Mg-H+ charge transfer and Mg line intensities in gaseous nebulae

Cross-sections have been computed for the charge-transfer reaction Mg(H+, H) Mg+. The electronic wavefunction was expanded as a linear combination of molecular orbitals, incorporating a common translation factor to account for the relative nuclear motion. In the domain of energies relevant to gaseous nebulae (⁠|(1 kT2)|⁠), charge transfer occurs into the 4s and 3p states of Mg+. Transfer into the 3p state proceeds via coupling to an intermediate molecular state, which correlates with H+Mg+(4s) at long range. As a consequence, there is pronounced ‘resonance’ structure in the variation of the charge-transfer cross-section with the collision energy. Rate coefficients are presented for thermal energies between 5000 and 30 000 K. The reaction is rapid enough (⁠|k = 1.9× 10⁻¹⁰cm³ s⁻¹| at 10 000 K) to ensure that only very weak Mg I lines are seen in planetary nebulae. From photo-ionization models (which include this process) of four nebulae, it is concluded that Mg abundances which derive from Mg I, Mg II or Mg V agree in any one nebula to within a factor 2. The mean derived abundance relative to oxygen, Mg/O=0.024, is only a factor 2 below the solar value. In our sample, which includes both high- and low-excitation nebulae, magnesium is probably depleted into grains (by factors between 1.3 and 4.0 only). Our results do not confirm the existence of a Mg-abundance gradient within nebulae.