Allowed beta decay

A beta decay transition whose leading lepton orbital term has $l=0$. Fermi transitions allow $\Delta J=0$ and Gamow-Teller transitions allow $\Delta J=0,1$, excluding a Gamow-Teller $0\to 0$ transition. Both preserve nuclear parity. Allowed describes the selection rules; cancellations in the nuclear matrix element can still make an allowed transition slow.

The approximate fifth-power scaling of an allowed beta decay rate with available energy when electron mass and Coulomb distortion are negligible and the nuclear matrix element is held fixed. It follows from ${\int }_0^Q{p}^2(Q-p{)}^{2}dp=Q^5/30$. Different nuclear matrix elements or nonrelativistic electron kinematics spoil an exact universal law.

With a momentum-independent allowed nuclear matrix element, negligible nuclear recoil and negligible neutrino mass, the electron spectrum in natural units is $d\Gamma /dp=CF(Z,E)p^2(E_0-E{)}^2$, where $E=\sqrt{p^2+m_e^2}$. Transforming to an energy spectrum requires the Jacobian determinant $dp/dE=E/p$.

The electron-nucleus Coulomb-distortion factor multiplying an otherwise plane-wave beta decay spectrum. It depends on daughter charge, lepton charge and lepton energy. Its energy dependence means that a pure fifth-power phase-space rule is not generally exact.

An especially strong allowed beta decay, conventionally including pure Fermi transitions between $0^{+}$ isobaric analog states. Those states have closely related spatial and spin structure, so the isospin ladder operator has a large overlap. A $0^{+}\to 0^{+}$ assignment alone fixes the allowed Fermi character, but does not establish analog-state overlap or a large rate; a small comparative half-life supplies additional evidence.