Question

Two protons, both with rest mass M and each with equal and opposite momenta, collide head-on. As measured in this center-of-mass frame, the protons have just enough energy to produce a neutral “eta” particle (η0) of rest mass M/2, through the reaction P + P → P + P + η0 Express your answer to parts (a) - (c) in terms of M. (a) In the center-of-mass frame, find the energy E1, speed v1 , and momentum p1 of each of the protons before the collision. Now consider the same reaction in the lab frame, in which one of the initial protons is at rest. (b) Find the energy E, speed v, and momentum p of the incident proton in the lab frame. (c) Find the momentum p1 of the η0 particle after the collision, in the lab frame. Shortly after it is produced, the η0 decays into two photons. η0 → γ + γ In the rest frame of the η0 , each of the two photons is emitted at 90◦ with respect to the direction of the incident proton. (If you have not completed parts (a) - (c), you may leave the answer to the following questions in terms of the speed v1 of the η0 in the lab frame.) (d) Find the energy E2 of each photon in the lab frame. (e) Find the angle θ of each photon with respect to the direction of the incident proton in the lab frame.

          Two protons, both with rest mass M and each with equal and opposite momenta,
collide head-on. As measured in this center-of-mass frame, the protons have just
enough energy to produce a neutral “eta” particle (η0) of rest mass M/2, through the reaction
P + P → P + P + η0
Express your answer to parts (a) - (c) in terms of M.
(a) In the center-of-mass frame, find the energy E1, speed v1 , and momentum p1 of each of the protons before the collision.
Now consider the same reaction in the lab frame, in which one of the initial protons
is at rest.
(b) Find the energy E, speed v, and momentum p of the incident proton
in the lab frame.
(c)  Find the momentum p1 of the η0 particle after the collision, in the lab frame.
Shortly after it is produced, the η0 decays into two photons.
η0 → γ + γ
In the rest frame of the η0 , each of the two photons is emitted at 90◦ with respect
to the direction of the incident proton.
(If you have not completed parts (a) - (c), you may leave the answer to the following
questions in terms of the speed v1 of the η0 in the lab frame.)
(d) Find the energy E2 of each photon in the lab frame.
(e) Find the angle θ of each photon with respect to the direction of the
incident proton in the lab frame.

Added by Priyanka T.

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