Nuclear Structure Studies in the Selenium Isotopes with (d, p) and (d, t) Reactions

Levels of ${\mathrm{Se}}^{77}$, ${\mathrm{Se}}^{78}$, ${\mathrm{Se}}^{79}$, ${\mathrm{Se}}^{81}$, and ${\mathrm{Se}}^{83}$ below about 5 MeV were investigated by observation of the energy and angular distributions of protons emitted in the ($d, p$) reactions at 15-MeV bombarding energy. Values of the transferred-neutron angular momenta and of the spectroscopic factors for levels were derived from the measurements by distorted-wave Born approximation calculations. The results for the degree of filling of shell-model states and locations of the "centers of gravity" of the shell-model levels were compared with the pairing theory of Kisslinger and Sorensen. It was found that the ${\frac{3}{2}}^{-}$, ${\frac{5}{2}}^{-}$, and ${\mathrm{½}}^{-}$ subshells are less full and the $g_{\frac{9}{2}}$ more full than expected. General agreement with pairing theory was obtained with the following parameters: ${\epsilon }_{{\frac{9}{2}}^{+}}=3.0\mathrm{}$ MeV, ${\epsilon }_{{\frac{1}{2}}^{-}}=2.5\mathrm{}$ MeV, ${\epsilon }_{{\frac{5}{2}}^{-}}=1.0\mathrm{}$ MeV, ${\epsilon }_{{\frac{3}{2}}^{-}}=0\mathrm{}$, and $\Delta =1.65\mathrm{}$ MeV from the odd-even mass difference. In ${\mathrm{Se}}^{83}$, an isomer of spin${\mathrm{½}}^{-}$ at 0.22 MeV was identified. Measurements on ($d, t$) reactions indicate that the $d_{\frac{5}{2}}$ subshell from the next (50-82) major shell is filling (∼0.6 particle) in the Se nuclei, even though the lower (28-50) major shell is not completely full.