  Few- and many-fermion systems on the verge of stability, and consisting of
strongly interacting particles, appear in many areas of physics. The
theoretical modeling of such systems is a very difficult problem. In this work
we present a theoretical framework that is based on the rigged Hilbert space
formulation. The few-body problem is solved by exact diagonalization using a
basis in which bound, resonant, and non-resonant scattering states are included
on an equal footing. Current experiments with ultracold atoms offer a
fascinating opportunity to study universal properties of few-body systems with
a high degree of control over parameters such as the external trap geometry,
the number of particles, and even the interaction strength. In particular,
particles can be allowed to tunnel out of the trap by applying a magnetic-field
gradient that effectively lowers the potential barrier. The result is a tunable
open quantum system that allows detailed studies of the tunneling mechanism. In
this Contribution we introduce our method and present results for the decay
rate of two distinguishable fermions in a one-dimensional trap as a function of
the interaction strength. We also study the numerical convergence. Many of
these results have been previously published (R. Lundmark, C. Forss\'en, and J.
Rotureau, arXiv: 1412.7175). However, in this Contribution we present several
technical and numerical details of our approach for the first time.
