Ortho–Para Mixing Hyperfine Interaction in the H₂O⁺ Ion and Nuclear Spin Equilibration

Abstract

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.

HERSCHELSURVEY OF GALACTIC OH+, H2O+, AND H3O+: PROBING THE MOLECULAR HYDROGEN FRACTION AND COSMIC-RAY IONIZATION RATE

“…In all cases, within uncertainties the OPR is consistent with a value of 3, the ratio expected in the high temperature limit based solely on nuclear spin statistical weights. While it is possible that reactive collisions, temperature, forbidden spontaneous emission (Tanaka et al 2013), and state-specific formation and destruction can skew the OPR away from 3, observations thus far have not conclusively demonstrated any such deviations in the diffuse ISM (Gerin et al 2013;Schilke et al 2013).…”

OH+and H2O+absorption toward PKS 1830–211

“…Tanaka et al (2013) looked into the ortho to para exchange from the spectroscopic point of view. They found several transitions that could facilitate such an exchange.…”

Interstellar processes: Ortho/para conversion, radiative association, and dissociative recombination

“…The ortho rotational states also show hyperfine structure. The strongly allowed transitions maintain the nuclear spin (para-para, ortho-ortho); transitions between para and ortho rotational states are very weakly allowed, but possibly detectable if nuclear spin is coupled to electronic spin, as occurs in radicals or ions such as H 2 O + [10]. In the absence of any constraints, the number of ortho states populated should be three times the number of para states for molecules with two identical protons, so that the ortho-to-para ratio (OPR) is exactly three [11].…”

“…None of these values equals the observed value of 4.8! In a final attempt to reproduce the observed OPR in diffuse clouds toward the galactic center, Tanaka et al [10] studied the possibility that, as the ortho and para forms of H 2 O + radiatively relax down their respective ladders following their formation in the exothermic reaction between OH + and H 2 , radiative transitions can occur between ortho and para states, especially for high rotational levels that are close to degeneracy. The effect is enhanced by an intense infrared radiation field that can maintain rotational excitation.…”