The radiation field and the molecular hydrogen photodissociation rate within spherically symmetric inhomogeneous clouds

A method is established for determining the radiation field and the H₂ photodissociation rate within spherically symmetric inhomogeneous clouds. The method initially determines the absorption due to non-scattering grains; the resulting expressions are then modified in a simple way to allow for the scattering properties of the grains. The accuracy of the procedure, where it may be compared with exact treatment, is satisfactory. In particular, the procedure has the correct behaviours in various limiting cases, and is thus an improvement on some other approximations to the radiation field which have appeared in the literature.