As shown in the figure, a particle of mass m=10⁻¹⁰ ~kg , moving with velocity v ₀=10^5 ~m / s approaches a stationary fixed target with impact parameter b from a large distance. If the fixed rigid target has a core with repulsive central force F(r)= K r^3 where constant K >0 and the particle scatters elastically. The closest distance of approach (if numerically K=b^2 ) is