(Abridged) We trace the interaction processes of galaxies at intermediate redshift by measuring the irregularity of their ionized gas kinematics, and investigate these irregularities as a function of the environment (cluster versus field) and of morphological type (spiral versus irregular). Our sample consists of 92 distant galaxies. 16 cluster (z~0.3 and z~0.5) and 29 field galaxies (mean z=0.44) of these have velocity fields with sufficient signal to be analyzed. We find that the fraction of galaxies that have irregular gas kinematics is remarkably similar in galaxy clusters and in the field at intermediate redshifts. The distribution of the field and cluster galaxies in (ir)regularity parameters space is also similar. On the other hand galaxies with small central concentration of light, that we see in the field sample, are absent in the cluster sample. We find that field galaxies at intermediate redshifts have more irregular velocity fields as well as more clumpy and less centrally concentrated light distributions than their local counterparts. Comparison with a SINS sample of 11 z ~ 2 galaxies shows that these distant galaxies have more irregular gas kinematics than our intermediate redshift cluster and field sample. We do not find a dependence of the irregularities in gas kinematics on morphological type. We find that two different indicators of star formation correlate with irregularity in the gas kinematics. More irregular gas kinematics, also more clumpy and less centrally concentrated light distributions of spiral field galaxies at intermediate redshifts in comparison to their local counterparts indicate that these galaxies are probably still in the process of building their disks via mechanisms such as accretion and mergers. On the other hand, they have less irregular gas kinematics compared to galaxies at z ~ 2.
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