# The riddle of the neutron

by bobie
Tags: neutron, riddle
P: 336
 Quote by tiny-tim what boson?
The diagram in the link showed neutron decaying into W-boson (100 times more massive than a proton) that in its turn decays into electron-antineutrino
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P: 26,167
 Quote by bobie The diagram in the link …
you mean ?

that's a "Feynman diagram", it's not a picture of what happens, it's a diagram that summarises the mathematical equations which tell us which processes are possible, andwhat their probability is

since that particular diagram works mathematically, we know that the particular "decay" it represents is possible

other diagrams with more Ws (and other particles) also work for the same process: that diagram is the simplest one, and it calculates most of the probability

the W (boson) is called a virtual particle because it isn't real

the diagram shows a W- being "lent" to the surrounding weak field ("emitted"), but it could equally well show a W+ being "borrowed" from the surrounding weak field ("absorbed")

the wikipedia article is misleading … it says that the neutron can either emit a W- (which it says decays after a very short time), or absorb a W+ (which … what? … it doesn't say … how can any time be involved?)
 … showed neutron decayng into a W …
no, it certainly doesn't show that, not even as a mathematical figment

(a neutron can't possibly decay into a W)

it shows the neutron decaying into the proton electron and neutrino

the W is shown as a "mediator" (a catalyst)
 P: 336 Tht diagram shows also the neutrino with an arrow pointing towards the proton, is that real or virtual? What happens in reality? The neutron emits an electron and a neutrino , at what angle? - why the speed of the electron can vary? why isn't it immediately attracted back by the Coulomb force?
 PF Gold P: 2,004 I think Bobie must be getting a bit confused. Just by googling you read stuff such as the W is a "virtual particle" or it can roughly be described as a "ripple in the field". At other places you read stuff such as it is "approximately 100 times more massive than the proton with a half life of about 10 to the minus 25 seconds" and "discovered in 1983 the W boson is a fundamental particle". This latter quote is from CERN (W Boson:Sunshine and Stardust)
PF Gold
P: 2,004
 Quote by bobie Tht diagram shows also the neutrino with an arrow pointing towards the proton, is that real or virtual? What happens in reality? The neutron emits an electron and a neutrino , at what angle? - why the speed of the electron can vary? why isn't it immediately attracted back by the Coulomb force?
The angle is such that the relevant conservation laws apply. The neutrino carries momentum and energy to keep these quantities in balance. Coulomb's law applies and as the particles separate there will be a conversion of KE to PE .Whether they subsequently approach or not depends on the original KE and other factors.
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P: 26,167
 Quote by bobie Tht diagram shows also the neutrino with an arrow pointing towards the proton, is that real or virtual
well-spotted!

the backwards arrow is because it's regarded as an anti-particle

it's actually an anti-neutrino (and is represented as such with a bar over the letter ##\nu##: ##\bar{\nu}##)

anti-neutrinos are shown in Feynman diagrams as moving backwards in time

of course they don't in reality!! … it's just a convention, and it helps with the maths

(electrons neutrons protons and up and down quarks are all regarded as particles, so they have forward arrows: their anti-particles are positrons anti-neutrons anti-protons and anti-up and anti-down quarks)

the end (initial and final) lines in a Feynman diagram represent real particles, the internal lines represent virtual particles

 why isn't it immediately attracted back by the Coulomb force?
because it's moving too fast
 P: 336 Thanks, Dadface, right you are, it's really maddening for a neophite: force which is not a force at all , particles that are virtual, nay, fundamental etc., that's why I am really thankful to you all for clearing my douts. Is this article reliable? http://en.wikipedia.org/wiki/Free_ne..._neutron_decay ? I asked you many times, but yet I do not understand: are not all neutrons identical? why a process can have different outcomes? if the decay energy is always 0.782 MeV how can the electron be emitted with different KE? , and sometimes there is also an extra γ ray: every single emitted electron should be slowed down by Coulomb law in the same way. Moreover, at the distance of m x 10^-15 the force is certainly stronger than 0.78 MeV (I reckon is in the excess of millions of MeV, isn't it) so the electron should be resucked onto the proton
Mentor
P: 10,864
 are not all neutrons identical? why a process can have different outcomes? if the decay energy is always 0.782 MeV how can the electron be emitted with different KE?
It is random, like many processes in quantum mechanics. The total energy of all three decay products is always the same and momentum is conserved as well, but it is random which part gets how much energy.
 and sometimes there is also an extra γ ray
Random as well.

 Moreover, at the distance of m x 10^-15 the force is certainly stronger than 0.78 MeV (I reckon is in the excess of millions of MeV, isn't it) so the electron should be resucked onto the proton
0.78 MeV is the energy the electron has at a large distance - the energy that is left after it moved away from the proton. And it is not millions of MeV, by the way.
P: 336
 Quote by mfb 0.78 MeV is the energy the electron has at a large distance - the energy that is left after it moved away from the proton. And it is not millions of MeV, by the way.
I thought that:
0.782 MeV is the available energy, the mass-energy the neutron loses (Mn- [Mp+Me+Mν]) and is tranformed into KE of the particles.
(If so,) the recoil of the proton and KE of neutrino is near to zero (say: 0.002), then 0.78 MeV (1.9 x 10^20 Hz) should be roughly the KE the electron can get anyway and the random variations may be only very small, considering the mass-span of the neutrino.
Am I wrong? the article I quoted says that sometimes the electron has less than a paltry 13-eV KE
and I read that sometimes it can get near C!

Since the electron is created near the neutron-proton at a distance of m x10^-14/15, how far can it go in such a strong electrostatic field , what is PE between mx10^-15 and 1m?
Mentor
P: 10,864
 Quote by bobie I thought that: 0.782 MeV is the available energy, the mass-energy the neutron loses (Mn- [Mp+Me+Mν]) and is tranformed into KE of the particles.
As pointed out multiple times, it is not.

The kinetic energy of the neutrino can be very small, very large or everything in between, there is no limit to it (apart from 0.78 MeV of course). The same is true for the electron (again, measured far away from the proton).

 Since the electron is created near the neutron-proton at a distance of m x10^-14/15, how far can it go in such a strong electrostatic field , what is PE between mx10^-15 and 1m?
This is not really a useful model, as you cannot ignore quantum-mechanical effects here. The electron does not get created at a specific point in space, it is always a distribution over some volume.
P: 336
 Quote by mfb The kinetic energy of the neutrino can be very small, .
What is the reason why mass-KE energy of the neutrino cannot be zero and the electron cannot take all available energy?
 Mentor P: 10,864 The kinetic energy of the neutrino can be as small as you like - "zero" as a single value has zero probability. The electron does not get all the energy in this case, the proton has to get some as well to conserve momentum, but this is just a small fraction of the released energy.

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