Pionic Fluctuations of Constituent Quarks and the Neutron Charge Radius

Pion loop fluctuations of the constituent $u$ and $d$ quarks are shown to contribute $+0.006 \div 0.014$ fm$^2$ to the intrinsic charge radius of the neutron, under the assumption that the pion-quark coupling constant has its conventional value, with a cut-off scale ranging from 800 MeV to 1 GeV. The range of calculated values encompasses the small positive empirical value $\simeq 0.009 \pm$0.002fm$^2$. The contribution from the pion loops to the anomalous magnetic moment of the neutron is small.