What is the "physical" meaning of the ft-value for a decay channel? From what I understand, the ft-value is inversely proportional to the square of the matrix element, hence I would expect a larger ft-value would correspond to a less probable decay route. Is this correct?


It is close. The matrix element is only a part of the game. It is $t_{1/2}$ (actually $1/{\tau}$) who is the definitive answer to the probability of the route. The other part are kinematic factors (see Fermi's Golden rule 1 )

$\lambda_{beta} = \frac{\log(2)}{t_{1/2}}= g^2 \frac{m_e^5 c^4 |M^L_{if}|^2}{2\pi^3\hbar^7} \Big[ \frac{1}{(m_ec)^5}\int_0^{p_{max}} dp S^L(p,q)F^{\pm}(Z^\prime,p)p^2q^2 \Big] $

The term in big bracket if $f_L$ is a spectrum shape dependent factor (influence of Coulomb and angular momenta) and a useful (famous) factorization can be done

$f t_{1/2} \sim \frac{1}{|M^L_{if}|^2}$.

This formula says that from measured characteristics and the half-life, one can deduce the information about the matrix element itself. See the normogram:

see http://oregonstate.edu/instruct/ch374/ch418518/lecture9rev.pdf

Different transition types have typical $\log(ft)$ values :

  • Superallowed - 2.9–3.7 (no parity change, $L_{beta}=0$, spin change $\Delta J=0$)
  • Allowed - 4.4–6.0 (no parity change, $L_{beta}=0$, spin change $\Delta J=0,1$)
  • First forbidden 6 – 10
  • etc.

A detected transition with a specific $\log ft$ should have corresponding characteristics (if known. if not, it may be used to deduce them).

1 http://www.umich.edu/~ners311/CourseLibrary/bookchapter15.pdf


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