Ultracold scattering processes in three-atomic helium systems

We review results on scattering observables for $^4$He--$^4$He$_2$ and $^3$He--$^4$He$_2$ collisions. We also study the effect of varying the coupling constant of the atom-atom interaction on the scattering length

The ^4He trimer as an Efimov system

We review the results obtained in the last four decades which demonstrate the Efimov nature of the $^4$He three-atomic system.Comment: Review article for a special issue of the Few-Body Systems journal devoted to Efimov physic

Bound States and Scattering Processes in the ^4He_3 Atomic System

We present a mathematically rigorous method for solving three-atomic bound state and scattering problems. The method is well suited for applications in systems where the inter-atomic interaction is of a hard-core nature. It has been employed to obtain the ground- and excited-state energies for the Helium trimer and to calculate, for the first time, the scattering phase shifts and wave-functions for the He atom-He dimer at ultra-low energies.Comment: 9 pages, main file 21 kB, 1 eps and 4 ps figure

The helium trimer with soft-core potentials

The helium trimer is studied using two- and three-body soft-core potentials. Realistic helium-helium potentials present an extremely strong short-range repulsion and support a single, very shallow, bound state. The description of systems with more than two helium atoms is difficult due to the very large cancellation between kinetic and potential energy. We analyze the possibility of describing the three helium system in the ultracold regime using a gaussian representation of a widely used realistic potential, the LM2M2 interaction. However, in order to describe correctly the trimer ground state a three-body force has to be added to the gaussian interaction. With this potential model the two bound states of the trimer and the low energy scattering helium-dimer phase shifts obtained with the LM2M2 potential are well reproduced.Comment: 15 pages, 3 figures, submitted to Few-Body System

Scaling limit of virtual states of triatomic systems

For a system with three identical atoms, the dependence of the $s-$wave virtual state energy on the weakly bound dimer and trimer binding energies is calculated in a form of a universal scaling function. The scaling function is obtained from a renormalizable three-body model with a pairwise Dirac-delta interaction. It was also discussed the threshold condition for the appearance of the trimer virtual state.Comment: 9 pages, 3 figure

Low-Energy Universality in Atomic and Nuclear Physics

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this "progress report", we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.Comment: Commissioned article for Few-Body Systems, 47 pp, 16 fig

Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

We propose a theory which deals with the structure and interactions of volume elements in liquid helium II. The approach consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic wave equation; it suggests the Gaussian-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. Our approach leads to a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to fit we reproduce at high accuracy not only the roton minimum but also the neighboring local maximum as well as the sound velocity and structure factor.Comment: 9 pages, 6 figure