Abstract
An effective spin-dependent interaction position of the particles from its dipole with that of an electron is used in determining
the geometrical structure of excess-electron environments in rigid media by magnetic spectroscopic means. This quantity
is obtained by averaging the corresponding point-dipole expression over the configurational distribution of the particles relative to their mean locations. Displacements of the relative position of the particles from its mean value which are distributed
axially symmetrically about their mean relative position vector rigorously yield the point-dipole expression that is a function of an effective relative position vector of the particles which is proportional to their actual mean relative position vector. For such displacement distributions which are spherical the proportionality factor equals the reciprocal cube root of that fraction of an excess electron located entirely within a certain sphere, having a radius equal to the distance between the mean positions of the electron and the nucleus. Such distributions yield sizeable, nonzero distributionally dependent lower bounds to all effective distances which may be determined. These bounds are shown to be essentially proportional to the mean dispersion-in-position of the excess electron. The resulting artifactitious cavity of the environment that will always seem to surround the electron is shown not to be restricted to spherical distributions.