In Born approximation,
f B ( θ ) = − m 2 π ℏ 2 ∫ V ( r ′ ) e − i q ⋅ r ′ d 3 r ′ {\displaystyle f_{B}(\theta )=-{\frac {m}{2\pi \hbar ^{2}}}\int V(r')e^{-i\mathbf {q} \cdot \mathbf {r} '}d^{3}r'}
where q = k ′ − k {\displaystyle \mathbf {q} =\mathbf {k} '-\mathbf {k} } with k {\displaystyle \mathbf {k} } and k ′ {\displaystyle \mathbf {k} '} are the wave vectors of the incident and scattered waves, respectively. Then
f B ( θ ) = − m 2 π ℏ 2 ∫ g δ 3 ( r ′ ) e − i q ⋅ r ′ d 3 r ′ = − m g 2 π ℏ 2 {\displaystyle f_{B}(\theta )=-{\frac {m}{2\pi \hbar ^{2}}}\int g\delta ^{3}(\mathbf {r} ')e^{-i\mathbf {q} \cdot \mathbf {r} '}d^{3}r'=-{\frac {mg}{2\pi \hbar ^{2}}}}
and the differential cross section is
σ ( θ ) = | f B ( θ ) | 2 = m 2 g 2 4 π 2 ℏ 4 {\displaystyle \sigma (\theta )=|f_{B}(\theta )|^{2}={\frac {m^{2}g^{2}}{4\pi ^{2}\hbar ^{4}}}} .
As the distribution is isotropic, the total cross section is
σ t = 4 π σ = m 2 g 2 π ℏ 4 {\displaystyle \sigma _{t}=4\pi \sigma ={\frac {m^{2}g^{2}}{\pi \hbar ^{4}}}} .
with 
and 
are the wave vectors of the incident and scattered waves, respectively. Then
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