  We have used the Low Resolution Imaging Spectrograph (LRIS) on the W.M. Keck
I telescope to obtain spatially resolved spectroscopy of a small sample of six
post-starburst and three dusty-starburst galaxies in the rich cluster CL0016+16
at z=0.55. We use this to measure radial profiles of the Hdelta and OII3727
lines which are diagnostic probes of the mechanisms that give rise to the
abrupt changes in star-formation rates in these galaxies. In the post-starburst
sample we are unable to detect any radial gradients in the Hdelta line
equivalent width - although one galaxy exhibits a gradient from one side of the
galaxy to the other. The absence of Hdelta gradients in these galaxies is
consistent with their production via interaction with the intra-cluster medium,
however, our limited spatial sampling prevents us from drawing robust
conclusions. All members of the sample have early type morphologies, typical of
post-starburst galaxies in general, but lack the high incidence of tidal tails
and disturbances seen in local field samples. This argues against a merger
origin and adds weight to a scenario where truncation by the intra-cluster
medium is at work. The post-starburst spectral signature is consistent over the
radial extent probed with no evidence of OII3727 emission and strong Hdelta
absorption at all radii i.e. the post-starburst classification is not an
aperture effect. In contrast the dusty-starburst sample shows a tendency for a
central concentration of OII3727 emission. This is most straightforwardly
interpreted as the consequence of a central starburst. However, other
possibilities exist such as a non-uniform dust distribution (which is expected
in such galaxies) and/or a non-uniform starburst age distribution. The sample
exhibit late type and irregular morphologies.
