Ge(n,n′γ)Reactions and Low-Lying States of Ge Isotopes

The 90° excitation functions of the $\gamma$-ray transitions in the $\mathrm{Ge}(n,n^{\prime }\gamma )$ reactions have been measured at incident neutron energies from 0.5 to 2.55 MeV. Angular distributions at $E_n=1.75, 2.13, \mathrm{and} 2.55$ MeV have also been measured. The $\gamma$-ray production cross sections and the neutron inelastic scattering cross sections have been obtained at these neutron energies. Theoretical model calculations have been performed and are in good agreement with the experimental results. The Wolfenstein-Hauser-Feshbach formalism was used for the calculations. The low-lying decay schemes of the four even-$A$ Ge isotopes determined in this work are in good agreement with previous investigations. Branching ratios, as well as mixing ratios, of the $\gamma$-ray decay from the second $2^{+}$ state for all the four even-$A$ Ge isotopes have been obtained. The 1698-keV level of ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$ has been confirmed and its decays to the first and second $2^{+}$ states have been established. The branching ratio and mixing ratios have been determined. A spin of 3 is tentatively assigned to that level for the first time in this work. In addition, a test of the fluctuation corrections to the statistical model at the mass region near $A=70\mathrm{}$ has been made. The corrections attempted worsen the agreement between theory and experiment.