A generalized Morse asymmetric potential and multiplets of its non-numerical exact bound states

The solvable Morse model with its asymmetric phenomenological potential V(r)=A(1-exp(-μ (r-rα)))2 is generalized: via a computer-assisted algebraic construction, we show that for certain three-component phenomenological potentials V(r)=A(1-exp(-μ (r-rα )))2+B(1-exp(-μ (r-rβ)))3+C(1-exp(-μ (r-rγ )))4 the closed and exact bound states may exist not only in singlets, but also in doublets and triplets. (author)