Study of Deformed Odd-ANuclei by the (d, p) Reaction

Abstract

${\mathrm{Yb}}^{176}$ (97.5%) and ${\mathrm{Hf}}^{178}$ (95.5%) targets have been bombarded with 12-MeV deuterons. The protons emerging from the ($d, p$) reaction were analyzed with ≈ 15-keV energy resolution at many angles utilizing a single gap, broad range magnetic spectrograph. Up to 3 MeV, 55 states have been observed in ${\mathrm{Yb}}^{177}$ and 60 in ${\mathrm{Hf}}^{179}$. Most of these states were previously unknown. The lowest energy levels in both ${\mathrm{Yb}}^{177}$ and ${\mathrm{Hf}}^{179}$ can definitely be identified with the intrinsic Nilsson orbitals $\frac{9}{2}+$ (624), $\frac{7}{2}-$ (514), and ½-(510) and their associated rotational bands. The absolute cross sections and the angular distributions of the protons were measured for the reaction ${\mathrm{Yb}}^{176}(d, p){\mathrm{Yb}}^{177}$. The experimental results agree very well with the predictions of the Satchler and Tobocman stripping theory for deformed nuclei. It is, therefore, established that this theory can furnish a valuable criterion for assigning spins and Nilsson orbitals in deformed nuclei. The discrepancy between experimental and calculated values of the decoupling parameter, $a$, for the ½- (510) band can be resolved if one replaces, in the expansion of the wave function, the theoretical Nilsson coefficients by experimentally determined coefficients. This seems to indicate that ($d, p$) reactions may be a useful aid in determining detailed properties of the wave functions for deformed nuclei. A comparison of the lowest states of the 107 neutron isotones ${\mathrm{Yb}}^{177}$, ${\mathrm{Hf}}^{179}$, ${\mathrm{W}}^{181}$, and ${\mathrm{Os}}^{183}$ is presented.