Small clusters of $$^4$$He atoms in finite-cutoff effective field theory

Abstract

Small clusters of \(^4\) He atoms are benchmark systems for universal few-body physics near the unitary limit. We study these systems using a finite-cutoff effective field theory calibrated to low-energy observables from the realistic LM2M2 potential. The chosen two-body cutoff reproduces both the atom–atom scattering length and effective range, while a regulated three-body interaction is adjusted to the trimer and tetramer ground-state energies. We distinguish total binding energies from the one-atom separation energies of the shallow excited states. Ground-state energies through \(A=8\) are reproduced at the few-percent level, but threshold-sensitive observables are less accurate. In particular, the calculated tetramer separation energy is \(S_4^*=2.85\) mK, compared with 0.92–0.96 mK in converged LM2M2 calculations, and the atom–trimer scattering length differs substantially from modern LM2M2 benchmarks. For \(A\ge 5\) , the available excited-state benchmarks are sparse and strongly method dependent. Comparison with another soft-core interaction suggests that the discrepancies primarily reflect short-distance physics and higher-order operators omitted from the finite-cutoff Hamiltonian rather than numerical convergence of the stochastic variational calculation. Finite-cutoff EFT therefore provides an efficient description of ground-state systematics, whereas shallow excited states and atom–cluster scattering require a controlled higher-order and cutoff-dependence analysis.