Among a total of 158 flares in which the soft X-ray morphologies present a single loop or a single-loop-dominated structure, about 16% show a redshift in the Ca XIX resonance line. The number distribution of redshifted events on the solar disk exhibits a limb-increasing tendency. Having analyzed the implications of redshifts, we find only seven events in which the redshifts may marginally be the result of mass downflows along the loop, while the redshifts in the other events can be explained either by the model of chromospheric evaporation or by the contribution of satellite lines to the resonance line. For the events with redshifts manifesting the downflows, the redshift takes place mainly in the wing of the line, the redshift appears just at the beginning of the rising phase, and the duration of the redshift is from less than 10 s to several tens of seconds. These downflows may be related to the thermal energy release in the loop with a high initial coronal density.
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