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Conservation of momenta

  1. Dec 11, 2007 #1

    malawi_glenn

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    1. The problem statement, all variables and given/known data
    An relativistic proton collides with a proton at rest (in Lab-frame), the collision is elastic.

    let incoming proton have momenta p, and the outgoing momenta = p1, p2.

    The following is conserved:

    [tex] \vec{p} = \vec{p}_1 + \vec{p}_2 [/tex]

    [tex] \sqrt{m^2+p^2} + m = \sqrt{m^2+p_1^2} + \sqrt{m^2+p_2^2} [/tex]

    Gives for the angle between p_1 and p_2 (in lab frame). A minima occurs, which means that [itex] p1 = p2 [/itex]. One can show that this minima occurs so that: [itex] p1 + p2 > p [/itex]. Explain why that is possible!


    3. The attempt at a solution

    MATLAB

    m = 0.93828; % proton mass in GeV

    p = 2; %GeV incomming proton

    p1 = [0.01:0.01:2]; %range of outgoin proton #1s momenta.

    p2 = sqrt((sqrt(m^2+p^2)+m-sqrt(m^2+p1.^2)).^2-m^2);

    omega = acos((p^2-p1.^2-p2.^2)./(2*p1.*p2));
    omega = 180/pi*omega;

    plotting gives minima för p = 1.2GeV/c

    I am very unsure about this, I think it is possible [itex] p1 + p2 > p [/itex] scince momenta is a vector quantity, so the magnitudes can change, but not the total (i.e the total vector after = total vector initial). More suggestions?
     
  2. jcsd
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