Mass-symmetry breaking in three-body ions

The ground-state energy of three-body ions $(M^+,M^+,m^-)$ evolves when the like-charge constituents are given different masses. The comparison of $(m_1^+,m_2^+,m^-)$ with the average of $(m_1^+,m_1^+,m^-)$ and $(m_2^+,m_2^+,m^-)$ reveals a competition between the symmetric term and the antisymmetric one. The former dominates in the Born--Oppenheimer regime such as the (p,t,e) case, while the latter wins for H$^-$-like systems with two negative light particles surrounding a heavy nucleus. A comparison is also made with the case of baryons in simple quark models with flavour independence.