The matrix element

We shall assume a point interaction that

• creates the and ,
• changes the neutron to a proton,
• has a coupling constant g, which describes its strength,
• is independent of energy.

(so we don't have to know anything about the weak interaction!)

The initial state contains an initial nuclear wave function; the final state contains a final nuclear wave function, an outgoing electron (which we will treat as a plane wave), and an outgoing antineutrino (also treated as a plane wave). The plane waves will be assumed to be normalized in a volume V.

The matrix element is then

where .

Now, MeV, so the maximum kinetic energies of the leptons are of this order. Thus where R is the nuclear radius. So over the nuclear volume,

Thus, in the simplest case,

If the initial and final states are similar (the same shell model states), then . These decays are known as ``superallowed''.