From this blog post, one should be inclined to think that for large nuclei it can at least contribute to the spin-orbit force, and then to the correction to N=50 and N=82 nuclear shells.

As QGR noted above, the exponential suppression of the potential does not need to be all the history. Note that usually the total potential in a nucleus is Woods-Saxon, where the exponential does not factor out.

Independently of particle mass, a low-momentum exchange is able to see all the nucleus; when a beta decay happens, the electron carries a momentum of less than 100 MeVs and then it is delocalized across all the nucleus. This is the same that when a electronic transition happens in an atom: the photon carries a momentum of only some electron-Volts, and then it is delocalised across all the orbital.

Consider that a typical contribution to nuclear shells must be about 2 or 3 MeVs. Most (well, a lot) of the nuclear shell correction comes from exchange of $\omega$ and other mesons, which have a mass around the 750 MeV range. Quotient by W mass, and we could expect linear corrections of the order of a 1%.

So, if some collective effect can do a linear correction to appear, it could be more or less in the range to be noticeable: (750 MeV)^2/81GeV=6.9 MeV.

To look for collective effects was the idea of the post I have referred in the first line: check the favored masses when the "liquid drop" nucleus splits in two pieces. The small fragment of fission channel S3 happens to have an average mass of 79.21 $\pm$ 1.14 GeV across a range of nuclei from 233Pa to 245Bk; the small frament of channel S2 happens to have an average mass of 92.34 $\pm$ 2.91 GeV.

From this blog post of mine, one should be inclined to think that for large nuclei it can at least contribute to the spin-orbit force, and then to the correction to N=50 and N=82 nuclear shells.

As QGR noted above, the exponential suppression of the potential does not need to be all the history. Note that usually the total potential in a nucleus is Woods-Saxon, where the exponential does not factor out.

Independently of particle mass, a low-momentum exchange is able to see all the nucleus; when a beta decay happens, the electron carries a momentum of less than 100 MeVs and then it is delocalized across all the nucleus. This is the same that when a electronic transition happens in an atom: the photon carries a momentum of only some electron-Volts, and then it is delocalised across all the orbital.

Consider that a typical contribution to nuclear shells must be about 2 or 3 MeVs. Most (well, a lot) of the nuclear shell correction comes from exchange of $\omega$ and other mesons, which have a mass around the 750 MeV range. Quotient by W mass, and we could expect linear corrections of the order of a 1%.

So, if some collective effect can do a linear correction to appear, it could be more or less in the range to be noticeable: (750 MeV)^2/81GeV=6.9 MeV.

To look for collective effects was the idea of the post I have referred in the first line: check the favored masses when the "liquid drop" nucleus splits in two pieces. The small fragment of fission channel S3 happens to have an average mass of 79.21 $\pm$ 1.14 GeV across a range of nuclei from 233Pa to 245Bk; the small frament of channel S2 happens to have an average mass of 92.34 $\pm$ 2.91 GeV.