Small clusters of He atoms in finite-cutoff EFT

Abstract

Small clusters of $^4$He atoms provide a paradigmatic setting for exploring universal phenomena in few-body quantum systems with large scattering length. Their weakly bound states serve as ideal test cases for studying Efimov physics and the emergence of universality beyond the three-body sector. In this work, we investigate few-$^4$He systems within a finite-cutoff effective field theory (EFT) framework. The EFT interactions are calibrated to reproduce low-energy observables obtained from the realistic LM2M2 potential, enabling a direct and systematic comparison between the two approaches. We demonstrate that, for suitably chosen finite cutoffs, the empirical effective range is accurately reproduced already at leading order, achieving next-to-leading-order precision without explicit higher-order corrections. Using these interactions, we solve the Schr\"odinger equation for systems of a few atoms, obtaining binding energies and scattering observables in excellent agreement with results derived from realistic interatomic potentials. In particular, we compute atom--tetramer scattering parameters and binding energies of clusters up to eight atoms, thereby extending the EFT description to larger helium systems. Our findings establish a quantitative bridge between realistic helium potentials and finite-cutoff EFT, showing that the latter provides an efficient and predictive framework for describing few-body universality in weakly bound quantum systems.