We present a new method for the simultaneous calculation of the cosmic ray ionization rate , \zeta _ { \mathrm { H } _ { 2 } } , and the ionization fraction , \chi _ { \mathrm { e } } , in dense molecular clouds .
A simple network of chemical reactions dominant in the creation and destruction of HCNH ^ { + } and HCO ^ { + } is used in conjunction with observed pairs of rotational transitions of several molecular species in order to determine the electron abundance and the H _ { 3 } ^ { + } abundance .
The cosmic ray ionization rate is then calculated by taking advantage of the fact that , in dark clouds , it governs the rate of creation of H _ { 3 } ^ { + } .
We apply this technique to the case of the star-forming region DR21 ( OH ) , where we successfully detected the ( J = 3 \rightarrow 2 ) and ( J = 4 \rightarrow 3 ) rotational transitions of HCNH ^ { + } .
We also determine the C and O isotopic ratios in this source to be ^ { 12 } \mathrm { C / ^ { 13 } \mathrm { C } } = 63 \pm 4 and ^ { 16 } \mathrm { O / ^ { 18 } \mathrm { O = 318 \pm 64 } } , which are in good agreement with previous measurements in other clouds .
The significance of our method lies in the ability to determine N ( \mathrm { H _ { 3 } ^ { + } } ) and \chi _ { \mathrm { e } } directly from observations , and estimate \zeta _ { \mathrm { H } _ { 2 } } accordingly .
Our results , \zeta _ { \mathrm { H } _ { 2 } } = 3.1 \times 10 ^ { -18 } \ > \mathrm { s } ^ { -1 } and \chi _ { \mathrm { e } } = 3.2 \times 10 ^ { -8 } , are consistent with recent determinations in other objects .