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.The models of self-interacting dark matter (DM) have aroused a lot of interest in the last time [1][2][3][4][5][6][7][8][9][10][11]. DM with long-range interaction (referring hereafter as to y-interaction) seems to be able to escape several problems of ordinary cold dark matter (CDM) scenario, such as an overproduction of subhalos and cuspy density profile in them [6,8,12,13]. At the same time, an ellipticity of big halos is not spoiled at some model parameters [8]. An enhancement of annihilation signal in the Galaxy (so called Sommerfeld-Gamov-Sakharov enhancement [14-16]), considered for the first time (to our knowledge) in [17], is one more possible bonus of the models of question. Analysis of recent observations of forming galactic cluster Abell 3827 also favours self-interacting DM [18]. Origin of supermassive black holes can be connected with an existence of DM component with strong self-interaction [19]. Generally, models with dissipative form of DM as sub-component find more applications [20,21].Essential feature of cosmological evolution of y-interacting DM is a formation of atomic-like bound states by DM particles with opposite y-charges. If oppositely y-charged particles are particle (a) and anti-particle (b =ā), then they annihilate, what may drastically affect their residual density [5,12,22]. If the bound particles are different species (a and b =ā) so bound state is stable, then depending on relative amount of bound and unbound particles, as it is obtained by the period of large scale structure formation, DM dynamics