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The beta decay energy of a triton is something like 18 500 eV. When (most of time) a free electron is emitted, its energy can acquire any continuous values - 100 eV or 110, or 100,10 or any value in between, because the rest is distributed to a neutrino, with flavour of antielectron.

The usual result is He3+ cation, hydrogenlike atom. Sometimes the emitted electron ionizes the existing electron on the way out, leaving an He-3 nucleus.

But surely an emitted electron does not have a free choice of energy on the end below a few tens of eV?

A He atom has no excited states within 20 eV of ground state.

So what is the probability that a T atom does not emit a free electron, but decays into a bound state of He-3 atom, giving all the rest of 18 500 eV to the neutrino? What is the probability that the bound state is specifically ground?

A ground state of He-3 is stable. It follows that its energy and momentum has no uncertainty whatsoever and can be measured to arbitrary precision.

A ground state T atom is long-lived. With lifetime in the order of 10ˇ8 s, the theoretical decay width of T should be around 10ˇ-23 eV

What is the present experimental uncertainty of triton decay energy, that 18 keV?? I guess bigger than 10ˇ-23 eV, but how big by last best estimates?

Suppose that a He-3 atom recoiled by neutrino emission could have its energy and momentum measured with a great precision, and the energy and momentum of original T were also known to a great precision, e. g. because of smallness.

How precisely could the rest mass of the roughly 18 500 eV neutrino be calculated from the measurement of the energy of the recoiled ground state He-3 atom? I. e. how does the uncertainty of recoil atom energy map into uncertainty of neutrino rest mass, perhaps depending on what the rest mass is?