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The geometry of Borromean three-body halos, such as two-neutron halo nucleior triatomic molecules close to dissociation, is investigated using athree-body model. This model enables to analytically derive the universalgeometric properties found recently within an effective-field theory for halosmade of a core and two resonantly-interacting particles [Phys. Rev. Lett., 128,212501 (2022)]. It is shown that these properties not only apply to the groundthree-body state, but also to all the excited (Efimov) states where thecore-particle interaction is resonant. Furthermore, a universal geometrypersists away from the resonant regime between the two particles, for any stateclose to the three-body threshold. This "halo universality" is different fromthe Efimov universality which is only approximate for the ground state. It isexplained by the separability of the hyper-radius and hyper-angles close to thethree-body dissociation threshold.

Universal geometry of two-neutron halos and Borromean Efimov states close to dissociation