Knowledge Bank

Nuclear spin conversion interaction of the water ion, H$2$O$+$, has been studied to derive the spontaneous emission lifetime between the {\em ortho}- and {\em para}-levels. The H$2$O$+$ ion is a radical with $2B1$ electronic ground state and the off-diagonal electron spin-nuclear spin interaction term, $Tab(Sa\Delta Ib+Sb\Delta Ia)$, connects {\em para} and {\em ortho} levels, because $ \Delta \mbox{\boldmath $I$} = \mbox{\boldmath $I$}_1 - \mbox{\boldmath $I$}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 {\em ortho} and {\em para} coupling channels below 900 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ caused by accidental near degeneracy of rotational levels. MG06, 2012.} For example, hyperfine components of the 4$\mathrm{<mrow\; data-mjx-texclass="ORD">2,2</mrow>}$($o$) and 3$\mathrm{<mrow\; data-mjx-texclass="ORD">3,0</mrow>}$($p$) levels mix each other by 1.2 x 10$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$ due to the near degeneracy ($\Delta E$ = 0.417 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$), but the lower lying 1$\mathrm{<mrow\; data-mjx-texclass="ORD">0,1</mrow>}$($p$) and 1$\mathrm{<mrow\; data-mjx-texclass="ORD">1,1</mrow>}$($o$) levels mix only by 8.9 x 10$\mathrm{<mrow\; data-mjx-texclass="ORD">-5</mrow>}$ because of their large separation ($\Delta E$ = 16.27 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$). In the present study, we solved the radiative rate equations including all the rotational levels below 900 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ to give the {\em o}-{\em 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 $Tr$ is 100, 60, 20 and 5 K. These results qualitatively help to understand the observed high $o$/$p$ ratio of 4.8 $\pm$ 0.5 (corresponding to the nuclear spin temperature of 21 K) toward Sgr B2, \textbf{521}, L11 (2010).} 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\sim$1cm$^{-3}$)ortheradiativetemperatureisveryhigh($T_r >$ 50K). , $in press$.}