  Dark Matter (DM) is generally assumed to be massive, cold and collisionless
from the structure formation point of view. A more correct statement however is
that DM indeed experiences collisional damping, but on a scale which is
supposed to be too small to be relevant for structure formation. The aim of
this paper is to present a Cold (although ``collisional'') Dark Matter particle
whose matter power spectrum is damped and see whether it is distinguishable
from standard candidates. To achieve this purpose, we calculate the collisional
damping and free-streaming scales of neutralinos and non conventional
candidates (say light particles heavier than ~1 MeV but lighter than O(10)
GeV). The latter can be considered as Cold Dark Matter (CDM) particles in the
sense that they become non relativistic before their thermal decoupling epoch.
Unlike neutralinos, however, their linear matter power spectrum can be damped
on scales of ~ 10^3 Msol due to their interactions. Since these scales are of
cosmological interest for structure formation, we perform a series of numerical
simulations to obtain the corresponding non linear matter power spectra
P(k)_{nl} at the present epoch. We show that because of small scale
regeneration, they all resemble each other at low redshifts, i.e. become very
similar to a typical CDM matter power spectrum on all but the smallest scales.
Therefore, even if lensing measurements at redshift below unity were to yield a
P(k)_{nl} consistent with CDM models, this would not constitute a sufficiently
robust evidence in favour of the neutralino to rule out alternative DM
candidates.
