E3andM2transition strengths inBi83209

The $1{i}_{\frac{13}{2}}\ensuremath{\rightarrow}1{h}_{\frac{9}{2}}\phantom{\rule{0.16em}{0ex}}(M2)$ and $3{s}_{\frac{1}{2}}\ensuremath{\rightarrow}2{f}_{\frac{7}{2}}\phantom{\rule{0.16em}{0ex}}(E3)$ reduced proton transition probabilities in $_{83}^{209}\mathrm{Bi}$ have been determined from the direct half-life measurements of the ${\frac{13}{2}}_{1}^{+}$ and ${\frac{1}{2}}_{1}^{+}$ states using the Romanian array for $\ensuremath{\gamma}$-ray SPectroscopy in HEavy ion REactions (RoSPHERE). The ${\frac{13}{2}}_{1}^{+}$ and ${\frac{1}{2}}_{1}^{+}$ states were found to have ${T}_{\frac{1}{2}}=0.120(15)$ ns and ${T}_{\frac{1}{2}}=9.02(24)$ ns respectively. Angular distribution measurements were used to determine an $E3/M2$ mixing ratio of $\ensuremath{\delta}=\ensuremath{-}0.184(13)$ for the 1609 keV $\ensuremath{\gamma}$-ray transition deexciting the ${\frac{13}{2}}_{1}^{+}$ state. This value for $\ensuremath{\delta}$ was combined with the measured half-life to give reduced transition probabilities of $B(E3,{\frac{13}{2}}_{1}^{+}\ensuremath{\rightarrow}{\frac{9}{2}}_{1}^{\ensuremath{-}})=12(2)\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{4.pt}{0ex}}{e}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{6}$ and $B(M2,{\frac{13}{2}}_{1}^{+}\ensuremath{\rightarrow}{\frac{9}{2}}_{1}^{\ensuremath{-}})=38(5){\ensuremath{\mu}}_{N}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{2}$. These values are in good agreement with calculations within the finite Fermi system. The extracted value of $B(E3,{\frac{1}{2}}_{1}^{+}\ensuremath{\rightarrow}{\frac{7}{2}}_{1}^{\ensuremath{-}})=6.3(2)\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{4.pt}{0ex}}{e}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{6}$ can be explained by a small ($\ensuremath{\sim}6%$) admixture in the wave function of the ${\frac{1}{2}}_{1}^{+}$ state.