The interaction between particles or macroscopic bodies is a key element of nature for building up nuclei, atoms, molecules, gaseous, liquid or solid states of matter, and even the system of planets with galaxies. Determined by physical conditions such as dimensionality, environment, and type of particles, their direct and indirect interactions can have short-range (nuclear and the van der Waals forces) and long-range (the Coulomb potential in atoms and molecules or the Newton potential in solar system, and dipole-dipole interaction) characters.
A system of two interacting non-relativistic bodies can easily be described due to the ability to separate the centre-of-mass motion from the relative one in free space. Each independent motion is governed by one-particle dynamics, which can basically be studied within the framework of both classical and quantum mechanics. However, when we add to our system a third particle, the resulting three-body problem becomes very complicated. The complexity of such a three-body system within the quantum-mechanical approach originates from the large variety of possible reaction channels (states of three-body system). Although adding more particles increases the complexity of system, in many cases, for a large enough number of particles, one can successfully apply the well-known mean-field approximation. Thus, few-particle systems (with three, four, or five particles) take a unique position between two simple cases, namely two- and many-body systems and their understanding is one of the central problem in modern physics.
