Bosons in cigar-shaped traps: Thomas-Fermi Tonks-Girardean regime, and in between

We present a quantitative analysis of the experimental accessibility of the Tonks-Girardeau gas in present-day experiments with cigar-trapped alkalis. For this purpose we derive, using a Bethe ansatz generated local equation of state, a set of hydrostatic equations describing one-dimensional, delta -interacting Bose gases trapped in a harmonic potential. The resulting solutions cover the Entire range of atomic densities.