correct, it does assume uniform density, if it didnt, you could say the density was zero throughout the sphere except for a small spherical region, and it would

correct, it does assume uniform density, if it didnt, you could say the density was zero throughout the sphere except for a small spherical region, and it would be trivially false then I was illustrating how in principle radii can be derived in a phenomenological sense. I didn't read the actual papers by the experimenters of the proton radius determination, but it would probably require a modification of the Hamiltonian for the hydrogen atom, since usually one treats the nuclei as point particles.