Four-body system of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts /><mml:none /><mml:mn>4</mml:mn></mml:mmultiscripts></mml:math> atoms: Dimer-dimer scattering

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