A new series of computations has been performed to obtain cross-sections and rate coefficients for state-to-state rotational transitions in the H$$_{2}^{+}$$ ion, induced by collisions with very low-energy electrons. Following our recent work on the HD⁺ ion (Motapon et al. 2014), and using the same molecular structure data sets, excitations $$N_{i}^{+} \rightarrow$$ $$N_{i}^{+}+2$$ for $$N_{i}^{+}=0$$ to 10, and de-excitations $$N_{i}^{+}$$ → $$N_{i}^{+}-2$$, for $$N_{i}^{+}=2$$ to 10, in the energy range 0.01 meV–0.3 eV, have been explored. The calculated cross-sections have been convolved in order to obtain Maxwell rate coefficients for electronic temperatures up to a few hundred of Kelvin. Moreover, Maxwell rate coefficients for dissociative recombination have been calculated for the same initial rotational levels.

The non-relativistic static and dynamic dipole polarizabilities of a hydrogen atom experiencing a cylindrical confinement are investigated. Two methods based on B-splines are used for computations of energies and wavefunctions. The first method is a variational-based method while the second one proceeds by a fit of the non-separable Coulomb potential in the product form. The computed energies compare very well with previous computations. They converge, as well as the dipole polarizability, to the exact unconfined free atom values with increasing basis size. The fit approach is found to be advantageous, as it helps to reduce the computational time without loss of accuracy.

We present calculations of cross sections and rate coefficients for the dissociative recombination of ${\mathrm{H}}_2^{+}$ ions initially in $v=0\mathrm{}–6$ vibrational levels, together with rate coefficients for the competing electron-induced vibrational deexcitation. We used the multichannel quantum defect theory with a second-order treatment of the K matrix, and show that electronic interactions dominate not only the dissociative recombination but also the vibrational relaxation induced by slow electrons. Most of our rate coefficients for dissociative recombination are in good agreement with the measurements at the TSR storage ring [S. Krohn et al., Phys. Rev. A 62, 032713 (2000)]. On the contrary, our rates for vibrational deexcitation, close to former results obtained by R-matrix calculations [B. K. Sarpal and J. Tennyson, Mon. Not. R. Astron. Soc. 263, 909 (1993)], are smaller by up to one order of magnitude than the experimental values which are deduced from the time evolution of the vibrational populations, measured by the Coulomb explosion imaging method.