Word Count : 515

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The reaction given is: [ \pi^+ + n \rightarrow \pi^0 + p^+ ] This is a charge-exchange reaction involving a pion ((\pi^+)) and a neutron ((n)) producing a neutral pion ((\pi^0)) and a proton ((p^+)). To solve this numerically, we will calculate the kinematics, assuming the neutron is initially at rest. --- Step 1: Rest masses * (m_{\pi^+} = 139.57 , \text{MeV/c}^2) * (m_{\pi^0} = 134.98 , \text{MeV/c}^2) * (m_n = 939.57 , \text{MeV/c}^2) * (m_p = 938.27 , \text{MeV/c}^2) --- Step 2: Energy-momentum conservation Let the incoming pion have kinetic energy (T_{\pi^+}) and momentum (p_{\pi^+}). The neutron is initially at rest. Total _____ _______ _____ _____ ______ ____ _______ ___ ____ __________ _________ ________.
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