Distribution of protons inside a large nucleus

[Kostik]

TL;DR Summary

Does coulomb repulsion result in an increasing charge density ρ(r) inside medium and large nuclei?

For medium to large nuclei, common sense suggests that protons should not be uniformly distributed inside the nucleus. Assuming the protons inside the nucleus are mobile (but supposing that it doesn't make sense to consider the nucleus a "conductor", in which case all charge would reside on the outer surface), the coulomb repulsion between protons should push them away from the center of the nucleus to some degree. It's not clear what the actual charge density ρ(r) should look like, but I suspect it should increase away from the center.

DOES THE nucleus, in fact, have a "neutron-rich" core and a "proton-rich" outer shell? Are protons relatively mobile within the nucleus?

 

[PeroK]

Summary:: Does coulomb repulsion result in an increasing charge density ρ(r) inside medium and large nuclei?

For medium to large nuclei, common sense suggests that protons should not be uniformly distributed inside the nucleus. Assuming the protons inside the nucleus are mobile (but supposing that it doesn't make sense to consider the nucleus a "conductor", in which case all charge would reside on the outer surface), the coulomb repulsion between protons should push them away from the center of the nucleus to some degree. It's not clear what the actual charge density ρ(r) should look like, but I suspect it should increase away from the center.

DOES THE nucleus, in fact, have a "neutron-rich" core and a "proton-rich" outer shell? Are protons relatively mobile within the nucleus?

You cannot model the atomic nucleus using the concepts of classical electromagnetism. The nucleus is governed by Quantum Theory: in particular QCD and QED. See here for example:

http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/shell.html