  We calculate the quartet potential energy surface for Li+NH and use it to
calculate elastic and spin-relaxation cross sections for collisions in
magnetically trappable spin-stretched states. The potential is strongly
anisotropic but spin-relaxation collisions are still suppressed by centrifugal
barriers when both species are in spin-stretched states. In the ultracold
regime, both the elastic and inelastic cross sections fluctuate dramatically as
the potential is varied because of Feshbach resonances. The
potential-dependence is considerably reduced at higher energies. The major
effect of using an unconverged basis set in the scattering calculations is to
shift the resonances without changing their general behaviour. We have
calculated the ratio of elastic and spin-relaxation cross sections, as a
function of collision energy and magnetic field, for a variety of potential
energy surfaces. Most of the surfaces produce ratios that are favorable for
sympathetic cooling, at temperatures below about 20 mK.
