Analysis of the Nuclear Reaction Spectroscopy of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Hf</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>177</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Hf</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>179</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Hf</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>181</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

This study of the nuclear levels in $^{181}\mathrm{Hf}$, $^{179}\mathrm{Hf}$, and $^{177}\mathrm{Hf}$ has utilized the reactions $^{180}\mathrm{Hf}(d,p)^{181}\mathrm{Hf}$, $^{180}\mathrm{Hf}(d,t)^{179}\mathrm{Hf}$, $^{178}\mathrm{Hf}(d,t)^{177}\mathrm{Hf}$, and $^{176}\mathrm{Hf}(d,p)^{177}\mathrm{Hf}$ 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 $^{180}\mathrm{Hf}(d,p)$, $Q=3475\ifmmode\pm\else\textpm\fi{}10$ keV; $^{180}\mathrm{Hf}(d,t)$, $Q=\ensuremath{-}1112\ifmmode\pm\else\textpm\fi{}4$ keV; $^{178}\mathrm{Hf}(d,t)$, $Q=\ensuremath{-}1364\ifmmode\pm\else\textpm\fi{}9$ keV; and $^{176}\mathrm{Hf}(d,p)$, $Q=4150\ifmmode\pm\else\textpm\fi{}7$ keV. Angular distributions were measured for the reactions $^{180}\mathrm{Hf}(d,p)^{181}\mathrm{Hf}$, $^{178}\mathrm{Hf}(d,t)^{177}\mathrm{Hf}$, and $^{176}\mathrm{Hf}(d,p)^{177}\mathrm{Hf}$, 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 ${\frac{7}{2}}^{+}[633]$, ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$[521], ${\frac{5}{2}}^{\ensuremath{-}}[512]$, ${\frac{7}{2}}^{\ensuremath{-}}[514]$, ${\frac{9}{2}}^{+}[624]$, ${\frac{1}{2}}^{\ensuremath{-}}[510]$, ${\frac{3}{2}}^{\ensuremath{-}}[512]$, ${\frac{7}{2}}^{\ensuremath{-}}[503]$, ${\frac{3}{2}}^{\ensuremath{-}}[501]$, ${\frac{5}{2}}^{\ensuremath{-}}[503]$, and ${\frac{13}{2}}^{+}[606]$. 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.