A new method for calculation of Efimov resonances

The recent observation of Efimov resonances in a cold gas [1] opens a new field. We have developed a method to calculate accurately the positions, widths and wave functions of three-body resonances. The calculations combine the hyperspherical adiabatic approach [2] and the slow variable discretization method of Ref.[3]. A sine grid basis set is used with a mapping procedure to introduce a variable grid step in the hyper-radius and in the two hyperangles; moreover, a complex absorbing potential is introduced. The method can be used to determine accurately both the short range and the long range wavefunctions. It has been checked on a model potential and compared with a R-matrix method [4] which necessitates a much larger basis set: the two calculations are in good agreement. [1] T. Kraemer \textit{et al.}, Nature \textbf{440}, 315 (2006), [2] V.Kokoouline and F.Masnou-Seeuws, Phys. Rev. A \textbf{73}, 012702 (2006), [3] O.I.Tolstikhin, S.Watanabe, and M.Matsuzawa, J. Phys. B: At. Mol. Opt. Phys. \textbf{29}, L389 (1996), [4] E. Nielsen, H. Suno, and B. D. Esry, Phys. Rev. A \textbf{66}, 012705 (2002).