Mass and range dependence in the binding energy of a three-body system

We have studied the bound-state solutions of a system of two particles of mass M which do not interact among themselves but which interact attractively with a third particle of mass 1\4 as a function of the ratio M1\4. In the limit M1\4'0, the solution of the system is well known since it corresponds to the problem of two independent particles in a well. We point out that in the limit M1\4' the solution is also very simple, and it corresponds to having the two particles of mass M fixed at the same point in space. We have found that the three-body binding energy tends to be proportional to the square of the range of the two-body interaction in momentum space, and that the sensitivity of the binding energy with respect to off-shell variations of the two-body amplitude increases when M1\4 increases.