  A series of Multichannel Quantum Defect Theory-based computations have been
performed, in order to produce the cross sections of rotational transitions
(excitations $N_{i}^{+}-2 \rightarrow$ $N_{i}^{+}$, de-excitations $N_{i}^{+}$
$\rightarrow$ $N_{i}^{+}-2$, with $N_{i}^{+}=2$ to $10$) and of their
competitive process, the dissociative recombination, induced by collisions of
HD$^+$ ions with electrons in the energy range $10^{-5}$ to 0.3 eV. Maxwell
anisotropic rate coefficients, obtained from these cross sections in the
conditions of the Heidelberg Test Storage Ring (TSR) experiments
($k_{B}T_{t}=2.8$ meV and $k_{B}T_{l}=45$ $\mu$eV), have been reported for
those processes in the same electronic energy range. Maxwell isotropic rate
coefficients have been as well presented for electronic temperatures up to a
few hundreds of Kelvins. Very good overall agreement is found between our
results for rotational transitions and the former theoretical computations as
well as with experiment. Furthermore, owing to the full rotational computations
performed, the accuracy of the resulting dissociative recombination cross
sections is considerably improved.
