  We propose a conjecture stating that for resonances, $\lambda_j$, of a
noncompactly supported potential, the series $\sum_j \operatorname{Im}
\lambda_j/|\lambda_j|^2$ diverges. This series appears in the Breit-Wigner
approximation for a compactly supported potential, in which case it converges.
We provide heuristic motivation for this conjecture and prove it in several
cases.
