  We have reviewed the chemistry and cooling behaviour of low-density (n<10^4
cm^-3) primordial gas and devised a cooling model wich involves 19 collisional
and 9 radiative processes and is applicable for temperatures in the range (1 K
< T < 10^8 K). We derived new fits of rate coefficients for the
photo-attachment of neutral hydrogen, the formation of molecular hydrogen via
H-, charge exchange between H2 and H+, electron detachment of H- by neutral
hydrogen, dissociative recombination of H2 with slow electrons,
photodissociation of H2+, and photodissociation of H2. Further it was found
that the molecular hydrogen produced through the gas-phase processes, H2+ + H
-> H2 + H+, and H- + H -> H2 + e-, is likely to be converted into its para
configuration on a faster time scale than the formation time scale. We have
tested the model extensively and shown it to agree well with former studies. We
further studied the chemical kinetics in great detail and devised a minimal
model which is substantially simpler than the full reaction network but
predicts correct abundances. This minimal model shows convincingly that 12
collisional processes are sufficient to model the H, He, H+, H-, He+, He++, and
H2 abundances in low density primordial gas for applications with no radiation
fields.
