Let \(D\subset \mathbb{R}^3\) be a bounded domain. \(q\in C(D)\) be a real-valued compactly supported potential, \(A(\beta, \alpha,k)\) be its scattering amplitude, \(k>0\) be fixed, without loss of generality we assume \(k=1\), \(\beta\) be the unit vector in the direction of scattered field, \(\alpha\) be the unit vector in the direction of the incident field. Assume that the boundary of \(D\) is a smooth surface \(S\). Assume that \(D\subset Q_a:=\{x: |x|\le a\}\), and \(a>0\) is the minimal number such that \(q(x)=0\) for \(|x|>a\). Formula is derived for \(a\) in terms of the scattering amplitude.
