Subleading contributions to N -boson systems inside the universal window

Paolo Recchia

Abstract:

We study bosonic systems in the regime in which the two-body system has a shallow bound
state or, equivalently, a large value of the two-body scattering length. Using the effective field
theory framework as a guidance, we construct a series of potential terms which have a decreasing
importance in the description of the binding energy of the systems. The leading order potential
terms consist in a two-body term, usually attractive, plus a three-body term, usually repulsive;
this last term is required to prevent the collapse of systems with more than two particles. At this
order, the parametrization of the two-body potential is done to obtain a correct description of the
scattering length, which governs the dynamics in this regime, whereas the three-body term fixes a
three-body datum. We investigate the role of the cut-off in the leading order description and we
extend the exploration beyond the leading order by including the next-to-leading order terms in
both, the two- and three-body potentials. We use the requirement of the stability of the N-body
system, whose energy is variationally estimated, to introduce the three-body forces. The potential
parametrization, as a function of the cut-off, is fixed to describe the energy of 4He clusters up to
seven particles within the expected accuracy. Finally, we also explore the possibility to describe at
the same time the atom-dimer scattering length.