Determination of the E-2 M-1 Multipole Mixing Ratios of the Gamma Transitions in Cd-110

TL;DR: In this paper, Bohrelson et al. measured the 1-2, 1-3, and 1-4 directional correlations, using two 30-cc coaxial Ge(Li) detectors in conjunction with a multichannel coincidence gating system.

Abstract: The multipole character and $\frac{E2}{M1}$ mixing ratios of all $\ensuremath{\gamma}$ transitions following the decay of ${\mathrm{Ag}}^{110m}$ to ${\mathrm{Cd}}^{110}$ have been determined by measuring the 1-2, 1-3, and 1-4 directional correlations, using two 30-cc coaxial Ge(Li) detectors in conjunction with a multichannel coincidence gating system. The analysis of the data clearly demonstrated the necessity for careful investigations of the effects of the Compton background on directional correlation measurements using Ge(Li) detectors. The directional correlation functions for mixed $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ cascades are given in terms of explicitly defined reduced matrix elements and their ratios $\ensuremath{\delta}({\ensuremath{\gamma}}_{n})$. The analysis of the 25 measured directional correlations yielded a consistent set of $\frac{E2}{M1}$ mixing ratios for all mixed multipole transitions. The $\frac{E2}{M1}$ amplitude ratios $\ensuremath{\delta}({\ensuremath{\gamma}}_{n})=\frac{〈{I}_{n+1}\ensuremath{\parallel}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{j}}}_{N}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}}_{2}^{E}\ensuremath{\parallel}{I}_{n}〉}{〈{I}_{n+1}\ensuremath{\parallel}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{j}}}_{N}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}}_{1}^{M}\ensuremath{\parallel}{I}_{N}〉}$ for the ${\mathrm{Cd}}^{110}$ $\ensuremath{\gamma}$ rays are (energies are in keV): $\ensuremath{\delta}(447)=\ensuremath{-}0.45\ifmmode\pm\else\textpm\fi{}0.20$, $\ensuremath{\delta}(620)=\ensuremath{-}0.80\ifmmode\pm\else\textpm\fi{}0.50$, $\ensuremath{\delta}(678)=\ensuremath{-}0.25\ifmmode\pm\else\textpm\fi{}0.20$, $\ensuremath{\delta}(687)=\ensuremath{-}{1.1}_{\ensuremath{-}0.4}^{+0.8}$, $\ensuremath{\delta}(707)=\ensuremath{-}1.0\ifmmode\pm\else\textpm\fi{}0.3$, $\ensuremath{\delta}(818)=\ensuremath{-}1.20\ifmmode\pm\else\textpm\fi{}0.15$, $\ensuremath{\delta}(1384)=\ensuremath{-}0.37\ifmmode\pm\else\textpm\fi{}0.03$, and $\ensuremath{\delta}(1505)=\ensuremath{-}0.55\ifmmode\pm\else\textpm\fi{}0.10$. In terms of the multipole moments $〈{I}_{n+1}\ensuremath{\parallel}\mathfrak{M}(\ensuremath{\pi}L)\ensuremath{\parallel}{I}_{n}〉$ of Bohr and Mottelson, the $\frac{E2}{M1}$ moment ratios $\ensuremath{\Delta}=\frac{〈{I}_{n+1}\ensuremath{\parallel}\mathfrak{M}(E2)\ensuremath{\parallel}{I}_{n}〉}{〈{I}_{n+1}\ensuremath{\parallel}\mathfrak{M}(M1)\ensuremath{\parallel}{I}_{n}〉}$ in natural units ($\ensuremath{\hbar}=m=c=1$) are: $\ensuremath{\Delta}(447)=\ensuremath{-}3.0\ifmmode\pm\else\textpm\fi{}1.3$, $\ensuremath{\Delta}(620)=\ensuremath{-}3.8\ifmmode\pm\else\textpm\fi{}2.4$, $\ensuremath{\Delta}(678)=\ensuremath{-}1.09\ifmmode\pm\else\textpm\fi{}0.88$, $\ensuremath{\Delta}(687)=\ensuremath{-}{4.7}_{\ensuremath{-}1.7}^{+3.4}$, $\ensuremath{\Delta}(707)=\ensuremath{-}4.2\ifmmode\pm\else\textpm\fi{}1.3$, $\ensuremath{\Delta}(818)=\ensuremath{-}4.3\ifmmode\pm\else\textpm\fi{}0.5$, $\ensuremath{\Delta}(1384)=\ensuremath{-}0.79\ifmmode\pm\else\textpm\fi{}0.06$, and $\ensuremath{\Delta}(1505)=\ensuremath{-}1.08\ifmmode\pm\else\textpm\fi{}0.20$.