Ortho-para mixing hyperfine interaction in the H2O+ ion and nuclear spin equilibration

The ortho to para conversion of water ion, H2O(+), due to the interaction between the magnetic moments of the unpaired electron and protons has been theoretically studied to calculate the spontaneous emission lifetime between the ortho- and para-levels. The electron spin-nuclear spin interaction term, Tab(SaΔIb + SbΔIa) mixes ortho (I = 1) and para (I = 0) levels to cause the "forbidden" ortho to para |ΔI| = 1 transition. The mixing term with Tab = 72.0 MHz is 4 orders of magnitude higher for H2O(+) than for its neutral counterpart H2O where the magnetic field interacting with proton spins is by molecular rotation rather than the free electron. The resultant 10(8) increase of ortho to para conversion rate possibly makes the effect of conversion in H2O(+) measurable in laboratories and possibly explains the anomalous ortho to para ratio recently reported by Herschel heterodyne instrument for the far-infrared (HIFI) observation. Results of our calculations show that the ortho ↔ para mixings involving near-degenerate ortho and para levels are high (∼10(-3)), but they tend to occur at high energy levels, ∼300 K. Because of the rapid spontaneous emission, such high levels are not populated in diffuse clouds unless the radiative temperature of the environment is very high. The low-lying 101 (para) and 111 (ortho) levels of H2O(+) are mixed by ∼10(-4) making the spontaneous emission lifetime for the para 101 → ortho 000 transition 520 years and 5200 years depending on the F value of the hyperfine structure. Thus the ortho ↔ para conversion due to the unpaired electron is not likely to seriously affect thermalization of interstellar H2O(+) unless either the radiative temperature is very high or number density of the cloud is very low.