  Ultracold collisions between spin-polarized Na atoms and vibrationally
excited Na_2 molecules are investigated theoretically, using both an inelastic
formalism (neglecting atom exchange channels) and a reactive formalism
(including atom exchange). Calculations are carried out on both pairwise
additive and non-additive potential energy surfaces for the quartet electronic
state. In both inelastic and reactive calculations, the Wigner threshold laws
are followed for energies below 10^{-6} K. It is found that vibrational
relaxation processes dominate elastic processes for temperatures below 10^{-3}
- 10^{-4} K. For temperatures below 10^{-5} K, the rate coefficients for
vibrational relaxation (v = 1 -> 0) from the full calculation are 4.8 x
10^{-11} and 5.2 x 10^{-10} cm^3 s^-1 for the additive and non-additive
potentials respectively.
