  The strong short-range repulsion, characteristic to realistic interatomic
potentials, complicates the description of weakly-bound few-body systems such
as those of \He atoms. The present work proposes an approach for solving this
problem and applies it to a realistic system of four ${}^4\mathrm{He}$ atoms.
The potential is gradually softened such that rigorous four-body equations for
bound and scattering tates can be accurately solved in the momentum-space
framework, and the results are extrapolated back to the limit of the original
potential. Linear correlations between three- and four body quantities are
observed, and the accuracy of the procedure is improved by extrapolating in one
of the three-body quantities. Results for the ${}^4\mathrm{He}$ tetramer ground
and excited state binding energies and atom-trimer scattering agree well with
at least some of earlier determinations and shed light on the existing
disagreements. An additional case of the Phillips correlation line is
established for the dimer-dimer scattering length. The trimer production rate
via the ultracold two-dimer collisions is estimated, it exhibits significant
finite-range effects despite the weak binding of the dimer.
