Charge radius are used to determine the recommended values. The 2014 CODATA recommended values are: Recent measurement of the Lamb shift in muonic hydrogen (an exotic atom consisting of a proton and a negative muon) indicates a significantly lower value for the proton charge radius, : the reason for this discrepancy is not clear. Charge radius The rms charge radius is a measure of the size of an atomic nucleus, particularly of a proton or a deuteron. It can be measured by the scattering of electrons by the nucleus and also inferred from the effects of finite nuclear size on electron energy
Particle in a ring in that case are identical to the energy eigenfunctions of the particle on a ring. The statement that any wavefunction for the particle on a ring can be written as a superposition of energy eigenfunctions is exactly identical to the Fourier theorem about the development of any periodic function in a Fourier series. This simple model can be used to find approximate energy levels of some ring molecules, such as benzene. In organic chemistry, aromatic compounds contain atomic rings, such as benzene rings (the Kekulé structure) consisting of five or six, usually carbon, atoms. So does the surface of "buckyballs"