Quadrupole Moment of the Lowest Rotational Band in Even Calcium Nuclei

Abstract

The static electric quadrupole moment of the $2_{1}^{+}$ state in $^{42}\mathrm{Ca}$ was measured to be $(\ensuremath{-}18.9\ifmmode\pm\else\textpm\fi{}8.1)e$ ${\mathrm{fm}}^{2}$. A $B(E2;{{2}_{1}}^{+}\ensuremath{\rightarrow}{{0}_{1}}^{+})=(81.5\ifmmode\pm\else\textpm\fi{}3.0){e}^{2}$ ${\mathrm{fm}}^{4}$ was obtained. The $E2$ properties of the lowest seven levels were used to decompose the levels into ${(\mathrm{fp})}^{2}$ states plus a deformed band with ${\ensuremath{\beta}}_{2}=+0.375\ifmmode\pm\else\textpm\fi{}0.006$. The band structure, moments of inertia, and ${\ensuremath{\beta}}_{2}$ values in $^{42}\mathrm{Ca}$ and $^{40}\mathrm{Ca}$ are nearly identical, implying that the lowest $K={0}^{+}$ band in $^{40}\mathrm{Ca}$ is also prolate.