Question

The following decays are all ascribed to the weak interaction, resulting in three final state particles. For each process, the available energy Q in the decay is given as well as the mean lifetime.

Apply Sergent’* law of radioactivity to show that the Q-values and mean lifetimes are compatible with the same weak coupling.

Answer 1

According to Sargent’* law, Γ ∝ Q5

| Decay | Q (MeV) | τ() | Q5τ (MeV5 − ) |
| | | | |

The numbers in the last column vary only over one order of magnitude which is small compared to the lifetimes which span over 15 orders of magnitude, thereby conforming to the Sargents’ law (τ ∝ 1/T5 max) and therefore favoring the same coupling constant for the weak decays.