Isomer Ratios from Low Primary Excitation of Residual Nuclei

A calculational procedure based on the Huizenga-Vandenbosch formalism for the determination of isomer ratios has been developed which is applicable also at low primary excitation energies of the residual nuclei, in contrast to earlier methods. This has been accomplished by introducing level densities which are based on the shell-model level calculations of Hillman and Grover rather than a level-density formula. Furthermore, the assumption that all the neutrons are emitted with the average energy $2T$ (where $T$ is the nuclear temperature) has been replaced by a more realistic neutron spectrum. In order to test this procedure, the isomer ratio of ${\mathrm{Y}}^{87}$ from the photonuclear reaction ${\mathrm{Y}}^{89}(\gamma ,2n)$, which has its reaction threshold at 20.8 MeV, was measured for bremsstrahlung of end-point energies 23, 25.6, 28.6, and 50 MeV. The results of our method are in much better agreement with the experiment than the original Huizenga-Vandenbosch approach. The analysis indicates that a relatively large fraction of the product nuclei is formed directly in the ground state and that quandrupole transitions are an important decay mode near the threshold.