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The low-temperature (up to about 100K) collisional (de)excitation crosssections are computed using the full coupled-channel (CC) quantum dynamics forboth Li$_2$ and Li$_2^+$ molecular targets in collision with $^4$He. Theinteraction forces are obtained from fairly accurate {\it ab initio}calculations and the corresponding pseudo-rates are also computed. The resultsshow surprising similarities between sizes of inelastic flux distributionswithin final states in both systems and the findings are connected with thestructural change in the molecular rotor features when the neutral species isreplaced by its ionic counterpart.

Rotational cooling efficiency upon molecular ionization: the case of Li$_2(a^3\Sigma_u^+)$ and Li$_2^+(X^2\Sigma_g^+)$ interacting with $^4$He