Isobar masses and beta decay

The masses of the isobars for a given A can be examined by considering them as a function of (i.e., in terms of the deviation from ).

Note the importance of the pairing term. For odd A it is zero, and all isobar masses lie on one parabola. For even A, the even-even and odd-odd nuclides lie on different parabolae. Decays will occur down to the lowest masses by beta decay, which can only connect neighbouring nuclides. There will thus be one minimum for odd A, and (one or) two for even A.

The beta decays are determined by the mass differences. Various modes of beta decay are possible.

decay

This is for . The decay can be written as

Note that the masses we deal with are atomic masses; in increasing the atomic number, the atom acquires another electron; this is `provided' by the beta decay process. Thus the overall atomic process is

The neutrino is massless. The energy released as kinetic energy is then

decay

This is for . The decay can be written as

However, the reduction in atomic number has liberated an atomic electron; in terms of atoms

The energy released as kinetic energy is then

Electron capture

The above process cannot occur if the mass difference is less than twice the electrom mass ( MeV). The competing process of electron capture then becomes important. The s electrons in particular have a non-vanishing density within the nuclear volume. An atomic electron can then be `captured' by a proton to yield

Electron numbers are now balanced and the energy release is

where is the binding energy of the captured electron.