The states of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ below 7.5 MeV have been studied using the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ reactions at a bombarding energy of 18 MeV. Angular distributions of the reaction products have been compared with distorted-wave Born-approximation predictions. The resulting spectroscopic factors are compared with those calculated using the rotational model and with experimental spectroscopic factors from the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\mathrm{}(p,d)\mathrm{}$ and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\mathrm{}(d,t)\mathrm{}$ reactions. The results suggest a $K^{\pi }=1^{-}$ $T=0\mathrm{}$ rotational band (2.21 MeV, $1^{-}$; 2.57 MeV, $2^{-}$; and 3.52 MeV, $3^{-}$) and a $K^{\pi }=2^{-}$, $T=0\mathrm{}$ band [4.58 MeV, $2^{-}$ ($0^{-}$, $1^{-}$, $3^{-}$) and 5.44 MeV, $3^{-}$ ($0^{-}$, $1^{-}$, $2^{-}$)] based on neutron pickup from the ${\frac{1}{2}}^{-}\mathrm{}\left[101\right]\mathrm{}$ Nilsson orbit. A comparison of the $l=1\mathrm{}$ ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )$ transition to the 5.95-MeV level in ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ with the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ results suggests that this state is the analog of the 5.14-MeV, $2^{-}$ state in ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ and that these levels correspond to the $K^{\pi }=2^{-}$, $T=1\mathrm{}$ band head based on nucleon pickup from the ${\frac{1}{2}}^{-}\mathrm{}\left[101\right]\mathrm{}$ Nilsson orbit. The results of the present study and a previous ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ study are discussed in terms of Nilsson configurations and associated rotational bands. It is found that the rotational model provides a reasonably adequate explanation for the observed spectroscopic factors of the negative-parity states up to 7.5 MeV and for the positive-parity states based on the ${\left({\frac{3}{2}}^{+}\mathrm{}\right[211\left]\right)}^2$ configuration if a deformation of $\delta \approx 0.5$ is assumed. The simple rotational model, however, is unable to account for the observed single-nucleon-transfer spectroscopic factors for the other positive-parity configurations.

• Received 10 May 1971

DOI:https://doi.org/10.1103/PhysRevC.4.1138