2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/204951There has been a recent flurry of interest in the possibility of condensates of $α$-particles in nuclei. In this letter we discuss occurrence conditions for such states. Using the quantality condition of Mottelson we show that condensates are only marginally expected in $α$-particle states. We proceed to demonstrate that few-body nuclear condensates are ill-defined, and emphasize the conflict between $α$-localization and $α$-condensate formation. We also explore the connection between Ikeda diagrams, linear chains, and Tonks-Girardeau gases. Our findings show that no new information is contained in the approximations of nuclear states as $α$-cluster condensates. Furthermore, condensates of more than three $α$-particles are very unlikely to exist due to couplings to other degrees of freedom.5 pages, revtex4 format. Final published version with date of submission, revision, and publicationNuclear TheoryOther Condensed Mattertext