Quadrupole Moment of the Lowest Rotational Band in Even Calcium Nuclei

The static electric quadrupole moment of the $2_1^{}{}_{}{}^{+}$ state in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ was measured to be $(-18.9\mathrm{}\pm 8.1)e$ ${\mathrm{fm}}^2$. A $B(E2;{2_1}^{+}\to {0_1}^{+})=(81.5\mathrm{}\pm 3.0)e^2$ ${\mathrm{fm}}^4$ was obtained. The $E2\mathrm{}$ properties of the lowest seven levels were used to decompose the levels into ${\mathrm{}\left(\mathrm{fp}\right)\mathrm{}}^2$ states plus a deformed band with ${\beta }_2=+0.375\mathrm{}\pm 0.006$. The band structure, moments of inertia, and ${\beta }_2$ 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.