= Scattering in a repulsive inverse-square potential
{title2=$r=r_{\min}\sec[\beta(\theta-\theta_0)]$}
For $V(r)=c/r^2$ with $c>0$, nonzero physical <angular momentum> $h$ and positive <energy> $E$, put $\beta=\sqrt{1+2mc/h^2}>1$ and $r_{\min}=\sqrt{(c+h^2/(2m))/E}$. Direct integration of the <effective potential> radial equation gives the displayed <orbit>. It has one radial minimum and two straight-line asymptotes separated by polar angle $\pi/\beta$. The repulsive scattering deflection is $\pi-\pi/\beta$; no bounded or circular orbit exists at finite positive energy.
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