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This article considers the bound states of two heavy and two light bosons,when a short-range force attracts the bosons of different mass, and ashort-range force repel the light bosons. The existence of such four-body boundstates results from the competition between these two forces. For a givenstrength of the attraction, the critical strength of the repulsion necessary tounbind the four particles is calculated. This study is motivated by theexperimental realisation of impurity atoms immersed in an atomic Bose-Einsteincondensate, and aims at determining in which regime only one boson contributesto binding two impurities.

Tetramers of two heavy and two light bosons