Complex scaling of the hyper-spheric coordinates and Faddeev equations

Abstract

We implement complex scaling of Faddeev equations using hyper-spheric coordinates and adiabatic expansion. Complex scaling of coordinates allows convenient calculations of three-body resonances. We derive the necessary equations and investigate the adiabatic spectrum at large distances. We illustrate the viability of the implementation by calculations of several three-body resonances: a $0^{+}$ resonance in a model benchmark system of three identical bosons; the $2^{+}$ resonance in the ${}^6$He nucleus within the $\alpha +n+n$ model; and the two $0^{+}$ resonances in ${}^{12}$C within the three-$\alpha$ model.

20 pages, 10 figures