We propose a new integrable Hamiltonian describing two interacting particles in a harmonic mean field in D = 1 dimensional space. This model is found to be both supersymmetric and shape invariant. We show that for a given domain of the coupling constant the irregular solution is acceptable and contributes to the spectrum. We also discuss two inequalities of the Bertlmann–Martin type, which link the ground state mean-square radius to the lowest excitation energy.