Studies of Low-Lying Levels of Erbium and Tungsten Isotopes with (d,p) Reactions

Abstract

Natural metal targets of erbium and tungsten and separated isotope targets of ${\mathrm{W}}^{182}$ and ${\mathrm{W}}^{183}$ were bombarded with an energy-analyzed 15-MeV deuteron beam and energy spectra of outgoing protons from the stripping reaction were taken using a precision magnetic analyzer and photographic plates. Ground-state rotational bands of even-even nuclei ${\mathrm{Er}}^{168}$ and ${\mathrm{W}}^{184}$ were observed in the highest energy region of the respective spectra. Relative intensities and angular distributions for different rotational levels agreed reasonably well with the predictions from the stripping reaction theory using the Nilsson eigenfunction for the captured neutron orbit. The next highest energy proton groups were assigned to the intrinsic two-quasi-particle or phonon excitation levels of the above even-even nuclei, on the basis of peak positions, yields, and angular distributions. Transition rates to the so-called $\gamma$-vibrational states were found quite high. Several prominent peaks with smaller $Q$ values were interpreted as due to those levels of the odd-$A$ isotopes which were associated with the Nilsson eigenstates involving low orbital angular momenta. The absolute cross sections for almost all transitions studied agreed with the predicted ones, using the distorted-wave Born approximation and the pairing interaction theory, within an accuracy of a factor of two or three.