Interatomic collisions in a tightly confined Bose gas

We discuss binary atomic collisions in a Bose gas tightly confined in one (axial) direction and identify two regimes of scattering. In the quasi-two-dimensional (quasi-2D) 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 $T\sim ħ{\omega }_0$ 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.