Exponential Potential Born Approximation

Using the Born approximation, find the differential cross section for the next exponential potential:

$V(r)=-V_{0}e^{-{\frac {r}{a}}}$

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If the potential V is spherical symmetric we can use the equation:

$f_{born}(\theta )={\frac {-2m}{\hbar ^{2}}}\int _{0}^{\infty }dr'V(r'){\frac {\sin(qr')}{qr'}}{r'}^{2}$

So,

$f_{born}(\theta )={\frac {-2mV_{0}}{\hbar ^{2}q}}\int _{0}^{\infty }r'sin(ar')e^{-{\frac {r'}{a}}}dr'$