It is established that "normal" electron orbitals are not stable in more than 3 spatial dimensions, as the available energy levels become unbounded from below. However, this result only applies given the electrostatic potential exterior to the nucleus.
Greg Egan has calculated the wave functions for bound electrons in 5+1 dimensions, and the result bears a good bit of resemblance to Thompson's plum-pudding model of the atom--the electron wavefunction is confined to the diameter of the nucleus, so you have a blob of high-mass positive charge with low-mass negative charges embedded in it.
What consequences does that have for nuclear and chemical structure in higher dimensions?
It would seem to me that the localization of electrons within the nucleus should act to offset the mutual electrostatic repulsion of protons, resulting higher nuclear stability, and thus an extended periodic table with many more stable high-atomic-number elements--with the side effect that nuclei could be destabilized by electronic ionization! With little or no external electric field, fusion reactions should also be considerably easier, and nuclear decay by electron capture should be extremely rapid.
But, I am left with two questions:
- Is there anything at all to keep different nuclei apart, or should be expect all collections of matter in such a universe to immediately undergo fusion into a single gigantic nucleus, like a neutron star?
- If atoms can indeed remain distinct, is there any chemistry possible? Robert Forward has proposed the possibility of chemistry based on nuclear reactions in neutron-star environments, with nucleon energy shells taking the place of electron shells (about which there is also this related question); if that is plausible it would seem to be provide a way for complex multi-atom structures to arise for these higher-dimensional atoms as well, but just how plausible is it? And would there be any electronic chemistry possible, with electrons being traded or shared between nuclei?
NOTE: For purposes of this question, assume that nuclear structure is not radically changed by increasing dimensionality; the precise structure of nucleon energy shells ought to change, as there is more room for more nucleons to fit in the same radius, and more possibilities for different angular momenta to fit more nucleons per shell, but we still get protons and neutrons bound in nuclei. To potentially challenge that assumption, see here.
EDIT: Per this answer, it would appear that quarks are not confined in spaces with 5 or more dimensions. I would count that as a "radical change", so if it matters, let's assume we'e working with electron wave functions in 4D space.