Calculate Differential Cross Section, Amplitude from Lagrangian

johnahn
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Lagrangian I have is little bit massy so I don't write in here.

Like in ψψ(dagger) , or ψ∅ -> ψ∅, How can I calculate the differential cross section or total, or amplitudes?
 
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Use Feynman diagrams to calculate the amplitude and then use the standard formula for 2 body scattering?
 


to get vertex factor write iL,then replace field operators by plane wave forms.leave out all factors which are taken care by other things such as normalization factors etc.rest is vertex factor.You may find relevant things in book of sakurai 'advanced quantum mechanics'.
 

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