Atomic Scattering in 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.Comment: 5 pages, 2 figures; list of atoms - candidates for the Tonks gas realisation is restricted to the positive scatt. length; Cs is excluded from the list; some new references added; minor changes in the text; accepted in PRL June 22, 199

A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model

We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $\delta$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasi-momenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength $\gamma_c\simeq 3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths