The paper presents a theoretical study of the low-energy dynamics of radiative association processes in the He++H-2 collision system. Formation of the triatomic HeH2+ ion in its bound rotation-vibration states on the potential-energy surfaces of the ground and of the first excited electronic states is investigated. Close-coupling calculations are performed to determine detailed state-to-state characteristics (bound <- free transition rates, radiative and dissociative widths of resonances) as well as temperature-average characteristics (rate constants, photon emission spectra) of the two-state (X <- A) reaction He+(S-2)+H-2(X(1)Sigma(g)(+))-> HeH2+(X(2)A('))+h nu and of the single-state (A <- A) reaction He+(S-2)+H-2(X(1)Sigma(g)(+))-> HeH2+(A(2)A('))+h nu. The potential-energy surfaces of the X- and A-electronic states of HeH2+ and the dipole moment surfaces determined ab initio in an earlier work [Kraemer, Spirko, and Bludsky, Chem. Phys. 276, 225 (2002)] are used in the calculations. The rate constants k(T) as functions of temperature are calculated for the temperature interval 1 <= T <= 100 K. The maximum k(T) values are predicted as 3.3x10(-15) s(-1) cm(3) for the X <- A reaction and 2.3x10(-20) s(-1) cm(3) for the A <- A reaction at temperatures around 2 K. Rotationally predissociating states of the He+-H-2 complex, correlating with the upsilon=0, j=2 state of free H-2, are found to play a crucial role in the dynamics of the association reactions at low temperatures; their contribution to the k(T) function of the X <- A reaction at T < 30 K is estimated as larger than 80%. The calculated partial rate constants and emission spectra show that in the X <- A reaction the HeH2+(X) ion is formed in its highly excited vibrational states. This is in contrast with the vibrational state population of the ion when formed via the (X <- X) reaction He(S-1)+H-2(+)(X(2)Sigma(g)(+))-> HeH2+(X(2)A('))+h nu.
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