  We discuss pair interatomic collisions in a Bose gas tightly confined in one
(axial) direction and identify two regimes of scattering. In the quasi2D
regime, where the confinement frequency $\omega_0$ greatly exceeds the gas
temperature $T$, the scattering rates exhibit 2D features of the particle
motion. At temperatures $T\sim\hbar\omega_0$ one has a confinement-dominated 3D
regime, where the confinement can change the momentum dependence of the
scattering amplitudes. We describe the collision-induced energy exchange
between the axial and radial degrees of freedom and analyze recent experiments
on thermalization and spin relaxation rates in a tightly (axially) confined gas
of Cs atoms.
