Asymptotically vanishing PT-symmetric potentials and negative-mass Schrödinger equations

In paper I [M. Znojil, G. Lévai, Phys. Lett. A 271 (2000) 327] we introduced the Coulomb-Kratzer bound-state problem in its crypto-Hermitian, PT-symmetric version. An instability of the original model is revealed here. A necessary stabilization is achieved, for almost all couplings, by an unusual, negative choice of the bare mass in Schrödinger equation.