malawi_glenn
Dec11-07, 11:00 AM
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:
\vec{p} = \vec{p}_1 + \vec{p}_2
\sqrt{m^2+p^2} + m = \sqrt{m^2+p_1^2} + \sqrt{m^2+p_2^2}
Gives for the angle between p_1 and p_2 (in lab frame). A minima occurs, which means that p1 = p2 . One can show that this minima occurs so that: p1 + p2 > p . 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 p1 + p2 > p 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?
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:
\vec{p} = \vec{p}_1 + \vec{p}_2
\sqrt{m^2+p^2} + m = \sqrt{m^2+p_1^2} + \sqrt{m^2+p_2^2}
Gives for the angle between p_1 and p_2 (in lab frame). A minima occurs, which means that p1 = p2 . One can show that this minima occurs so that: p1 + p2 > p . 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 p1 + p2 > p 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?