We have found that the distribution of X-ray core radii for clusters i
n bimodal systems, subclusters nearly equal in luminosity which are se
parated by approximately 1 Mpc in projection, have a larger mean value
(0.53 Mpc) than various comparison samples consisting of clusters wit
h and without optical or X-ray substructure (mean core radius of 0.26
Mpc). There is 0.01%-0.3% probability that the bimodal and any of the
comparison samples are related using the core radius as a test paramet
er. If the bimodal system subclusters, which are observed before merge
r, represent the final stage prior to the hierarchical formation of th
e clusters that make up the four comparison samples, then the X-ray co
re radius of subclusters decreases during the merger process. For an i
sothermal gas or a nonisothermal gas in which the temperature profile
has a similar core radius to the density profile, a smaller X-ray core
radius indicates a more centrally concentrated cluster mass distribut
ion. Since the cluster mass distribution is dominated by dark matter,
the decrease in core radius during cluster merger may result from a ch
ange in the dark matter distribution during the merger, implying that
the mass becomes more concentrated to the center of the cluster. Compa
rison of the results to various n-body simulations and to the mean opt
ical core radius implies that rich clusters may be characterized by a
constant mass-to-light ratio before merger, and by a mass-to-light rat
io that is higher in the central region after merging.