For the potential in Problem 10.4, (a) calculate f(), D(), and , in the low-energy Born approximation;

For the potential in Problem 10.4,
(a) calculate f(θ), D(θ), and σ, in the low-energy Born approximation;
(b) calculate f(θ) for arbitrary energies, in the Born approximation;
(c) show that your results are consistent with the answer to Problem 10.4, in the appropriate regime.

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Example 10.4 Low-energy soft-sphere scattering. 16 Suppose Vo, (ra), 0, (r > a). In this case the low-energy scattering amplitude is V(r) = m 2πh² (independent of and ), the differential cross-section is f(0,0) ~ ==1/1² = do ΦΩ and the total cross-section is o ≈ 4л 4 Vo 2m Vou 3/² 2m Voa" 3ħ² (10.81) (10.82) (10.83) (10.84)