Analysis of the Nuclear Reaction Spectroscopy ofHf177,Hf179, andHf181

This study of the nuclear levels in ${}_{}{}^{181}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$ has utilized the reactions ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,p)\mathrm{}{}_{}{}^{181}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,t)\mathrm{}{}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,t)\mathrm{}{}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,p)\mathrm{}{}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$ at incident deuteron energies of 10-12 MeV. The emergent particles were analyzed in a broad-range magnetic spectrograph. The ground-state $Q$ values were determined to be ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,p)\mathrm{}$, $Q=3475\mathrm{}\pm 10$ keV; ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,t)\mathrm{}$, $Q=-1112\mathrm{}\pm 4$ keV; ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,t)\mathrm{}$, $Q=-1364\mathrm{}\pm 9$ keV; and ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,p)\mathrm{}$, $Q=4150\mathrm{}\pm 7$ keV. Angular distributions were measured for the reactions ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,p)\mathrm{}{}_{}{}^{181}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,t)\mathrm{}{}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}\mathrm{}(d,p)\mathrm{}{}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$, and interpreted with the aid of the distorted-wave Born approximation theory. $l$ values have been assigned and spectroscopic factors extracted. The assignment of $l$ values has resulted in the interpretation of the structure of ${}_{}{}^{181}{}_{}{}^{}\mathrm{Hf}$ and ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$ up to 2 MeV. The ($d,t$) study of ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$ has been used in conjunction with previously reported ($d,p$) data, and has resulted in an extension of the previous analysis. Nilsson states identified in one or more nuclei are the ${\frac{7}{2}}^{+}\mathrm{}\left[633\right]\mathrm{}$, ${\mathrm{½}}^{-}$[521], ${\frac{5}{2}}^{-}\mathrm{}\left[512\right]\mathrm{}$, ${\frac{7}{2}}^{-}\mathrm{}\left[514\right]\mathrm{}$, ${\frac{9}{2}}^{+}\mathrm{}\left[624\right]\mathrm{}$, ${\frac{1}{2}}^{-}\mathrm{}\left[510\right]\mathrm{}$, ${\frac{3}{2}}^{-}\mathrm{}\left[512\right]\mathrm{}$, ${\frac{7}{2}}^{-}\mathrm{}\left[503\right]\mathrm{}$, ${\frac{3}{2}}^{-}\mathrm{}\left[501\right]\mathrm{}$, ${\frac{5}{2}}^{-}\mathrm{}\left[503\right]\mathrm{}$, and ${\frac{13}{2}}^{+}\mathrm{}\left[606\right]\mathrm{}$. In addition a large number of $K=\frac{1}{2}$ and $\frac{3}{2}$ bands have been observed which do not have a simple interpretation in the Nilsson theory. While the low-lying (predominantly Nilsson) states agree quite well with the calculations of Soloviev, the higher states do not.