E2M1Mixing Ratio of the 123-keV Transition inFe57Determined from a Mössbauer Coincidence Experiment

For gamma cascades $\mathrm{}\left(2\right)\mathrm{}\stackrel{{\gamma }_2}{\to }\mathrm{}\left(1\right)\mathrm{}\stackrel{{\gamma }_1}{\to }\mathrm{}\left(0\right)\mathrm{}$ in nuclei where the separate magnetic components of the ground-state transition (1) → (0) can be observed by the Mössbauer effect because there is a strong internal magnetic field, information about the multipole character of ${\gamma }_2$ and ${\gamma }_1$ can be obtained by measuring the relative intensities of the magnetic components of ${\gamma }_1$ in coincidence with ${\gamma }_2$ for specified emission angles of ${\gamma }_1$ and ${\gamma }_2$ with respect to an external polarizing field. In particular, the mixing ratio of ${\gamma }_2$ can be determined if the spins of the levels and the multiple character of ${\gamma }_1$ are known. One advantage of this method over normal $\gamma -\gamma$ directional correlation experiments is that the populations of the sublevels of state (1) are independent of the precession of the nuclear spin axis around the field direction. This makes the method especially suitable for cases where the lifetime of state (1) is so long that the directional correlation is appreciably affected by the precession. Another advantage of the method is that there is no averaging effect of the summation over the sublevels. The method has been used to determine the $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratio of the 123-keV transition in the $(\frac{5}{2}-)\stackrel{123 \mathrm{keV}}{\to }(\frac{3}{2}-)\stackrel{14.4 \mathrm{keV}}{\to }(\frac{1}{2}-)$ cascade in ${\mathrm{Fe}}^{57}$. Both gamma rays were observed under angles of 90° with respect to the field magnetizing the Armco foil in which the ${\mathrm{Co}}^{57}$ activity was diffused. Designating the intensities of the components of ${\gamma }_1$ observed in coincidence with ${\gamma }_2$ by $I_1^{}{}_{}{}^c\cdots I_6^{}{}_{}{}^c$ (from low to high energy) the following ratios were measured: $\frac{I_1^{}{}_{}{}^c}{I_2^{}{}_{}{}^c}=0.91\mathrm{}\pm 0.035$ and $\frac{I_6^{}{}_{}{}^c}{I_5^{}{}_{}{}^c}=0.89\mathrm{}\pm 0.035$. Taking into account incomplete magnetization of the source and finite solid angles of the counters, an $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratio $\delta =-0.15\mathrm{}\pm 0.035$ is derived from these ratios.