  Two different ab initio potential energy surfaces are employed to investigate
the efficiency of the rotational excitation channels for the polar molecular
ion HeH$^+$ interacting with He atoms. We further use them to investigate the
quantum dynamics of both the proton-exchange reaction and the purely rotational
inelastic collisions over a broad range of temperatures. In current modeling
studies, this cation is considered to be one of the possible cooling sources
under early universe conditions after the recombination era and has recently
been found to exist in the Interstellar Medium. Results from the present
calculations are able to show the large efficiency of the state-changing
channels involving rotational states of this cation. In fact, we find them to
be similar in size and behaviour to the inelastic and to the reaction rate
coefficients obtained in previous studies where H atoms were employed as
projectiles. The same rotational excitation processes, occurring when free
electrons are the collision partners of this cation, are also compared with the
present findings. The relative importance of the reactive, proton-exchange
channel and the purely inelastic channels is also analysed and discussed. The
rotational de-excitation processes are also investigated for the cooling
kinetics of the present cation under cold trap conditions with He as the buffer
gas. The implications of the present results for setting up more comprehensive
numerical models to describe the chemical evolution networks in different
environments are briefly discussed.
