In order to prepare for an exam I have started solving exercies problems and have gotten most of them right but have quetion a regarding a solution.

In this probelm I used the first order Born approximation in order to calculate the differential and total cross section for the potential,

[tex] V(r) = \lambda e^{-r^2 / 4a^2}. [/tex]

Now, how can I see the limits of this approximation? E.g. can we see if it is valid for a particle with a given mass assuming that we have [tex]ka \ll 1[/tex]?