  We report results for reaction and vibrational quenching of the collision D
with para-H$_2$($v,j=0$) and ortho-H$_2$($v,j=1$) at cold and ultracold
temperatures. We investigate the effect of nuclear spin symmetry for barrier
dominated processes ($0\le v\le 4$) and for one barrierless case ($v=5$). We
find resonant structures for energies in the range corresponding to 0.01--10 K,
which depend on the nuclear spin of H$_2$, arising from contributions of
specific partial waves. We discuss the implications on the results in this
benchmark system for ultracold chemistry.
