STABILIZATION AND THE ZERO-RANGE MODELS

It is shown that the high-frequency approximation describes the lack o f stabilization for the zero-range models in dimensions higher than 1. The same conclusion has been drawn from the exact solution of this mo del in the three-dimensional space. Hence, there are no contradictions between the predictions of the exactly soluble models and the high-fr equency approximation. On the other hand both the exact numerical anal ysis and this approximation leads to the stabilization for the one-dim ensional delta potential. This means that the high-frequency approxima tion does correctly predict both the presence and the absence of stabi lization effects.