# Charge structure of the neutron

David Griffiths’ book on elementary particles says that the neutron is positive at the center and edges, negative in between. (Introduction to Elementary Particles, Wiley, 1987, p. 21).

But Wikipedia disagrees, saying the opposite, with what seems to be an unimpeachable reference: Miller, G.A., “Charge Densities of the Neutron and Proton”, Physical Review Letters, 99, #11, p. 112001, doi 10.1103/PhysRevLett.99.112001.

Is this an error in Griffiths? Or has the theory about the interior of the neutron been revised since 1987? The Miller abstract does say that the negative-at-the-center distribution is “in contrast with many expectations”. What is the history here?

• The Miller paper is available as a PDF on JLAB's website: userweb.jlab.org/~punjabi/… I don't know the answer but anything from JLAB is later than 1987. The first physics papers from the lab were in the early 1990s. – dmckee Jul 18 '16 at 21:57
• Did you miss this line: "Here we present the first phenomenological analysis of existing data to determine $\rho(\mathbf{b})$ for the neutron and proton. The results for the neutron contradict the long-standing notion, derived from both gluon-exchange and meson-cloud models" from the first column of the first page in the JLAB PDF. – dmckee Jul 18 '16 at 22:01
• I looked for the Miller paper online, but didn't find anything except the abstract. – MJD Jul 18 '16 at 22:22

Griffith's 1987 book correctly states a totally reasonable hypothesis, that the neutron's core is positive. Here's a simple model which probably goes back to Fermi: the neutron ought to spend part of its time as a virtual proton-$\pi^-$ pair, in a strong-interaction analog to the photon spending part of its time as an electron-positron pair; since the proton is heavier than the pion, you'd expect to find the positive charge concentrated near the neutron's core.

Wikipedia correctly observes that Miller shows, using data that did not exist in 1987, that the electric and magnetic form factors required to describe scattering from nucleons at different momentum transfer don't describe a charge distribution with a positive core. The simple virtual-$\pi^-$-cloud model is wrong. A better model for the neutron has a negatively-charged core and a slightly negatively-charged halo, with the charge cancelling due to a positively-charged layer in between.

The quarks that make up the neutron carry different fractions of the neutron's momentum. The most likely fraction of the momentum to be carried by any particular quark is $x=\frac13$, since there are three valence quarks. However these fractions fluctuate, as quantum-mechanical properties do. Apparently the data show that the neutron's $d$ quarks are more likely to carry more of its momentum (large $x$) than its $u$ quarks. The high-momentum quarks, with more relativistic energy, are more likely to be found near the neutron's center of mass; since these are more likely to be $d$ quarks, the neutron's core is negative.

• Why are high-momentum quarks more likely to be found at the center of mass? I would have thought it was the opposite. – MJD Jul 4 at 13:30
• Naïve explanation: the high-momentum quarks have more total energy $E^2=p^2+m^2$, so the center of the neutron's total mass-energy distribution is nearer to them. I suspect the explanation by Miller and Arrington referred to in the linked article is more technical. – rob Jul 5 at 0:03