Examine the validity of the Born approximation for the Yukawa potential V(r)=βe−μr/r.
(a) Show that at low energies (ka≪1, where a=1/μ), the Born approximation is valid provided ℏ2μ2m∣β∣≪1.
(b) Show that at high energies (ka≫1), the Born approximation is valid provided ℏ2k2m∣β∣≪1.