Notes. Polynomials of degree 4 are used; they are of the form aP⁴ + bP³ + cP² + dP + e, with P = lnU_imp where U_imp is the bulk speed of the impinging solar wind particle (either H⁺ or He²⁺) in m s^-1. Resulting analytical cross sections are in units of m². Fits are performed for H⁺ on the calculations of Mada et al. (2007) increased by 25% to match the measured value of Lindsay et al. (1997) at 1.5 keV energy. For He²⁺, we fitted the measured values of Greenwood et al. (2004). Because low-energy cross sections are not available, these fits are valid for speeds above 60 km s^-1 (100 km s^-1) for H⁺ (He²⁺) impact on H₂O. We take the cross sections to be 0 when the extrapolated cross-section fit returns negative values.