  We argue that the proton's charge-radius contributes differently to shifts of
Hydrogen-like energy levels than naively expected due to an incorrect choice
for the boundary condition at the proton's position in standard calculations.
In particular we show how to obtain the correct boundary condition, which
depends on the charge radius itself in a predictable way. We argue this
difference in boundary conditions only matters when they are imposed at a
radius $r=\epsilon < Z \alpha/m$ where $m$ is the orbiting-particle mass,
because only then is the particle relativistic at these distances. The boundary
condition difference is therefore important for ordinary Hydrogen while not for
muonic Hydrogen. The boundary condition can be interpreted in terms of a second
type of nuclear moment, and a prediction is made for the proton-radius energy
shift as a function of charge-radius, $r_p$, this second nuclear moment, $h$,
and orbiting particle mass, $m$. The observed difference between electronic and
muonic contributions to the Lamb shift is accounted for with $r_p \simeq 0.87$
fm similar to its traditional value, and $2mh$ of order a few fm.
