  Motivated by the physical relevance of a spectral singularity of interacting
many-particle system, we explore the dynamics of two bosons as well as fermions
in one-dimensional system with imaginary delta interaction strength. Based on
the exact solution, it shows that the two-particle collision leads to
amplitude-reduction of the wave function. For fermion pair, the
amplitude-reduction depends on the spin configuration of two particles. In both
cases, the residual amplitude can vanish when the relative group velocity of
two single-particle Gaussian wave packets with equal width reaches the
magnitude of the interaction strength, exhibiting complete particle-pair
annihilation at the spectral singularity.
