Structure of T- and S-Matrices in Unphysical Sheets and Resonances in Three-Body Systems

Abstract

Abstract. Algorithm, based on explicit representations for the analytic continuation of Faddeev components of the three-body T-matrix in unphysical energy sheets, is employed to study mechanism of disappearance and formation of the Efimov levels of the helium 4 He trimer.

The 4He Trimer as an Efimov System

“…Apparently, the most detailed numerical study of the nature of the excited state in the 4 He trimer has been performed in [58] (see also [91] and [92]). Notice that the Aziz et al potential [13] was employed in [58] and the number of the partial-wave Faddeev components was reduced to one.…”

Resonances in the three-neutron system

“…In the framework of the hyperspherical harmonic method and using complex scaling with model potentials a subthreshold 3n resonance for J π = 1/2 − has been located in [11]. Recently mathematical foundations have been laid on the analytical continuation of the three-body Faddeev equations into unphysical energy sheets [12] and an application thereof to the 4 He trimer appeared in [13].…”

Ultracold Scattering and Universal Correlations

“…When the scattering length is large and negative, the virtual state turns into a bound state. We studied this mechanism in detail in [11]. In this limit of the large but negative scattering length the linear dependence is again restored.…”

“…In this case, we study graph surfaces of the real and imaginary parts of the scattering matrix S 0 (z) in the domain of its holomorphy (curve 1 on Fig. 2, see for details [11]). The root lines of the functions Re S 0 (z) and Im S 0 (z) presented in Fig.…”