  Rigorous quantum scattering calculations on ultracold molecular collisions in
external fields present an outstanding computational problem due to strongly
anisotropic atom-molecule interactions that depend on the relative orientation
of the collision partners, as well as on their vibrational degrees of freedom.
Here, we present the first numerically exact three-dimensional quantum
scattering calculations on strongly anisotropic atom-molecule (Li+CaH)
collisions in an external magnetic field based on the parity-adapted total
angular momentum representation and a new three-dimensional potential energy
surface (PES) for the triplet Li-CaH collision complex using the unrestricted
coupled cluster method with single, double and perturbative triple excitations
[UCCSD(T)] and a large quadruple-zeta type basis set. We find that while the
full three-dimensional treatment is necessary for the accurate description of
Li ($M_S=1/2$)+CaH ($v=0,N=0,M_S=1/2$) collisions as a function of magnetic
field, the magnetic resonance density and statistical properties of
spin-polarized atom-molecule collisions are not strongly affected by
vibrational degrees of freedom, justifying the rigid-rotor approximation used
in previous calculations. We observe rapid, field-insensitive vibrational
quenching in ultracold Li ($M_S=1/2$)+CaH ($v=1,N=0, M_S=1/2$) collisions,
leading to efficient collisional cooling of CaH vibrations.
