# How can the radius of a bare neutron be negative?

This interactive table of nuclides shows the radius of a bare neutron to be -0.1149 fm (femtometers). How can that radius be negative?

The page uses interactive mouse-clicking, so I've included a screenshot with the neutron info at the bottom. The radius is circled in red.

To get to the neutron info, click on the bottom-most square on the chart.

Also, you can select color-coding with the drop-down menu on the right, and choose "radius (fm)". Note that only the bare neutron has a negative radius, according to this page.

• The neutron's valence quarks are two ds, negatively charged, and a u, positively charged. Very crudely, the ds exclude each other and find themselves on average farther away from the center than the u, and thus contribute a higher r-squared moment than the u, which is what is summarized in a negative R. – Cosmas Zachos Feb 26 '17 at 14:35

If you compare with another source, like the neutron data from the Particle Data Group, you'll find that what is called R in your source is what the PDG booklet calls "mean square charge radius" (see p. 5 in the PDF).

Now the negative sign for the charge radius is just a convention you use when dealing with the neutron, which is an uncharged particle. The corresponding Wikipedia article states:

In [the case of a particle with net zero electric charge], 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 (...)

The best known particle with a negative squared charge radius is the neutron. (...)

• You've altered that quote in a misleading way. Wikipedia says that this is only done for some particles with net-zero electric charge. (And I think that's essential to understanding the quote, because otherwise the bit about "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" makes no sense, since inverting the electric charge of each quark would still result in net-uncharged particle.) – ruakh Feb 26 '17 at 19:13
• It is not just a convention, the sign is meaningful – Thomas Feb 26 '17 at 20:59

The table refers to the electric charge radius which can be both negative or positive, depending on the distribution of charge. The reason we focus on the charge radius rather than (for example) the baryon radius is because the electric charge radius can be measured in electron scattering, whereas the Baryon charge radius cannot be directly measured.

The fact that the neutron charge radius is negative means that we can picture the neutron as a positively charged core surrounded by a negatively charged corona. A simple explanation of this fact is provided by the idea that Quantum mechanically the neutron sometimes fluctuates into a proton and a negatively charged pion. The proton is heavy and forms a positively charged core, where is the pion his light and forms a cloud. Note that the neutron can also fluctuate into a negatively charged Delta resonance and a positively charged pion, but this process is less likely because the Delta resonance is heavy.