# Differences between neutrons from electron capture and positron emission

I imagine that the mass of a neutron from $\beta^{+}$ decay is about $2.5 Em$ lighter than one obtained by electron capture. Is that so?

Can you tell me how wide neutron mass can range, and if there are other differences? In particular I'd like to know if magnetic moment is the same, and why. Also, do you know what happens when a $\beta ^+$ decays, does it still emit a neutrino and one electron and how this new electron is formed?

• A neutron is a neutron (no matter how small...) – Jon Custer Sep 20 '16 at 12:27
• Why do you imagine that the mass of a neutron from beta-plus decay is about 2.5 Em lighter than one obtained by electron capture? Can you explain the mechanism for this mass difference? – John Rennie Sep 20 '16 at 13:02
• @JohnRennie, well: a proton acquires an electron, p+1 a proton loses a positron p -1, it's 2 Em difference, plus neutrino and KE's... I made a round figure! if that's so, something might affect the magnetic moment, or whatever – user104372 Sep 20 '16 at 13:47
• The Wikipedia article on beta decay will at least show you the actual initial and final products. – Jon Custer Sep 20 '16 at 15:07

Suppose we have a nucleus with $n$ neutrons and $p$ protons - I'll write this as $np$. In $\beta^{+}$ decay a proton decays into a neutron, a positron and a neutrino, while in electron capture a proton absorbs an electron to produce a neutron and neutrino. So the two processes are:
\begin{align} np &\rightarrow (n+1)(p-1) + \bar{e} + \nu \\ np + e &\rightarrow (n+1)(p-1) + \nu \end{align}
Although in both cases we end up with the same nucleus, $(n+1)(p-1)$, in $\beta^{+}$ decay overall we lose an electron while in electron capture overall we gain an electron. If the mass of the nucleus is the sum of the proton and neutron masses then this implies the extra neutron created must have a different mass in the two cases.