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\centerline{Summary of Discussions - Session on Photorates}
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{\bf Molecular Hydrogen}
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The self-shielding of H$_2$ can be treated (Tielens \& Hollenbach 1985) through
a one-line approximation, $R_{\rm diss}=R_0\beta (\tau)e^{-kA_V}$ with
$k\approx 1.8$ for the FUV dust opacity. This is an approximation of the full
H$_2$ treatment as in Black \& van Dishoeck (1987) or Sternberg \& Dalgarno
(1989). One has
$$\beta (\tau )=\{\tau^{-1}[ln(\tau /\surd\pi )]^{-0.5}+(b/\tau )^{0.5}\} erfc(\tau b\pi^{-1}v_1^{-2})^{0.5},$$
for the optical depth $\tau > 10$, $b=9.2\times 10^{-3}/\delta v$,
$v_1=500/\delta v$, $\delta v$ the turbulent Doppler line width in km/s, and
with an approximate power series expansion for $\tau\le 10$
$$\beta (\tau)=\Sigma_{n=0}^{\infty}{{(-1)^n\tau^n}\over{n!(n+1)^{1/2}\pi^{n/2}}}.$$
Note that there is a correction for a sphere versus a slab geometry caused by
the dust attenuation length of UV photons that is different (see J\"urgen's
comments) and that it is difficult to find a simple scaling for shielding
effects because $G_0/n_{\rm H}$ alone does not determine the H-H$_2$
transition if the chemical and thermal balance are treated self-consistently.

An important issue is the impact of line overlap. It is unclear at this point
in time whether the Draine \& Bertoldi (1996) treatment of H$_2$ line overlap
is sufficient when compared to Gary's 'big molecule' computation. This should
be resolved. It is also important to assess the contribution of the many
atomic lines that Gary includes and others do not (see also Gary's and
Jacques' contributions in Marco's powerpoint presentation).
In any case, for $G_0/n_{\rm H}>1$ the importance of self-shielding is
diminished and dust attenuation plays a greater role, rendering the one-line
approximation better (see also Mark's and Jacques' comments in Marco's
powerpoint presentation).
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{\bf Photorates with Depth}
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As to photorates, one should determine thin rates with
$$\int I(\lambda) \sigma (\lambda) d\lambda ,$$
where $\sigma$ is the cross section for the photo-process, $I$ is the radiation
field and $\lambda$ is the wavelength. The use of a fit is dangerous when the
impinging radiation field is scaled only with total energy, say between 6-13.6
eV, while its spectral content also changes. It is important
to realize that the impinging radiation field cannot always be parameterized
accurately with the Draine or Habing radiation field because of the temperature
of the illuminating star or the presence of strong absorption features when
the stellar radiation field traverses circumstellar and
interstellar matter (see John's comments).
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{\bf Line Transfer}
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Finally, for line transfer it is important to realize that the geometry can
have a big impact on the level populations. For example, an optically thick,
effectively thin line has more population in its upper level for a sphere than
for a slab, for the same temperature distribution, because the warm edge of a
PDR subtends a larger solid angle in the spherical case. When the line optical
depth becomes much larger than one, for an effectively thin line, significant
differences can occur in the rate of convergence for Monte Carlo versus ALI
methods. Any numerical tests in this respect should concentrate on the level
populations rather than just the radiation temperature or total intensity.

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