A rigorous criterion to identify the validity of the Born approximation

This paper intends to identify the validity of the orn approximation bya new universal criterion, which is ultimately reduced to thecalculation of an operator norm. With the purpose of enabling thecriterion to be applicable to general scattering problems, a method isproposed to estimate the norm of the operator concerned. Comparedwith the conventional criterion, this method excels in its abilityto acquire a quantificational upper bound of the relative error byBorn approximation as well as to extend its valid frequency to awider range. Two canonical scattering examples are given as evidencefor the validity of the criterion.