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We study the universality of the three-body parameters for systems relevantfor ultracold quantum gases with positive $s$-wave two-body scattering lengths.Our results account for finite-range effects and their universality is testedby changing the number of deeply bound diatomic states supported by ourinteraction model. We find that the physics controlling the values of thethree-body parameters associated with the ground and excited Efimov states isconstrained by a variational principle and can be strongly affected by $d$-waveinteractions that prevent both trimer states from merging into the atom-dimercontinuum. Our results enable comparisons to current experimental data and theysuggest tests of universality for atomic systems with{positive scatteringlengths.

Efimov-van-der-Waals universality for ultracold atoms with positive scattering lengths