Solving the Charge Conundrum in Negative Beta Decay

[misogynisticfeminist]

There's a question which bugged me for quite a while.

Say, in negative beta decay, in a tritium nucleus. 2 neutrons, 1 proton, 1 orbital electron. The neutron changes into a proton, by the exchanging of a W- particle which soon decays into a electron and an antineutrino. charge is conserved at the point where the W- decayed but, the electron is soon expelled from the nucleus as a beta particle. So now, er've got 1 neutron and 2 protons to deal with but only 1 orbiting electron, so how do the atom take care of this +1 charge?

 

[marlon]

I answered this question already to somebody else. the clue of the story is this : the electron has NOTHING to do with the mother-nucleus in question. This process was one of the problems that triggered the development of QFT.

In QFT particles can be created out of the fysical vacuum. Basically this means that partcles can be created out of NOTHING and this is what happens with the electron in de beta-decay. In QFT this is done by the creation and annihilation operators that are a result of the second-quantization-procedure.

So the electron is not taken away from the atom (nukleus to be correct) that decays, but it is created out of nothing in order to repsect the conservation laws that are active...

regards
marlon

 

[marlon]

As an addendum,

both the electron and the anti-neutrino, involved in de negative beta decay are created out of the QED-vacuum. This was even postulated by the great Enrico Fermi, prior to the advent of quantum field theory.

n->p + electron + antineutrino
Conservation laws are OK.
1) baryonnumber : both on the left as on the right hand side of the equation we have a nucleon.

2) leptonnumber is ok : left it is zero, on the right it is also zero because the electron is a lepton and the antineutrino is an anti-lepton.

3) charge is ok since the antineutrino has no charge

4) isospin is NOT ok : neutron has a value -1/2 and the proton has isospin +1/2 . This loss of symmetry gave rise to the socalled weak-interactions. Both electron and antineutrino have isospin zero since they don't feel the strong force.



regards
marlon

 

[marlon]

The neutrino's were postulated by Enrico Fermi because conservation of energy was not respected by the "original" beta decay which was : n->p + electron (this was proposed by Iwanenko in 1932)

In experiments the observed energies for the electron varied continuously from zero to a maximal energy that was equal to the difference in rest-energy (sorry the for language, but i mention rest for clarity, ok?) of the three particles involved. This difference was also equal to the kinetic energy of the electron. Basically, theory predicted a discrete emission-spectrum for the electron yet a continuous one was observed. this is the reason why neutrino's were postulated in order to maintain the conservation law of energy.

The decay-energy is devided between the electron and the neutrino. the proton is not taken into account because it is 1836 times more heavy then the electron, so it is the latter that takes all the energy.

Neutrino's have spin 1/2 in order to respect the spin balance of the equation. They have to be neutral and the must interact weakly (because it was not observed). The restmass is zero because the maximum energy of the electron is equal to the difference in rest-energies of the neutron, proton and the electron. just write down conservation of energy and you will see what i mean.

Apart from a discussion on the gauge-bosons of the weak force and the breaking of parity (very important in QFT AND QCD) , this is all you can say about the beta decay.

regards
marlon

 

[misogynisticfeminist]

yea ok, so if the beta particle was created out of the vacuum, the beta particle is virtual? and according to the uncertainty relation, the beta particle would actually have to return back its energy to the vacuum, right? So by right, the beta particle should not exist for very long and should have even a shorter range than an alpha particle...>??

 

[marlon]

yea ok, so if the beta particle was created out of the vacuum, the beta particle is virtual? and according to the uncertainty relation, the beta particle would actually have to return back its energy to the vacuum, right? So by right, the beta particle should not exist for very long and should have even a shorter range than an alpha particle...>??

Not at all ...

The electron is never virtual here because there is enough energy available due to the decay, to give it it's valid reason to exist. With the available energy an electron is constructed out of the vacuum. That is the way you got to look at it ...

regards
marlon

 

[misogynisticfeminist]

hmmmm, so you're saying that instead of something like virtual photons which actually borrow energy from the vacuum and it is created from the vacuum, the beta particle is created from the vacuum, but the energy is not from the vacuum but rather from the decay...

is that it?

 

[marlon]

Yes that is what i am saying. Don't mix things up with virtual particles, they are of a totally different nature and use.

Another example : When two quarks that are confined are pulled away from each other, their potential energy increases. At a certain length there will be enough energy available (not from the vacuum but from the two quarks being pulled away) that a new quark-anti-quarkpair will be created out of the vacuum. The fluxtube connecting the two "original" quarks breaks up and we get two quarkpairs in stead of one pair with a great distance between the quarks...

regards
marlon

 

[misogynisticfeminist]

yea, with that whole quark thing, I've understood what you mean. So, its the whole e=mc squared thing plus the uncertainty relation. Thanks a lot dude...

: )

 

[marlon]

indeed,
you wellcome