# particle physics question (neutrinos and deuterium at SNO)

OK, I think I understand how an electron neutrino combines with a deuterium nucleus to produce two protons and an electron. Something like:
n -> p + W-
W- + ν[sub]e[/sub] -> e

But how does the reaction work if the neutrino involved is a muon or tau neutrino? Also, the above reaction is a charged-current reaction, so I’m guessing the other ones must be the neutral-current reactions they mention – but I can’t see how a neutral current interaction could change one of the neutrons into a proton.

(Also, can anyone tell me if there’s a way to include Greek letters such as nu in my posts? The closest I could come was the letter v.)

This page looks like it covers how neutrinos are detected at Sudbury.

It looks like they don’t detect the decay or disassociation of muon or tau neutrinos—this would violate the conservation of lepton number, which AFAIK should not occur in weak reactions. Instead, they look for scattering reactions, where one of those neutrinos transfers energy to material in the tank.

OK, I think I get how it works. The muon or tau neutrino provides the energy to overcome the binding of the deuteron, and then the neutron decays on its own into a proton, electron, and anti-electron neutrino. Something like:

v[sub]x[/sub] + d -> v[sub]x[/sub] + p + n
n -> p + e + anti-v[sub]e[/sub]

Or, for people like me who like things really spelled out:
neutral current reaction:
v[sub]x[/sub] -> v[sub]x[/sub] + Z[sup]0[/sup]
Z[sup]0[/sup] + d -> p + n

neutron decay:
n -> p + e + anti-v[sub]e[/sub]

So, all in all:
v[sub]x[/sub] + d -> p + p + e + anti-v[sub]e[/sub]

If the incoming neutrino is an electron neutrino, I guess we could get either this or the charged current reaction I posted above.

If someone in the know sees that these reactions I’ve written are wrong, let me know. I’m still just learning this particle physics stuff.

Also, if anyone can tell me how to put a bar above v[sub]e[/sub], rather than having to write “anti-” like I did, I’d appreciate it. And I’m still wondering how I can write Greek letters.

tim314, you’re right about the dissociation of deuterium, but the subsequent neutron decay is sort of irrelevant. What’s unique about SNO is that deuterium will capture the freed neutrons with a release of 6.25 MeV of energy in the form of gamma rays. It’s this burst of gammas that reveals the neutron’s presence (and, thus, the presence of the neutrino that dissociated a deterium nucleus in the first place.)

That’s actually the first phase of SNO. They’ve also finished their phase II salt run. For this, they added salt to the detector so that the neutrons can capture on chlorine (which they do more efficiently), with a release of 8.6 MeV. There is a third phase (in progress) in which they will detect neutrons directly with He-3 proportional counters.

So, the relevant reactions in SNO are:

charged current: [symbol]n[/symbol][sub]e[/sub] + d --> e[sup]-[/sup] + p + p
Only [symbol]n[/symbol][sub]e[/sub] can do this in SNO because the solar neutrinos don’t have enough energy to produce a [symbol]m[/symbol] or a [symbol]t[/symbol]. These reactions are identified by the Cerenkov light from the outgoing e[sup]-[/sup] and the direction of the outgoing e[sup]-[/sup] relative to the direction to the sun.

neutral current: [symbol]n[/symbol][sub]x[/sub] + d --> [symbol]n[/symbol][sub]x[/sub] + p + n
The three flavors all have the same reaction rate for this one. These are identified by the neutron detection mechanisms above (different for each phase.)

elastic scatter: [symbol]n[/symbol][sub]x[/sub] + e[sup]-[/sup] --> [symbol]n[/symbol][sub]x[/sub] + e[sup]-[/sup]
[symbol]n[/symbol][sub]e[/sub] have a different cross section than [symbol]n[/symbol][sub][symbol]u[/symbol][/sub] and [symbol]n[/symbol][sub][symbol]t[/symbol][/sub] for this one because the [symbol]n[/symbol][sub]e[/sub] can do this via either the charged current or the neutral current but the other two only get to use the neutral current (since the target is an electron). These reactions are also identified by the Cerenkov light from the outgoing e[sup]-[/sup] and the direction of the outgoing e[sup]-[/sup] relative to the direction to the sun.

I just skimmed the article you linked to in the OP. The couple of paragraphs I read revealed that they didn’t know what they were talking about, so you should probably not read too finely into the physics they’re presenting.

SNO’s actually a pretty neat – and not very easy – experiment, with quite convincing results. It took 'em a while (~10 years), but they did an excellent job.

(Also: you can use the “symbol” tag for Greek letters. I don’t know about the overbar.)