between the antiproton wavefunction and the nucleus is small.

The idea is that electrons, muons and antiprotons have stable orbitals, where they can stay forever. For one electrons, muons or antiprotons, they have the same shape and classification, but they don't have the same size. They are all stable.

It's a bad idea to imagine them like a planet orbiting around the Sun, or that they suddenly make a turn and decide to head to the nuclei, or that they are going in spirals until they colide.

In some case, electrons can interact with the nuclei, and the nuclei absorbs them, one proton changes into a neutron and the process releases a neutrino https://en.wikipedia.org/wiki/Electron_capture But the electron is in a stable orbital and suddenly it interact with the nuclei.

Something similar happens with the antiproton. The antiproton is in a stable orbital and suddenly it interact with the nuclei and is annihilated.

The stranger case is really the electron, which just sits there and never falls to the nucleus (that's the original conundrum of the model of the atom as negative electrons orbiting a positive nuclear center). Physicists applying QM to the hydrogen electron found that the electron could only exist in certain energy levels, and drew the analogy of standing waves to explain it, hence 'wave equations'. The electron is no longer a point orbiting another point, but a wave function delocalized over the entire orbital.

These electron quantum rules don't work the same for an antiproton, which is 1800X more massive than an electron. There's probably some other factors, like the antiproton can get close enough to the nucleus for strong force effects etc.

I am not a physicist, but I suppose it is because the s-orbital has an amplitude peak at r=0?

In other words, it is not so much the antiproton falling to the nuclear surface as much as the antiproton finding itself at the nuclear surface.

EDIT: The context is that the antiproton was in an orbital with large principal and azimuthal quantum numbers. Still, there would be some non-zero probability of the antiproton finding itself close to the nucleus, no?

My rudimentary guess is either due to the strong and/or weak forces combined with lack of orbital/shell velocity.

The antiproton is negative.

The protons with neutrons are collectively positive.

The orbital velocity of the antiproton is slower than that of an electron (being something like 180x more massive).

And along with above, the - and + charges attract strongly. So the antiproton orbit rapidly decays to the nucleus.

Not too literate in this, but I'd say that the mass of a proton is large enough so that quantum effects (such as the quantization of of energy) become less relevant than classical mechanics (which lets the antiproton get pulled toward the proton).

Correct me if I'm wrong though.