  The active Phase-Field-Crystal (aPFC) model combines elements of the Toner-Tu
theory for self-propelled particles and the classical Phase-Field-Crystal (PFC)
model that describes the transition between liquid to crystalline phases. In
the liquid-crystal coexistence region of the PFC model, crystalline clusters
exist in the form of localized states that coexist with the homogeneous
background. At sufficiently strong self-propulsion strength (or activity) they
start to travel. We employ numerical path continuation and direct time
simulations to first investigate the existence regions of different types of
localized states for a one-dimensional system. The results are summarized in
morphological phase diagrams in the parameter plane spanned by activity and
mean concentration. Then we focus on the interaction of traveling localized
states studying their collision behavior. As a result we distinguish 'elastic'
and 'inelastic' collisions. In the former, localized states recover their
properties after a collision while in the latter they may annihilate or form
resting or traveling bound states. In passing, we describe oscillating and
modulated traveling localized states that have as the steadily traveling
localized states no counterpart in the classical PFC model.
