Magnetic Dipole and Electric Quadrupole Hyperfine Effects inBi209Muonic X Rays

Abstract

The muonic x rays from the spherical nucleus ${\mathrm{Bi}}^{209}$ were detected by Li-drifted germanium detectors with an energy resolution of 0.14% at 6-MeV $\ensuremath{\gamma}$ energy. The following information was obtained: (1) The hfs due to the $M1$ and $E2$ interactions between the muon and the nuclear charge and magnetic moment distributions was observed. The theoretically predicted splittings based on different nuclear models were compared with the experimental results. (2) The parameters of the spherical charge distribution as described by the "Fermi distribution" were determined from the transition energies of the $K$ and $L$ muonic x rays: $c=({{1.126}_{\ensuremath{-}0.006}}^{+0.008}){A}^{\frac{1}{3}}$ fm and $t=4{log}_{e}3$ (${0.511}_{\ensuremath{-}0.033}^{+0.026}$) fm. (3) The experimental results confirm the anomalous intensity ratios previously observed in Bi muonic x rays. The observed intensity ratios were $(2{p}_{\frac{3}{2}}\ensuremath{\rightarrow}1{s}_{\frac{1}{2}}):(2{p}_{\frac{1}{2}}\ensuremath{\rightarrow}1{s}_{\frac{1}{2}})=1.38\ifmmode\pm\else\textpm\fi{}0.1$, $(3{d}_{\frac{5}{2}}\ensuremath{\rightarrow}2{p}_{\frac{3}{2}}):(3{d}_{\frac{3}{2}}\ensuremath{\rightarrow}2{p}_{\frac{1}{2}})=1.5\ifmmode\pm\else\textpm\fi{}0.1$, and $(4{f}_{\frac{7}{2}+\frac{5}{2}}\ensuremath{\rightarrow}3{d}_{\frac{5}{2}}):(4{f}_{\frac{5}{2}}\ensuremath{\rightarrow}3{d}_{\frac{3}{2}})=1.29\ifmmode\pm\else\textpm\fi{}0.3$. (4) The cascade transitions in the sequence $4f\ensuremath{\rightarrow}3d\ensuremath{\rightarrow}2p\ensuremath{\rightarrow}1s$ are approximately equal in intensity within an uncertainty of 15%.