Mechanism of the emergence of Efimov states in the He-4 trimer

A mechanism of the emergence and disappearance of Efimov levels in the He-4 (3) trimer in response to variations in the strength of pair interaction ha s been investigated. It has been established that these levels arise from v irtual levels, which in turn appear to be descendant of (quasi)resonances a pproaching the real axis. In order to calculate resonances, including virtu al levels, a method has been used that relies on solving, at complex energy values, a boundary-value problem for the Faddeev differential equations th at corresponds to the (2 + 1 --> 2 + 1; If I + 1) scattering processes. All the calculations have been performed with the well-known HFD-B He-He inter atomic potential due to R.A. Aziz. A very strong repulsive component inhere nt in this potential at small distances between helium atoms has been appro ximated by a hard core. Special attention has been given in the present stu dy to validating the method used to calculate resonances and to studying th e range of its applicability.