The sign and value of the neutron mean squared intrinsic charge radius

The connection between the neutron mean squared intrinsic charge radius (r^2(E,in))N and the neutron-electron scattering length a(ne) measured in low-energy neutron physics is discussed. Special attention is paid to the validity of the Foldy formula giving this connection. It is shown that there are two different ways of deriving the Foldy formula. A table is presented of the experimental data obtained during the period 1947-1997 which allow the determination of a(ne). These data split into two groups. One group leads to (r^2(E,in))N>0, and the other (including the Dubna data) to (r^2(E,in))N<0. The sources of possible systematic errors in the experiments are discussed. In particular, the effect of resonance nuclear scattering on the measured value of a(ne) is studied. The experimental results on the measurement of a(ne) in low-energy neutron physics are compared with the theory. It is shown that if the data leading to (r^2(E,in))N>0 are correct, then the modern theoretical ideas about the structure of the neutron (including the well developed Cloudy Bag Model) must be fundamentally changed.