Tonks-Girardeau gas, super-Tonks-Girardeau gas, and bound states of   one-dimensional bosons in a hard-wall trap
  We investigate the Bose gas with repulsive or attractive interactions between atoms in the scheme of Bethe Ansatz equation in a hard wall trap. Three typical quantum phases in the current research of 1D interacting cold atoms are clarified in terms of the energy spectrum, single particle density distribution and two-particle correlation function. We identify two matching points in the phase diagram, i.e. the TG and STG gas show the same profiles at the strongly interacting point $-1/\gamma=0$, and in the weakly interacting limit $\gamma=0$ the ground states TG and BS join to each other smoothly. 
Hua Li, Taifeng Liu, Yaojiang Hao and Yunbo Zhang
cond-mat.quant-gas quant-ph