  We test here the first stage of a route of modifications to be applied to the
public GADGET2 code for dynamically identifying accretion centers during the
collision process of two adjacent and identical gas cores. Each colliding core
has a uniform density profile and rigid body rotation; its mass and size have
been chosen to represent the observed core $L1544$; for the thermal and
rotational energy ratios with respect to the potential energy, we assume the
values $\alpha=0.3$ and $\beta=0.1$, respectively. These values favor the
gravitational collapse of the core. We here study cases of both -head-on and
off-center collisions, in which the pre-collision velocity increases the
initial sound speed of the barotropic gas by up to several times. In a
simulation the accretion centers are formed by the highest density particles,
so we here report their location and properties in order to realize the
collision effects on the collapsing and colliding cores. In one of the models
we observe a roughly spherical distribution of accretion centers located at the
front wave of the collision. In a forthcoming publication we will apply the
full modified GADGET code to study the collision of turbulent cores.
