Nuclear-Orientation and Angular-Correlation Studies ofFe57andFe58

The $E2:M1\mathrm{}$ multipole mixing ratio of the ${\frac{5}{2}}^{-}\to {\frac{3}{2}}^{-}$ and $2^{+}\to 2^{+}$ transitions between the second and first excited states in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}$, respectively, have been measured. The nuclear-orientation sources were prepared by diffusing cobalt activity into iron. Nuclear polarization was obtained by cooling the sample to 25 mK using a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ dilution refrigerator and applying sufficient external magnetic field to saturate the iron. The value $\delta =0.120\mathrm{}\pm 0.002$ was obtained for the 122-keV transition in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ by a nuclear-orientation measurement. The ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}$ $\gamma \gamma$ angular-correlation results used (a) NaI(Tl)-NaI(Tl) and (b) Ge(Li)-NaI(Tl) detector combinations and gave consistent results: (a) $A_{22}=0.460\mathrm{}\pm 0.013$, $A_{44}=0.150\mathrm{}\pm 0.021$; (b) $A_{22}=0.45\mathrm{}\pm 0.04$, $A_{44}=0.08\mathrm{}\pm 0.09$. The orientation experiment yielded $A_2=0.33\mathrm{}\pm 0.03$. These values give $\delta =0.69\mathrm{}\pm 0.05$ for the 865-keV transition. From a knowledge of the temperature of the orientated nuclei the Fermi to Gamow-Teller matrix element ratio of the two $2^{+}$-$2^{+}$ electroncapture and ${\beta }^{+}$ transition from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$ were obtained. For the transition to the 1675-keV level $\lambda =0.07\mathrm{}\pm 0.06$ and to the 810-keV level $\lambda =0.04\mathrm{}\pm 0.06$. The mixing ratio measurements remove existing possible ambiguities and illustrate the very useful advantages of combining nuclear-orientation and angular-correlation methods.