  Cold dark matter (DM) scenario may be cured of several problems by involving
self-interaction of dark matter. Viability of the models of long-range
interacting DM crucially depends on the effectiveness of recombination of the
DM particles, making thereby their interaction short-range. Usually in numeric
calculations, recombination is described by cross section obtained on a
feasible quantum level. However in a wide range of parameter values, a
classical treatment, where the particles are bound due to dipole radiation, is
applicable. The cross sections, obtained in both approaches, are very different
and lead to diverse consequences. Classical cross section has a steeper
dependence on relative velocity, what leads to the fact that, after decoupling
of DM particles from thermal background of "dark photons" (carriers of DM
long-range interaction), recombination process does not "freeze out",
diminishing gradually density of unbound DM particles. Our simplified estimates
show, that at the taken parameter values (the mass of DM particle is $100$ GeV,
interaction constant is $100^{-1}$, and quite natural assumptions on initial
conditions, from which the result is very weakly dependent) the difference in
residual density reaches about $5$ orders of magnitude on pre-galactic stage.
This estimate takes into account thermal effects induced by dipole radiation
and recombination, which resulted in the increase of both temperature and
density of DM particles by a half order of magnitude.
