Bose gases near resonance: Renormalized interactions in a condensate

► A Bose gas becomes nearly fermionized when its chemical potential approaches a maximum near resonance. ► At the maximum, an onset instability sets in at a positive scattering length. ► Condensates strongly influence the renormalization flow of few-body running coupling constants. ► The effective two-body interaction constant changes its sign at a positive scattering length.