  The neutron is electrically neutral, but its substructure consists of charged
quarks so it may have an internal charge distribution. In fact it is known to
have a negative mean square charge radius (MSCR), the second moment of the
radial charge density. In other words the neutron has a positive core and
negative skin. In the first Born approximation the neutron MSCR can be simply
related to the neutron-electron scattering length b_ne. In the past this
important quantity has been extracted from the energy dependence of the total
transmission cross-section of neutrons on high-Z targets, a very difficult and
complicated process. A few years ago S.A. Werner proposed a novel approach to
measuring b_ne from the neutron's dynamical phase shift in a perfect crystal
close to the Bragg condition. We are conducting an experiment based on this
method at the NIST neutron interferometer which may lead to a five-fold
improvement in precision of b_ne and hence the neutron MSCR.
