Lieb-Liniger gas in a constant force potential

We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions). The ground state properties of the gas in the wedge-like trapping potential are calculated in the strongly interacting regime by using Girardeau's Fermi-Bose mapping and the pseudopotential approach in the $1/c$-approximation ($c$ denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an $N$-dimensional Fourier transform as in the case of free expansion

Nonleptonic Ω−\Omega^{-} decays and the Skyrme model

Nonleptonic $\Omega^{-}$ decay branching ratios are estimated by means of the QCD enhanced effective weak Hamiltonian supplemented by the SU(3) Skyrme model used to estimate the nonperturbative matrix elements. The model has only one free parameter, namely the Skyrme charge $e$, which is fixed through the experimental values of the octet-decuplet mass splitting $\Delta$ and the axial coupling constant $g_{A}$. The whole scheme is equivalent to that which works well for the nonleptonic hyperon decays. The ratios of calculated amplitudes are in agreement with experiment. However, the absolute values are about twice too large if short-distance corrections and only ground intermediate states are included.Comment: 4 pages, 1 figure, 1 table, version to appear in Phys.Rev.