Properties of the Hydrogen Molecular Ion I: Quadrupole Transitions in the Ground Electronic State and Dipole Transitions of the Isotopic Ions

The Einstein spontaneous emission coefficients and the oscillator strengths due to the quadrupole moment connecting the vibrational-rotational levels of H 2 + are evaluated using two-centre wave functions. All (ν', J ') - (ν'', J '') lines arising from combinations of the following values of the quantum numbers are treated: ν' = 0, 1, 2 or 3; ν'' = 0; J ' and J '' = 0, 2, 4, 6 or 8 (with Δ J = 0 ± 2). In the case of the higher harmonics serious cancellation occurs in certain of the integrations, but the results should be reliable as the calculations do not involve approximations. The dipole transitions of the isotopic ions are also investigated, though less fully.