Recombination of ions and electrons on grains and the ionization degree in dense interstellar clouds

We investigate the processes relevant to the recombination of ions and electrons on grains. The sticking probability of thermal electrons on grains is found to be between 0.3 and 1.0, and that of the ions about 1.0. The charge-state distribution of grains is determined as a function of the grain radius and the gas temperature, and it is found that most grains have one excess electron. With some reasonable grain models the recombination rate per unit volume per unit time of the electron and the ion X+ is given by αsub(g)n sub(H)n (X+), where n sub(H) = n (H) + 2n (H2) and n (X+) are the number densities of hydrogen and the ion X+, respectively, and αsub(g) asymptotically equals 5 x 10-17 cm3 s-1 for the metal ions. By using a simplified reaction scheme in the gas phase together with the recombination of ions and electrons on grains, the ionization degree of the gas in the steady state is investigated and it is found that the ionization degree x (e) decreases at least by a factor of 10 compared with that without grain surface recombination, and that x (e) agrees well with the values estimated from the observations without assuming the extreme depletion of metals in the gas phase. (author)