Why proton and electron collision doesn't result in annihilation?

[aditya23456]

I am new to particle physics, but I heard that electron and positron annihilate each other in case of contact mainly because both have opposite charge( even same mass). Consider an electron is given enough kinetic energy such that it compensates mass differentiation between proton and electron, and undergoes perfect collision, then we should observe annihilation. In case they don't annihilate there's some other parameter which is main reason for annihilation other than opposite charge. Am I right?

 

[kjhskj75]

Particles can only annihilate with their exact anti-particles. Electrons and Positrons are exactly anti to one another, electrons and protons are not.

There are also issues with Baryon and Lepton number conservation.
(See http://en.wikipedia.org/wiki/Baryon_number and
http://en.wikipedia.org/wiki/Lepton_number)

 

[ChrisVer]

The reason has already been stated by kjhskj... Annihilation occurs between particles-antiparticles. The electron's antiparticle is the positron and not the proton.
At first when Dirac found out the existence of "antiparticles" in his theory and tried to interpret this result. Quote from wiki http://en.wikipedia.org/wiki/Positron:

Dirac wrote a follow-up paper in December 1929[3] that attempted to explain the unavoidable negative-energy solution for the relativistic electron. He argued that "... an electron with negative energy moves in an external [electromagnetic] field as though it carries a positive charge." He further asserted that all of space could be regarded as a "sea" of negative energy states that were filled, so as to prevent electrons jumping between positive energy states (negative electric charge) and negative energy states (positive charge). The paper also explored the possibility of the proton being an island in this sea, and that it might actually be a negative-energy electron. Dirac acknowledged that the proton having a much greater mass than the electron was a problem, but expressed "hope" that a future theory would resolve the issue.

Robert Oppenheimer argued strongly against the proton being the negative-energy electron solution to Dirac's equation. He asserted that if it were, the hydrogen atom would rapidly self-destruct.[4] Persuaded by Oppenheimer's argument, Dirac published a paper in 1931 that predicted the existence of an as-yet unobserved particle that he called an "anti-electron" that would have the same mass as an electron and that would mutually annihilate upon contact with an electron.

Kinetic energy doesn't really play much of a role for the rest masses to be equal.
In general you can have INTERACTION between the proton and the electron... it can be electromagnetic interactions [between the e and the p, or maybe the proton's sea and valance quarks] or it can be weak interactions [electron capture- an alternative form of the beta+ decay]. But these are not annihilations.

[OUT OF SCIENCE COMMENT ]
I have also heard this thing about Dirac and the proton as electron's antiparticle as a joke...as for example Dirac's colleagues would knock on his door and ask him every now or then if he finally discovered his antiparticle, and one day Dirac replied "yes I did and it's the proton" or something like that...I don't actually remember it.

 

[aditya23456]

Really thanks for reply. So I can conclude that to form annihilation pairs, it's not just that 2 particles should possesses opposite charge.

Actually I am trying to understand how boson can be turn into fermion or viceversa. I found annihilation as a process to change fermions to boson. Can you please list similar reactions ( natural or experimental made) which involves change of fermion to bosons or viceversa.

Also, I want to know whether there are any experimental efforts done to try change spin of an elementary particle?

Also I have a weird question. Consider the fermion before annihilation has some temperature say 32 C, after annihilation does light beam( boson) have that temperature? I guess not, then where does this temperature go?

Note:- I am just naive and trying my best to learn QM on my own, my questions may be ridiculous, please just give me links where I can study about them. Really thanks for your time.

 

[DrClaude]

Actually I am trying to understand how boson can be turn into fermion or viceversa. I found annihilation as a process to change fermions to boson. Can you please list similar reactions ( natural or experimental made) which involves change of fermion to bosons or viceversa.

You can't "change" a fermion into a boson, but you can have two fermions resulting in a boson, or a boson giving two fermions, as in the decay of neutral pions
$$
\pi^0 \rightarrow \gamma + e^- + e^+
$$
Angular momentum (spin) has to be conserved.

Also, I want to know whether there are any experimental efforts done to try change spin of an elementary particle?

This is like trying to change the charge of the electron. Spin is an intrinsic property.

Also I have a weird question. Consider the fermion before annihilation has some temperature say 32 C, after annihilation does light beam( boson) have that temperature? I guess not, then where does this temperature go?

Individual particles don't have temperatures, they have energy. Conservation of energy does apply, you get as much energy after annihilation as the total energy of the particles before annihilation.

 

[aditya23456]

Individual particles don't have temperatures, they have energy. Conservation of energy does apply, you get as much energy after annihilation as the total energy of the particles before annihilation.

Thanks for reply. But I read that at high temperatures, electromagnetism and weak forces to be same. Here temperature is temperature of particles( photons,W,Z boson's ) or ambient temperature? I feel temperature has an effect on particle(energy) nature, because at big bang when all forces were united , temperature of primodial soup was in billions and at this temperature, matter existed in bosonic form only. As universe temperature decreased, we found fermionic form. So was curious if there is any relation of temperature with change of fermionic to bosonic form. Also we know at absolute zero, matter( mass form) ceases to exist. Is there any study on this?

 

[stevendaryl]

Really thanks for reply. So I can conclude that to form annihilation pairs, it's not just that 2 particles should possesses opposite charge.

Actually I am trying to understand how boson can be turn into fermion or viceversa. I found annihilation as a process to change fermions to boson. Can you please list similar reactions ( natural or experimental made) which involves change of fermion to bosons or viceversa.

If you think of a collision as something like a chemical reaction with inputs and outputs, then the rules are:

1. The total charge must be conserved (same before and after)
2. The total angular momentum must be conserved.
3. The total energy must be conserved.
4. The total momentum must be conserved.
5. In most interactions, the quantities B (baryon number) and L (lepton number) are conserved. B is "baryon number", which for ordinary matter counts the number of protons and neutrons.
   L is "lepton number", which for ordinary matter counts the number of electrons and neutrinos (there are other kinds of leptons, but they are not found in ordinary matter). Anti-particles have negative baryon numbers or lepton numbers.

The rules for combining angular momentum are a little complex: If you two particles with spin (intrinsic angular momentum) S_1 and S_2, then the total angular momentum (which includes both spin and orbital angular momentum) of the two of them can be any integer greater than |S_1 - S_2|. So an electron and its anti-particle (the positron), which have spin-1/2 can be combined to produce angular momentum 0, 1, 2, etc. Two photons, each of which have spin-1, can be combined to produce angular momentum 0, 1, 2, etc. So an electron and a positron can collide to produce two photons. (They can't collide to produce just one photon, because you can't get the energy and momentum to work out, although angular momentum works out.)

 

[Orodruin]

Thanks for reply. But I read that at high temperatures, electromagnetism and weak forces to be same. Here temperature is temperature of particles( photons,W,Z boson's ) or ambient temperature? I feel temperature has an effect on particle(energy) nature,

Temperature is not a property of a single particle, but of a (large) collection of particles. It is related to the average energy of the particles and when the temperature is high particles tend to have large energy. The statement that forces unite at high temperatures is really just saying that when the universe was very hot, particles would generally have so high energies that the forces unite.

because at big bang when all forces were united , temperature of primodial soup was in billions and at this temperature, matter existed in bosonic form only. As universe temperature decreased, we found fermionic form. So was curious if there is any relation of temperature with change of fermionic to bosonic form. Also we know at absolute zero, matter( mass form) ceases to exist. Is there any study on this?

Could you provide references to those statements please? What do you mean by fermionic and bosonic form? Fermions and bosons are different types of particles and there is nothing preventing either from existing in the early universe.

 

[snorkack]

If you think of a collision as something like a chemical reaction with inputs and outputs, then the rules are:

1. The total charge must be conserved (same before and after)
2. The total angular momentum must be conserved.
3. The total energy must be conserved.
4. The total momentum must be conserved.
5. In most interactions, the quantities B (baryon number) and L (lepton number) are conserved. B is "baryon number", which for ordinary matter counts the number of protons and neutrons.
   L is "lepton number", which for ordinary matter counts the number of electrons and neutrinos (there are other kinds of leptons, but they are not found in ordinary matter). Anti-particles have negative baryon numbers or lepton numbers.

The rules for combining angular momentum are a little complex: If you two particles with spin (intrinsic angular momentum) S_1 and S_2, then the total angular momentum (which includes both spin and orbital angular momentum) of the two of them can be any integer greater than |S_1 - S_2|. So an electron and its anti-particle (the positron), which have spin-1/2 can be combined to produce angular momentum 0, 1, 2, etc. Two photons, each of which have spin-1, can be combined to produce angular momentum 0, 1, 2, etc. So an electron and a positron can collide to produce two photons. (They can't collide to produce just one photon, because you can't get the energy and momentum to work out, although angular momentum works out.)

The angular momentum combining rules indeed behave oddly.

When electron and positron annihilate to produce two photons, this is only possible if these photons have exactly opposite spin AND no orbital angular momentum whatsoever. This requires the combined spin to have been 0, so that the spins of electron and positron had been opposite.

If spins of electron and positron are parallel, total spin 1, then they have no way whatsoever to annihilate into two photons. They cannot annihilate into two photons spin 1 into different direction totalling 1, nor can they annihilate into two photons with combined intrinsic spin 0, but orbital angular momentum 1 relative to each other (emitted off-center). No, orthopositronium lives 1000 times longer than parapositronium and eventually decays into 3 photons, most of the time. There is an alternative, that happens to one in a million orthopositroniums - and that is decay into 5 photons! Meaning that for over 1 000 000 000 times the lifetime of parapositronium, orthopositronium has no way to decay into 2 or 4 photons by any mechanism.

Proton and antiproton annihilate into pions. But pions have no spin whatsoever! Then how can orthoprotonium annihilate and dispose of its spin, seeing that annihilation into particles with orbital angular momentum is utterly impossible for positronium? Yet orthoprotonium appears to annihilate without any obvious trouble...

 

[kjhskj75]

Proton and antiproton annihilate into pions. But pions have no spin whatsoever! Then how can orthoprotonium annihilate and dispose of its spin, seeing that annihilation into particles with orbital angular momentum is utterly impossible for positronium? Yet orthoprotonium appears to annihilate without any obvious trouble...

With 1876 MeV from the proton & antiproton there is enough energy to create a rho meson (774 MeV & J=1) in addition to pions.

But then rho (J=1) decays to pi + pi (J=0) ?

 

[mfb]

Angular momentum from the relative motion of the particles can solve that.