  The transition from the amplification of spontaneous emission to
superfluorescence in a three-level and swept-gain medium excited by an X-ray
free electron laser pulse is theoretically investigated. Given the specific
time scale of X-ray free electron laser pulse, we investigate the swept pumping
process in detail and our results show that the temporal structure of an X-ray
free electron laser pulse plays a more critical role than its peak intensity
does for producing population inversion. The typical watershed of two radiant
regions depends on the optical depth of the gain medium for a given coherence
time, namely, particle number density and the medium length are equally
important. However, we find that medium length plays more important role than
particle density does for making the forward-backward asymmetry. The transient
gain length and the total medium length are identified as two important factors
to observe length induced backward transition. The present results suggest an
application of parametric controls over a single-pass-amplified light source.
