  We use the Barnard 68 dark globule as a test case for a spherically symmetric
PDR model exposed to low-UV radiation fields. With a roughly spherical
morphology and an accurately determined density profile, Barnard 68 is ideal
for this purpose. The processes governing the energy balance in the cloud
surface are studied in detail. We compare the spherically symmetric PDR model
by Stoerzer, Stutzki & Sternberg (1996) to observations of the three lowest
rotational transitions of 12CO, 13CO J = 2-1 and J = 3-2 as well as the [CI]
3P_1-3P_0 fine structure transition. We study the role of Polycyclic Aromatic
Hydrocarbons (PAHs) in the chemical network of the PDR model and consider the
impact of depletion as well as of a variation of the external FUV field. We
find it difficult to simultaneously model the observed 12CO and 13CO emission.
The 12CO and [CI] emission can be explained by a PDR model with a external FUV
field of 1-0.75 chi_0, but this model fails to reproduce the observed 13CO by a
factor of ~2. Adding PAHs to the chemical network increases the [CI] emission
by 50% in our model but makes [CII] very faint. CO depletion only slightly
reduces the 12CO and 13CO line intensity (by <10% and <20%, respectively).
Predictions for the [CII] 2P_3/2-2P_1/2, [CI] 3P_2-3P_1 and 12CO J= 5-4 and 4-3
transitions are presented. This allows a test of our model with future
observations (APEX, NANTEN2, HERSCHEL, SOFIA).
