The inverse scattering problem for multidimensional Schrödinger operator is studied.
More exactly we prove a new formula for the first nonlinear term to estimate more accurately
this term. This estimate allows to conclude
that all singularities and jumps of the unknown potential can be recovered from the Born
approximation. Especially, we show for the potentials in $L^p$ for certain values of $p$ that
the approximation agrees with the true potential up to the continuous function.% Text of abstract