We present results of quantum mechanical scattering calculations on the vib
rational relaxation of CO induced by collisions with He-3 at ultracold temp
eratures and compare them with the corresponding results for the He-4-CO sy
stem. The low energy cross sections are controlled by shape resonances supp
orted by the van der Waals well. For a thermal rotational population the cr
oss sections for the quenching of the v=1 vibrational level are larger for
He-3 than for He-4 collisions. Because of the absence of a Feshbach resonan
ce, the cross sections at low energies for the quenching of the j=1 rotatio
nal level are much smaller than those for He-4-CO. Very good agreement is f
ound for the rate coefficients for the vibrational relaxation of the v=1 le
vel with the measurement data that are available at temperatures above 35 K
. There are small discrepancies between the calculated rate coefficients wi
th earlier calculations for the relaxation of the v=1 vibrational level, si
milar to those found for He-4-CO collisions, but the discrepancies tend to
be larger with decrease of temperature. (C) 2001 American Institute of Phys
ics.