A Model for Nuclear Fission — Question 7

Question 7

Competing decay widths determine a fission branching fraction

An excited compound state has partial widths $\Gamma_f=.30$ eV, $\Gamma_n=.50$ eV and $\Gamma_\gamma=.20$ eV. Use $\tau=\hbar/\Gamma_{\mathrm{total}}$ and $\hbar=6.582\times10^{-16}$ eV s.

1. Find the state mean life and the probability of decay by fission.

2. If a model correction doubles only the fission width, calculate the new mean life and branching probability.

Question 7 - Solution

Competing decay widths determine a fission branching fraction

(a) Method and calculation

$$\Gamma=\Gamma_f+\Gamma_n+\Gamma_\gamma=1.00\,\mathrm{eV}\Rightarrow\boxed{\tau=6.582\times10^{-16}\,\mathrm s}.$$$$\boxed{b_f=\Gamma_f/\Gamma=.300}.$$

(b) Interpretation and further calculation

$$\Gamma\prime=.60+.50+.20=1.30\,\mathrm{eV}\Rightarrow\boxed{\tau\prime=5.0631\times10^{-16}\,\mathrm s}.$$$$\boxed{b_f\prime=.60/1.30=.46154\ne2b_f}.$$

Physical check

Changing one channel changes the normalization of all branching fractions. Partial widths add because they represent competing decay rates.