## Ionization Rate

In the dense clouds, the ionization fraction is low. Since the uv/optical radiations from stars can not reach the cloud center, potential ionization comes from the cosmic ray particles. In this case the rate of ionization per volume is given as , where . In Figure 4.6, the ionization fraction for various density is shown (Nakano, Nishi, & Umebayashi 2002). This clearly shows that the fraction of ions decrease approximately in proportion to for . This is understood as follows: Equilibrium balance between one kind of ion and its neutral

 (4.45)

is considered. The recombination (reaction from the right to left) rate per unit volume is expressed , while the ionization rate (left to right) per unit volume is , where means the recombination rate coefficient. Nakano (1984) obtained in the range of
 (4.46)

where the numerical factor .

Kohji Tomisaka 2009-12-10