# Meaning of ft-values in nuclear physics

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:

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).