  We have performed experimental investigations of methanol formation via the
reactions of low energy $CH_{3}^{+}$ ions with an amorphous solid water (ASW)
surface around 10 K. A newly developed experimental apparatus enabled
irradiation of the ASW surface by several eV ions and detection of trace
amounts of reaction products on the surface. It was found that methanol
molecules were produced by low-energy $CH_{3}^{+}$ irradiation of the ASW
surface and that hydroxy groups in produced methanol originated from water
molecules in ASW, as predicted in a previous theoretical study. Little
temperature dependence of observed methanol intensity is apparent in the
temperature range 12 - 60 K. Ab-initio molecular dynamics simulations under
constant temperature conditions of 10 K suggested that this reaction
spontaneously produced a methanol molecule and an $H_{3}O^{+}$ ion, regardless
of the contact point of $CH_{3}^{+}$ on the ASW surface. We have performed
simulation with an astrochemical model under molecular-cloud conditions, where
the reaction between $CH_{3}^{+}$ and $H_{2}O$ ice, leading to methanol
formation, was included. We found that the impact of the reaction on methanol
abundance was limited only at the edge of the molecular cloud (< 1 mag) because
of the low abundance of $CH_{3}^{+}$ in the gas phase, whereas the reaction
between the abundant molecular ion $HCO^{+}$ and $H_{2}O$ ice, which has not
yet been confirmed experimentally, can considerably affect the abundance of a
complex organic molecule. This work sheds light on a new type of reaction
between molecular ions and ice surfaces that should be included in
astrochemical models.
