Need help with the reaction of neutrons and electrons

Main Question or Discussion Point

Please let me know if the following reaction is possible for high energy electrons colliding with neutrons or neutron-rich nuclei:
$$n+e^{-}\to \Delta^{-}+\nu_e.\tag{1}$$
If it is forbidden for some conservation law or for some other reason, please give me an explanation why. This reaction is analogous to the following ones, which are not forbidden:
$$\begin{gather} p+p\to D+e^{+}+\nu_e,\tag{2}\\ n\to p+e^{-}+\bar\nu_e,\tag{3}\\ p+e^{-}\to n+\nu_e.\tag{4} \end{gather}$$

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phinds
Gold Member
2019 Award
Is this homework?

No. Not a homework assignment. I am 57, too old for homework. I just want to discuss the reaction that I did not find anywhere on the Web.

ORF
Hello,

The interaction for case (1) is weak, because a charged lepton is turned into neutral lepton. So, the quantum numbers that must be conserved are electrical charge (ok), barionic number (ok), energy (ok?). Lets see angular momentum:

J(n) = 1/2
J(e-)=1/2
J(D-)=3/2
J(ne)=1/2

The combination of J_in = 1/2 x 1/2 = {1,0} (neutron + electron angular momentum)
The combination of J_out = 3/2 x 1/2 x L = {2,1,0} x L (D- + neutrino angular momentum

So if L = 3,2,1 or 0, the total angular momentum is conserved. Lets say angular momentum can be conserved.

If the reaction is mediated by the weak interaction, parity can be violated.

Maybe I am forgetting something, but I don't remember other quantum numbers that must be conserved for weak interactions.

From the experimental point of view, if neutrinos are involved in the reaction, the effects of electromagnetic force neutron-electron (which are orders of magnitude stronger) will disguise/shadow of the weak interactions; ie, the cross section of this reaction will be much smaller than other possible reactions (n+e- -> other things).

I hope it can help.

Regards,
ORF

ChrisVer
Gold Member
Please let me know if the following reaction is possible for high energy electrons colliding with neutrons or neutron-rich nuclei:
$$n+e^{-}\to \Delta^{-}+\nu_e.\tag{1}$$
If it is forbidden for some conservation law or for some other reason […]
I just want to discuss the reaction that I did not find anywhere on the Web.
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Well it is not so absent from out there... it's very similar to the neutrino deep inelastic scattering processes, where the electron and neutrino are swapped (you shoot neutrinos and study the inner structure of the protons/neutrons). Of course the charges need readjustment.

energy (ok?)
You don't really have to think about the energy in MANY--->MANY processes in order to say if they are forbidden or not. Of course you might need a threshold to produce the final state particles but that doesn't forbid the interaction for you.

mfb
Mentor
Well it is not so absent from out there... it's very similar to the neutrino deep inelastic scattering processes, where the electron and neutrino are swapped (you shoot neutrinos and study the inner structure of the protons/neutrons). Of course the charges need readjustment.
For neutrinos you have weak interactions only, so it is (comparatively) easy to study them. For electrons at the energies needed for this reaction you have the electromagnetic interaction which will completely dominate the collision processes.

ChrisVer
Gold Member
For neutrinos you have weak interactions only, so it is (comparatively) easy to study them. For electrons at the energies needed for this reaction you have the electromagnetic interaction which will completely dominate the collision processes.
Yup. Noting though that I was referring to whether the interaction is forbidden or not.