  A Sturmian theory of three-body recombination is presented which provides a
unified treatment of bound states, quasi-bound states, and continuum states.
The Sturmian representation provides a numerical quadrature of the two-body
continuum which may be used to generate a complete set of states within any
desired three-body recombination pathway. Consequently, the dynamical
calculation may be conveniently formulated using the simplest energy transfer
mechanism, even for reactive systems which allow substantial rearrangement. The
Sturmian theory generalizes the quantum kinetic theory of Snider and Lowry [J.
Chem. Phys. 61, 2330 (1974)] to include metastable states which are formed as
independent species. Steady-state rate constants are expressed in terms of a
pathway-independent part plus a non-equilibrium correction which depends on
tunneling lifetimes and pressure. Numerical results are presented for H$_2$
recombination due to collisions with H and He using quantum mechanical coupled
states and infinite order sudden approximations. These results may be used to
remove some of the uncertainties that have limited astrophysical simulations of
primordial star formation.
