The problem of defining a radius for the atomic nucleus has some similarity to that of defining a radius for the entire atom; neither has well defined boundaries. However, basic liquid drop models of the nucleus imagine a fairly uniform density of nucleons, theoretically giving a more recognizable surface to a nucleus than an atom, the latter being composed of highly diffuse electron clouds with density gradually reducing away from the centre. For individual protons and neutrons or small nuclei, the concepts of size and boundary can be less clear. A single nucleon needs to be regarded as a "color confined" bag of three valence quarks, binding gluons, and a so-called "sea" of quark-antiquark pairs. Also, the nucleon is surrounded by its Yukawa pion field responsible for the strong nuclear force. It could be difficult to decide whether to include the surrounding Yukawa meson field as part of the proton or nucleon size or to regard it as a separate entity.
Fundamentally important are realizable experimental procedures to measure some aspect of size, whatever that may mean in the quantum realm of atoms and nuclei. Foremost, the nucleus can be modeled as a sphere of positive charge for the interpretation of electron scattering experiments: the electrons "see" a range of cross-sections, for which a mean can be taken. The qualification of "rms" (root mean square) arises because it is the nuclear cross-section, proportional to the square of the radius, which is determining for electron scattering.
This definition of charge radius is often applied to composite hadrons such as a proton, neutron, pion, or kaon, that are made up of more than one quark. In the case of an anti-matter baryon (e.g. an anti-proton), and some particles with zero net electric charge, the composite particle must be modeled as a sphere of negative rather than positive electric charge for the interpretation of electron scattering experiments. In these cases, the square of the charge radius of the particle is defined to be negative, with the same absolute value with units of length squared equal to the positive squared charge radius that it would have had if it was identical in all other respects but each quark in the particle had the opposite electric charge (with the charge radius itself having a value that is an imaginary number with units of length). It is customary when charge radius takes an imaginary numbered value to report the negative valued square of the charge radius, rather than the charge radius itself, for a particle.
The best known particle with a negative squared charge radius is the neutron. The heuristic explanation for why the squared charge radius of a neutron is negative, despite its overall neutral electric charge, is that this is the case because its negatively charged down quarks are, on average, located in the outer part of the neutron, while its positively charged up quark is, on average, located towards the center of the neutron. This asymmetric distribution of charge within the particle gives rise to a small negative squared charge radius for the particle as a whole. But, this is only the simplest of a variety of theoretical models, some of which are more elaborate, that are used to explain this property of a neutron.
For deuterons and higher nuclei, it is conventional to distinguish between the scattering charge radius, r (obtained from scattering data), and the bound-state charge radius, R, which includes the Darwin–Foldy term to account for the behaviour of the anomalous magnetic moment in an electromagnetic field and which is appropriate for treating spectroscopic data. The two radii are related by
where m and m are the masses of the electron and the deuteron respectively while λ is the Compton wavelength of the electron. For the proton, the two radii are the same.