Quadrupole association and dissociation of hydrogen in the early Universe

Radiative association and photodissociation rates are calculated for quadrupole transitions of H₂. A complete set of bound and unbound states are included in a self-consistent master equation to obtain steady-state concentrations for a dilute system of hydrogen atoms and molecules. Phenomenological rate constants computed from the steady-state concentrations satisfy detailed balance for any combination of matter and radiation temperature. Simple formulas are derived for expressing the steady-state distributions in terms of equilibrium distributions. The rate constant for radiative association is found to be generally small for all temperature combinations. The photodissociation rate constant for quadrupole transitions is found to dominate the rate constants for other H₂ photodestruction mechanisms for T_R ≤ 3000 K. Implications for the formation and destruction of H₂ in the early Universe are discussed.