On the limit of existence of Borromean binding in three-particle systems with screened Coulomb interactions

Molecular-type systems, ( m 1 ) ± ( m 2 ) ± ( m 3 ) ∓ , consisting of three particles of masses m i and of unit electric charges with the Coulomb interactions weakened by the Debye screening are considered. Existence and range of Borromean binding in symmetric systems (of masses m 1 = m 2 ) is investigated with respect to the masses of their constituents. It is shown that such systems can exist in Borromean ground states if the mass ratio q = m 3 / m 1 is less or equal to 1.668. This improves considerably the lower bound to the limit of existence of the Borromean binding of symmetric systems suggested by Pont and Serra (2009 Phys. Rev. A 79 032508) as q ⩽ 1. Qualitative meaning of the improvement is that the Borromean binding occurs not only for systems where two identical particles are heavier than the third one but it is also possible for systems of the opposite mass relation. The range of screening parameter in which a system is Borromean known as a Borromean window is also determined for μ + μ + e − , π + π + μ − , π + μ − μ − and e + e − e − .