# Proton anti-proton annihilation.

Homework Helper

## Homework Statement

state why p + p_bar --> 1 photon

is forbidden

## The Attempt at a Solution

I have checked all quantum numbers and they are okay. I wondering altough if p_bar has intrinsic parity -1 (p has parity +1)??

According to the soloution, it is forbidden because of energy and momentum conservation. I have not been giving a single word about the production conditions and so forth. HOW can this (E and p) be violated if I choose whatever annihilation condition so that p and E is not violated??!!

Related Advanced Physics Homework Help News on Phys.org
George Jones
Staff Emeritus
Gold Member
Which special frame of reference is often used in collision problems?

Homework Helper
Center of mass. But that is not statet OFTEN CM frame is used. Sometimes I just want to **** my teachers.. :P

George Jones
Staff Emeritus
Gold Member
Centre of momentum frame. Is there a center of momentum frame for a system consisting of of a proton and an anti-proton? Is a there center of momerntum frame for a system consisting of a single photon?

Sometimes I just want to **** my teachers.. :P
Good! This means that they're making you think! Homework Helper
And who are saying that the proton and antiproton has EXACTLY opposite momenta?

What if for example p has little more momentum than the p_bar? Is not one-photon creation possible then?

And if two photons are created, then parity is violated? So there must be a three photon creation in order to conserve all, IF the p and p_bar is travelling at exaclty the same momenta (but opposite). Is that right?

I had a question similar to your one I had to solve. The question was "Show that a photon cannot spontaneously disintegrate into and electron-positron pair". The lecturer mentioned I could tackle this problem using four-momentum or classical conservation of energy and momentum.

I used the classical way, so I didn't have to deal with tensors :tongue2:
An assumption is made at the start, that the electron-positron pair don't move at relativistic speeds. Thus, a classical "Newtonian" means can be applied to the question.

So, all I did was work out the initial/final energy and momentum of the system. Using the conservation of energy equation I substituted it into the conservation of momentum equation and solved for the velocity v (This was the velocity of the electron and positron) . I found v to equal 2c, where c is the speed of light. This implies that the electron and positron was going at twice the speed of light which cannot happen.
This implies that the photon cannot spontaneously disintegrate.

I know this wasn't the same as your question, but I think the logic is the same but reversed and you may obtain a final velocity less than c. Not too sure though.

I hope this helps.

Homework Helper
But protons are not elementary particle systems.

And if the photon has enough energy and is in the field of a nucleus, pair production is posssible.

The correct analogy would be "why can not an electron and positron annihilate and produce a single photon"
I know that two photons are produced, but that would violate parity if the electron and positron has relative angular momentum = zero. ?

I really love to think of the problems on a deeper level than just knowing the answer. I want to understad these things how they work.

If we look att this electron positron annihilation: e + posit = 2 fotons
parity_initial = (-1)(+1) (if zero angular momentum)
parity_final = (-1)(-1) i.e parity is violated??

I did the similar for the p + p_bar and either one or three photons are emitted, depending on how p and p_bar moves relative each other.

How would all the pro's out there solve this?;)

Sorry mate, I don't seem to know enough about parities. I remember being it mentioned in quantum.

The question I got was from a relativistic dynamics unit.

Which topic of physics are you studying at the moment?

Homework Helper
Sorry mate, I don't seem to know enough about parities. I remember being it mentioned in quantum.

The question I got was from a relativistic dynamics unit.

Which topic of physics are you studying at the moment?
Iam studiyn nuclear and particle physics.

I wanna have all points on the exam tomorrow =( but exersices hwere no background information or descriptions of the collision and decays, I often want to give all possible solutions, because I am never sure what the teacher want me to answer...

as in this p + p_bar annihilation, why do they have to collide with exactly the same momenta (but reverse)? There is nothing in the text.. it really makes me angry :P

So my question for everyboy who know this stuff;
can the p and p_bar create a single photon if any of them has higher momentum than the other one? And if they collide with same but opposite momenta, do they create 3 photons to conserve parity?

George Jones
Staff Emeritus
Gold Member
can the p and p_bar create a single photon if any of them has higher momentum than the other one?
No.

If the total spatial momenta of the proton anti-proton system is non-zero, then you can always transform to a frame in which the total spatial momentum is zero. The spatial momentum of a single photon is non-zero in all frames.

Last edited:
Dick
Homework Helper
If you don't like thinking about a special frame then think about a general frame and 4 vectors. Forgetting factors of 'c', we have E^2-p^2=m^2. So in these units the spatial momentum of a proton is always less in magnitude than its energy. Now ask yourself whether two such vectors can add together to yield a vector like the photon with E=p. Clearly not, it seems to me anyway.

Homework Helper
okey, than I am fine =) Thanks!

We have not talked about this during the lecutres or lessons. And nothing in the book either..

So how would then the p + p_bar annihilate? 2 or 3 photons?

Dick
Homework Helper
Either should be kinematically possible, though I'm really not sure. I think in general real world ppbar annihilation is pretty messy since they are composite particles. Ask the folks at CERN or the Tevatron.

Homework Helper
okey, but is 2photon creation possible due to parity?
each photon has negative parity right? And no relative angular momentum between p and p_bar should give them negative parity. 2photons would have positive. am I totaly lost now? =)

Meir Achuz