RADIATIVE LIFETIME FOR NUCLEAR SPIN CONVERSION OF WATER-ION, H_{2}O^{+}

\underline{KEIICHI TANAKA}, Department of Applied Chemistry, National Chiao Tung University, Hsinchu, 30010, TAIWAN and Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka, 812-8581 JAPAN; KENSUKE HARADA, Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka, 812-8581 JAPAN; TAKESHI OKA, Department of Astronomy and Astrophysics and Department of Chemistry, the Enrico Fermi Institute, the University of Chicago, Chicago, Illinois, 60637, USA.

Nuclear spin conversion interaction of the water ion, H_{2}O^{+}, has been studied to derive the spontaneous emission lifetime between the ortho- and para-levels. The H_{2}O^{+} ion is a radical with ^{2}B_{1} electronic ground state and the off-diagonal electron spin-nuclear spin interaction term, T_{ab}(S_{a}ΔI_{b} + S_{b}ΔI_{a}), connects para and ortho levels, because ΔI = I_{1} − I_{2} has nonvanishing matrix elements between I = 0 and 1. The T_{ab} coupling constant, derived by an ab initio calculation in MRD-CI/Bk level to be 72 MHz, is larger than that of H_{2}O by 4 orders of magnitude, makes the ortho to para conversion of H_{2}O^{+} faster than that of H_{2}O by 8 orders of magnitude and possibly competitive with other astrophysical processes. Last year we reported ortho and para coupling channels below 900 cm^{−1} caused by accidental near degeneracy of rotational levels.^{a} For example, hyperfine components of the 4_{2,2}(o) and 3_{3,0}(p) levels mix each other by 1.2 x 10^{−3} due to the near degeneracy (ΔE = 0.417 cm^{−1}), but the lower lying 1_{0,1}(p) and 1_{1,1}(o) levels mix only by 8.9 x 10^{−5} because of their large separation (ΔE = 16.27 cm^{−1}). In the present study, we solved the radiative rate equations including all the rotational levels below 900 cm^{−1} to give the o-p conversion lifetime to be 0.451, 3.27, 398 and 910 years for the equilibrium o/p ratio of 3.00, 3.00, 4.52, and 406 when the radiation temperature T_{r} is 100, 60, 20 and 5 K. These results qualitatively help to understand the observed high o/p ratio of 4.8 ± 0.5 (corresponding to the nuclear spin temperature of 21 K) toward Sgr B2,^{b} but they are too slow to compete with the reaction by collision unless the number of density of H_{2} in the region is very low (n ∼1 cm^{−3}) or the radiative temperature is very high (T_{r} > 50K). ^{c}

aK. Tanaka, K. Harada, and T. Oka, the 67th OSU Symposium MG06, 2012.

bP. Schilke, et al., A&A 521, L11 (2010).

cK. Tanaka, K. Harada, and T. Oka, J. Phys. Chem. A, in press.