# Why is beta negative decay more common than beta positive?

In simple terms, why is beta negative decay more common than beta positive?

I know it's something to do with occuring inside/outside the nucleus - but I can't find a simple, easy to understand explanation!

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## 2 Answers

The beta-decay may be "locally" reduced to a decay of a proton or a neutron inside a nucleus. The beta-minus decay contains the microscopic process $$n\to p + e^- + \bar \nu_e + O(1{\rm \,MeV})$$ where the last term indicates the rough increase of the kinetic energy of the decay products. On the other hand, the beta-plus decay contains the process $$p + O(1{\rm \,MeV})\to n + e^+ + \nu_e$$ which means that the proton has to acquire some extra energy if it wants to decay to a neutron and a positron. In realistic beta-plus decays, it takes it from the surrounding nucleons in the nucleus.

Obviously, decays to lighter products where the energy conservation allows to give the final products some extra kinetic energy are more frequent than decays which only occur if an extra energy is found at the beginning. For example, among the bare processes above (for free nucleons), only the decay of the neutron may occur. The proton is stable (ignoring very infrequent processes linked to grand unification).

At the end, the inequality between the two types of the decay boils down primarily to the fact that the neutron is heavier than the proton which subsequently boils down to the fact that the down-quark is heavier than the up-quark (the rest masses).

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And there is K-capture, a kind of beta positive. – Georg Nov 7 '11 at 11:07
I haven't done anything with the kinetic energy of the decay products before - and yet this is still a question we have. Is there a simpler way of explaining it without discussing kinetic energy? – Parachuting Panda Nov 7 '11 at 11:10
Dear @Georg, you should be careful about the terminology. K-capture is sometimes called "inverse beta decay" but "beta negative decay" – despite the similar origin of "negative" and "inverse" – has to include positron emission. Comparisons of beta decays emitting electrons or positrons with K-capture is a subtle question because the two classes are qualitatively different. – Luboš Motl Nov 7 '11 at 11:11
Dear @ParachutingPanda, could you please be more specific about which concepts we are allowed to use in the answer if the concept of energy is already too difficult? – Luboš Motl Nov 7 '11 at 11:12

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Nope, @ParachutingPanda, both proper beta-decays, positive and negative, occur inside the nucleus. I don't know how to simplify this thing more than the trivial assertion it is now. Can you please define "simple"? AdamRedwine: all beta-decays are ultimately mediated by W-bosons. (There are also similar interactions mediated by Z-bosons, but they only occur - with a few irrelevant exceptions - when there is an electromagnetic interaction of the same kind as well, and the electromagnetic one is much more important in such cases.) W-bosons only become important at high energies, 100 GeV or so... – Luboš Motl Nov 7 '11 at 12:55
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Beta-minus decay occurs in nuclei with an excess of neutrons, while beta-plus decay takes place in neutron-deficit nuclei. A lot of natural background radiation on Earth is due to fission or alpha-decay of heavy radioactive elements. The remains of fission or alpha-decay are neutron-rich nuclei, so beta-minus decay is more common on Earth.

Whereas on stars beta-plus decay is typical, because neutron-deficit nuclei are produced in nuclear fusion.

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I would just add that "neutron heavy" or "neutron deficit" is relative to the island of stability, not N=Z.  I remember that there is one process for one direction and 2 processes for the other direction, so in that context I think you're missing one.  Internal capture for N-1 and Z+1?  Anyway, that's not fully in the scope of the question. – AlanSE Nov 7 '11 at 13:43
– voix Nov 7 '11 at 14:21
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