Validity of theξApproximation for the72−(β)72+Decay inCe14158

The energy dependence of the beta-gamma directional correlation was measured for the ${\frac{7}{2}}^{-}\left(\beta \right){\frac{7}{2}}^{+}\left(\gamma \right){\frac{5}{2}}^{+}$ beta-gamma cascade in the decay of ${}_{58}{}^{}{}_{}{}^{}\mathrm{Ce}_{}^{141}{}_{}{}^{}$ with a slow-fast scintillation assembly in the beta energy region 165.5-422.5 keV. Results from the integral correlation showed that the correlation coefficient ${\epsilon }_4$ was zero within experimental errors, while those from the differential correlation experiment showed that the coefficient ${\epsilon }_2$ was small throughout the energy range and the results were in accordance with the use of the $\xi$ approximation to explain the inner beta transition of ${\mathrm{Ce}}^{141}$.