Word Count : 432

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Let’s solve this step by step. We are asked to show that the average cosine of the scattering angle in the LAB system, (\bar{\mu}_L = \langle \cos\theta_L \rangle), is: [ \bar{\mu}_L = \frac{2}{3A} ] where (A) is the mass number of the nucleus. --- Step 1: Relation between CM and LAB angles For elastic scattering of a neutron on a nucleus of mass number (A), the relation between the scattering angle in the centre of mass (CM) frame (\theta_{CM}) and the LAB frame (\theta_L) is: [ \cos \theta_L = \frac{\cos \theta_{CM} + \alpha}{1 + \alpha \cos \theta_{CM}} ] where (\alpha = \frac{1}{A}) (since for neutron scattering, the neutron _______ _______ _______ ______ __________ _______ ______ __________ ______.
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