The emissivity (power per unit volume,
erg cm-3 s-1)
for an optically thin
spectral line at wavelength 
is
given by:
where 
s-1) is the Einstein
spontaneous emission
coefficient (A value); 
is the
electron number density (cm-3);
Nj(X+m) is the number density of the level
j of the
ion X+m:
where 
is the population of level j relative to the
total N(X+m)
number density of ion X+m and is a function
of the electron
temperature and density;
is the ionization ratio of ion
X+m
which is predominantly a function of temperature;
is the element abundance relative to hydrogen
which varies in different
astrophysical plasmas and also in different solar
features;
is the hydrogen abundance relative to electron
density (
).
The flux at the Earth (erg cm-2 s-1)
in a spectral line is given by:
where V is the volume of emission and R is the earth-to-object distance.
In low density plasmas the collisional excitation processes are generally faster than ionization and recombination timescales, therefore the collisional excitation is dominant over ionization and recombination in populating excited states. The low lying level populations can then be treated separately from the ionization and recombination processes.
The number density population of level j must be calculated by solving the statistical equilibrium equations for a number of low lying levels and including all the important collisional and radiative excitation and de-excitation mechanisms:
with 
and 
the electron and proton
collisional excitation rate coefficients
(cm3 s-1), Rj,i the stimulated
absorption
rate coefficient (s-1) and Aj,i
the spontaneous radiation transition probability
(s-1).
In this release of CHIANTI, we do not include proton excitation rates, which are important for fine structure transitions in highly ionized systems. An extensive review of theoretical work, together with recommended data has been compiled by Copeland et al. (1996).
The ratios of emission line intensities provide a multitude of spectroscopic diagnostics for determining the plasma parameters. Extensive reviews have recently been provided by Mason & Monsignori Fossi (1994), Dwivedi (1994) and Doschek (1997),
together with a very useful bibliography by Keenan (1996).