Using the angular momentum projection approach with the $l^2$-depressing parameter ${\mu }_{\mathrm{p}}$ in the Nilsson model reduced by 15%, the band heads of the $0_2^{+}$, $0_3^{+}$, and $0_4^{+}$ bands in ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$ are calculated to lie at 1221, 1426, and 1823 keV, respectively, in good agreement with recent experimental data. An additional low-lying $0^{+}$ band with a band head at 1966 keV is also predicted. A general criterion for the existence of a low-lying $0^{+}$ excited band is described and invoked to substantiate the calculated results.

• Received 13 April 1987

DOI:https://doi.org/10.1103/PhysRevC.36.2159