  The ionization fraction is an important factor in determining the chemical
and physical evolution of star forming regions. In the dense, dark starless
cores of such objects, the ionization rate is dominated by cosmic rays; it is
therefore possible to use simple analytic estimators, based on the relative
abundances of different molecular tracers, to determine the cosmic ray
ionization rate.
  This paper uses a simple model to investigate the accuracy of two well-known
estimators in dynamically evolving molecular clouds. It is found that, although
the analytical formulae based on the abundances of H3+,H2,CO,O,H2O and HCO+
give a reasonably accurate measure of the cosmic ray ionization rate in static,
quiescent clouds, significant discrepancies occur in rapidly evolving
(collapsing) clouds. As recent evidence suggests that molecular clouds may
consist of complex, dynamically evolving sub-structure, we conclude that simple
abundance ratios do not provide reliable estimates of the cosmic ray ionization
rate in dynamically active regions.
