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.