Dipole transitions in the bound rotational-vibrational spectrum of the heteronuclear molecular ion HD${}^{+}$

The nonrelativistic three-body Schrödinger equation of the heteronuclear molecular ion HD${}^{+}$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states $v=0–3$ are calculated for total orbital momenta from 0 to 47. Energies are given with an accuracy from about 12 digits for the lowest vibrational level to at least nine digits for the third vibrational excited level. With a simple calculation using the corresponding wave functions, accurate dipole transition probabilities per time unit between those levels are given over the whole $v=0–3$ rotational bands. Results are presented with six significant figures.

Figure 1

Four lowest ${\Sigma }_g$ rotational bands of the HD${}^{+}$ molecular ion. The two dissociation energies $E_d^{{\mathrm{H}+\mathrm{D}}^{+}}$ and $E_d^{{\mathrm{D}+\mathrm{H}}^{+}}$ can not be distinguished.

Figure 2

Oscillator strengths for $L_f=L_i+1$ transitions.

Figure 3

Oscillator strengths for $L_f=L_i-1$ transitions.

Figure 4

Lifetimes $\tau$ in seconds for the first four rotational bands ($v=0–3$).