  (abridged) We measure spectral indices for 1823 galaxies in the CNOC1 sample
of fifteen X-ray luminous clusters at 0.18<z<0.55, to investigate the
mechanisms responsible for differential evolution between the galaxy cluster
and field environments. The radial trends of D4000, Hdelta and [OII] are all
consistent with an age sequence, in the sense that the last episode of star
formation occurred more recently in galaxies farthest from the cluster center.
Throughout the cluster environment, galaxies show evidence for older mean
stellar populations than field galaxies. From the subsample of galaxies more
luminous than M_r=-18.8 + 5log h, we identify a sample of K+A galaxies, which
may result from recently terminated star formation. Corrected for a systematic
effect which results from the large uncertainties on individual spectral index
measurements, we estimate that K+A galaxies make up only 1.5 +/- 0.8 % of the
cluster sample, and 1.2 +/- 0.8 % of the field. We compare our data with
spectrophotometric models and conclude that up to 1.9 +/- 0.8 % of the cluster
population may have had its star formation recently truncated without a
starburst. However, this is still not significantly greater than the fraction
of such galaxies in the field, 3.1 +/- 1.0 %. Furthermore, we do not detect an
excess of cluster galaxies that have unambiguously undergone a starburst within
the last 1 Gyr. Our results imply that these cluster environments are not
responsible for inducing starbursts; thus, the increase in cluster blue galaxy
fraction with redshift may not be a strictly cluster--specific phenomenon. We
suggest that the truncation of star formation in clusters may largely be a
gradual process, perhaps due to the exhaustion of gas in the galactic disk over
fairly long timescales.
