- #1
Lightf
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Homework Statement
Find the deflection angle of the particle if it is scattered by this central field.
$$ U = \frac{α - β r - γ r^2}{r^2} $$
Homework Equations
Angle of deflection is given by:
$$θ = ∫ \frac{Mdr}{r^2\sqrt{2m(E-U) - \frac{M^2}{r^2}}}$$
The Attempt at a Solution
$$θ = ∫ \frac{Mdr}{r^2\sqrt{2m(E-U) - \frac{M^2}{r^2}}}$$
$$θ = ∫ \frac{Mdr}{r^2\sqrt{2m(E-\frac{α-βr-γr^2}{r^2}) - \frac{M^2}{r^2}}}$$
$$θ = ∫ \frac{Mdr}{r\sqrt{2m(Er^2 - α - βr - γr^2) - M^2}}$$
$$θ = ∫ \frac{Mdr}{r\sqrt{2m(E-γ)r^2 - 2mβr - (2mα - M^2)}}$$
I am not sure how to solve this integral.