A spinless particle is scattered by a weak Yukawa potential where > 0 but V 0
Question:
A spinless particle is scattered by a weak Yukawa potential
where μ > 0 but V0 can be positive or negative. It was shown in the text that the first-order Born amplitude is given by
(a) Using f(1)(θ) and assuming |δl| ≪ 1, obtain an expression for δ1 in terms of a Legendre function of the second kind, 
(b) Use the expansion formula
to prove each assertion.
(i) δl is negative (positive) when the potential is repulsive (attractive).
(ii) When the de Broglie wavelength is much longer than the range of the potential, δl is proportional to k2l+ 1. Find the proportionality constant.
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This problem can be solved by first expressing the phase shift l in terms of Legendre functions of t...View the full answer
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