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The strong short-range repulsion, characteristic to realistic interatomicpotentials, complicates the description of weakly-bound few-body systems suchas those of \He atoms. The present work proposes an approach for solving thisproblem and applies it to a realistic system of four ${}^4\mathrm{He}$ atoms.The potential is gradually softened such that rigorous four-body equations forbound and scattering tates can be accurately solved in the momentum-spaceframework, and the results are extrapolated back to the limit of the originalpotential. Linear correlations between three- and four body quantities areobserved, and the accuracy of the procedure is improved by extrapolating in oneof the three-body quantities. Results for the ${}^4\mathrm{He}$ tetramer groundand excited state binding energies and atom-trimer scattering agree well withat least some of earlier determinations and shed light on the existingdisagreements. An additional case of the Phillips correlation line isestablished for the dimer-dimer scattering length. The trimer production ratevia the ultracold two-dimer collisions is estimated, it exhibits significantfinite-range effects despite the weak binding of the dimer.

Four-body system of ${}^4\mathrm{He}$ atoms: Dimer-dimer scattering