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Electrodynamics and Relativity. Please Help

  1. Mar 3, 2012 #1
    Electrodynamics and Relativity. Please Help!!!!

    1. The problem statement, all variables and given/known data

    Consider the decay of a particle.

    (a) Find the threshold kinetic energies of the incident particles in each of
    the following reactions:

    (i) ∏+ + p →∏++ ∏° + p
    (ii) p + n →p + n + ∏° + ∏°

    The incident particle is the first particle listed in the reactions; the target particle is at rest. The masses of the ∏+ and ∏° ions are 139.567MeV/c2 and 134.963 MeV/c2 respectively while the masses of the neutron and proton are respectively 939.566 MeV/c2 and 938.272 MeV/c2.




    2. Relevant equations

    The teacher suggested that I will need to use the following equations to get the solution
    (Here P is the momentum and Px is the momentum of the incident particle ∏+in the X direction, assuming it hits the target particle p(proton) horizontally, so no P(momentum) in y or z direction)

    ƩPiu=0

    PuPu=m2c2= E2/C2-P2

    Also said that using this notations will be useful to solve the problem

    For ∏+, the incident particle:
    Pu=(E/C, Px, 0, 0)
    Pu=(E/C, -Px, 0, 0) where Px is the momentum of the incident particle, and no need to worry about y and z direction so just put zeros.


    3. The attempt at a solution
    This is what I have done so far to solve for part i, but I have no clue how to continue.
    Since we are solving for the threshold kinetic energy, so assuming that ∏+, ∏° and p are at rest after the reaction.

    (E/C, Px, 0, 0) +(mpC2, 0, 0, 0) - (m+C2,0, 0, 0 ) -(m∏°C2,0, 0, 0 ) - (mpC2,0, 0, 0 ) = 0

    mp, m+, m∏° are just the rest mass.

    PLEASE PLEASE help me to do this problem!!! thank you so much!
     
  2. jcsd
  3. Mar 3, 2012 #2

    fzero

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    Science Advisor
    Homework Helper
    Gold Member

    Re: Electrodynamics and Relativity. Please Help!!!!

    As you see, trying to have all 3 final state particles at rest is impossible due to conservation of momentum. You need to allow for some final momenta and then think about what being at threshold implies.
     
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