Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons

We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated “cigar”-shaped atomic trap. We show that, in the low-energy scattering regime, the scattering process degenerates to a total reflection, suggesting an experimental realization of a famous model in theoretical physics—a one-dimensional gas of impenetrable bosons (“Tonks” gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.