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Special Relativity: Photoproduction of Mesons?

  1. Nov 25, 2013 #1
    1. The problem statement, all variables and given/known data
    12-16 K + mesons can be photoproduced by the reaction γ + p → K+ + Λ where the initial proton is at rest in the lab. From the conservation laws, discover if it is possible for either the K+ or the Λ to be at rest in the lab, and for what photon energy (in terms of the particle masses) this could happen.


    2. Relevant equations
    E^2 = p^2c^2 + m^2c^4
    p = mv
    E = mc^2


    3. The attempt at a solution
    2upzqbq.png

    I'm really stuck on this problem. It's probably more of an algebraic answer, because I believe I'm supposed to somehow get the two equations of energy and momentum conservation to have like terms and then combine them somehow, but I'm at a loss as to what to do. Any help is appreciated.
     
  2. jcsd
  3. Nov 25, 2013 #2
    I think you already have the equations.
    Conservation of Momentum: [itex]\displaystyle{p_\gamma =p_\Lambda \Rightarrow E_\gamma =p_\Lambda c\Rightarrow E_\gamma ^2=E_\Lambda ^2-m_\Lambda ^2c^4}[/itex]
    If you combine this with the conservation of energy you have two equations and two uknowns, [itex]\displaystyle{E_\gamma }[/itex] and [itex]\displaystyle{E_\Lambda}[/itex].

    Another way to solve such problems without algebraic difficulties is by using the momentum 4-vector (also known as 4-momentum). In this problem the calculations are not so tough, because there are only two momenta, so the 4-momentum solution is not much different. But I think it's worth reading about this method, because sometimes it's really helpful.
     
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