  Matched resolution multi-frequency VLA observations of four radio galaxies
are used to derive the asymptotic low energy slope of the relativistic electron
distribution. Where available, low energy slopes are also determined for other
sources in the literature. They provide information on the acceleration physics
independent of radiative and other losses, which confuse measurements of the
synchrotron spectra in most radio, optical and X-ray studies. We find a narrow
range of inferred low energy electron energy slopes, n(E)=const*E^-2.1 for the
currently small sample of lower luminosity sources classified as FRI (not
classical doubles). This distribution is close to, but apparently inconsistent
with, the test particle limit of n(E)=const*E^-2.0 expected from strong
diffusive shock acceleration in the non-relativistic limit. Relativistic shocks
or those modified by the back-pressure of efficiently accelerated cosmic rays
are two alternatives to produce somewhat steeper spectra. We note for further
study the possiblity of acceleration through shocks, turbulence or shear in the
flaring/brightening regions in FRI jets as they move away from the nucleus.
Jets on pc scales and the collimated jets and hot spots of FRII (classical
double) sources would be governed by different acceleration sites and
mechanisms; they appear to show a much wider range of spectra than for FRI
sources.
