Proton–Proton Collision
المؤلف:
Sidney B. Cahn And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 1 , p 40
13-7-2016
1431
Proton–Proton Collision
A proton with 
collides elastically with a proton a rest. If the two protons rebound with equal energies, what is the angle θ between them?
SOLUTION
Since the energies of the protons after the collision are equal, they will rebound at the same angle θ/2 relative to the initial momentum of the proton (see Figure 1.2). Again we use c = 1. In these units before the
Figure 1.2
collision
Using momentum conservation, we have
(1)
or
(2)
where 
and 
stand for β and γ after the collision. Energy conservation yields
(3)
or
(4)
Now,
(5)
So, we obtain by using (4)
(6)
Substituting (6) into (2) and using (5) gives
For γ ≈ 1, i.e., in the classical limit of low velocity, cos θ = 0, and we obtain the familiar result that the angle between billiard balls rebounding with equal energy is 90°. If γ >> 1 (extremely relativistic case), then cos θ ≈ 1 and θ → 0.
الاكثر قراءة في مواضيع اخرى
اخر الاخبار
اخبار العتبة العباسية المقدسة
