These routines make use of the fact that that most of the common ions that dominate the nebular cooling rate have either , , or ground-state electron configurations, which have five low-lying levels. The major physical assumption within this algorithm is that only these five levels are physically relevant for calculating the observed emission line spectrum; higher levels in these ions are not significantly populated through collisions, recombinations, or other mechanisms. Schematics of the energy-level diagrams for the ground electron configurations are shown in Figure 1 .

For such ions, collisional and radiative transitions can occur between any of the levels. For each excitation level for a given ion, the equations of statistical equilibrium may be written:

where is the fraction in level , is the electron density (cm), are the electron (de)excitation rate coefficients (cm s), and are the radiative transition probabilities (s). The first term on the left includes the collisional (de)excitation rate from the (upper) lower levels, and the second term gives the radiative transition rate from an upper level. The third term is the collisional (de)excitation rate from (upper) lower levels, and the last term is the radiative transition rate from the level itself.

The are independent of temperature, and are inversely proportional to the lifetimes of the upper level, but the are temperature-dependent. The de-excitation rate (i.e., ) is given by:

where is the statistical weight of level , and is the mean (dimensionless) collision strength which is temperature-dependent. The collisional excitation rate is related to the de-excitation rate via:

where is the excitation energy difference between levels
and ; and is Boltzmann's constant. It is equation **nebular** library to determine the
level populations.

The atomic data that are independent of temperature-, ,
and (the energy level separations above the ground state)-are
tabulated within the **nebular** source code and are selected at run time
for a given ion. The temperature-dependent atomic data-i.e, the collision
strengths for each transition-are computed at run time for a specified
temperature. While the collision strengths are really continuous functions
of temperature, they are often tabulated in the literature at only a few
fixed temperatures between 5000 K and 20,000 K. In the **nebular** routines,
the actual collision strengths for a given are derived from low-order
polynomial fits of the published as a function of temperature.
The allowed range of temperature in the **nebular** tasks is therefore
restricted to 2000 K <T
< 36,000 K for most ions (to avoid excessive
extrapolations of the polynomials), unless the published cross sections for a
particular ion are tabulated over a wider range. The atomic data were
generally taken from the compilation by Mendoza (1983), except where noted
in Table 1 for several ions. Note, however, that the atomic data
(particularly the cross sections) are likely to be updated in the future (see
§ 5 ).

where is the relative population in the upper level of ion , is Planck's constant, and is the frequency of the photon emitted in the transition. As the density increases, collisional de-excitation becomes important. A benchmark called the ``critical density'' for a level is defined as the density at which the collisional de-excitation rate equals the radiative transition rate. That is:

Thu Aug 8 17:23:06 EDT 1996