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The given reaction is: [ K^- + p^+ \rightarrow \pi^0 + \Lambda^0 ] To solve this numerically, we need to check energy and momentum conservation and calculate the threshold energy of the proton in the lab frame (assuming the kaon is at rest). Let the rest masses be: * (m_{K^-} = 494~\text{MeV}/c^2) * (m_p = 938~\text{MeV}/c^2) * (m_{\pi^0} = 135~\text{MeV}/c^2) * (m_\Lambda = 1116~\text{MeV}/c^2) The threshold energy formula in the lab frame (where (K^-) is at rest) is: [ E_p^{\text{lab}} = \frac{(m_{\pi^0} + m_\Lambda)^2 - m_{K^-}^2 - m_p^2}{2 m_{K^-}} ] Step 1: Compute ((m_{\pi^0} + m_\Lambda)^2) [ m_{\pi^0} +
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