Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/phme2432/public_html/wp-content/plugins/latex/latex.php on line 47

# What I Learned Today

No frills, just learn

## Beta decay logft

The comparative half life ft is useful to compare the strength of the  and electron-capture processes over different nuclei. -decay half lives can span several orders of magnitude, from fraction of seconds to thousands of time the age of the universe. Some of these striking differences are due to relatively trivial energetic conditions, but the more interesting from a nuclear structure point of view are due to the wavefunction superposition and the angular momentum coupling.

The comparative half life ft is useful to purge from energetic and kinematic details the reaction and analyze just the nuclear structure behind. For example superallowed decays, that go from a  ground to a  ground state, should have very similar structure overall conditions, thus similar ft, even if the half life vary by orders of magnitude. And in fact the value of  for all the known superallowed decays even if the half life span from few seconds to few milliseconds.

The comparative half life is given by

where the Matrix element  for superallowed,  for allowed, and lesser for forbidden type of decays (superallowed, allowed and forbidden type of decays are dependent on the eventual unit of angular momentum and parity the radiation has to carry away, cf. Wikipedia for a list), and

thus, considering ft in the unit of seconds we have

with C the square matrix element in natural unit.

Making use of the ft value expressed in second we can deduce a common value in the Beta-decay jargon that is the logft, that is now trivially


Common example of values of logft are, ~ 3.5 for superallowed decays (as specified above), ~5.5 for allowed, ~8 for first forbidden and ~11 for second forbidden.

Check Appendix A of Towner and Hardy

Example of Calculation
Next post

The mistery of Nature's sons
Previous post