Lifetimes of the $6_1^{+}$ states in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ and $E2\mathrm{}$ effective charges in ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^{\pm 2}$ nuclei

The mean lifetimes of the $6_1^{+}$ states in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ti}$ at 3041 keV and ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ at 2974 keV have been measured with the pulsed beam method to be $\tau =5\mathrm{}\pm 2 \mathrm{ns}\mathrm{and} 15.2\pm 0.8 \mathrm{ns}$, respectively. The states were populated via the reactions ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\left({}_{}{}^3{}_{}{}^{}\mathrm{He}n\right){}_{}{}^{42}{}_{}{}^{}\mathrm{Ti}$ at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=12\mathrm{}$ MeV and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(\alpha , \alpha 2n){}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ at $E_{\alpha }=50\mathrm{}$ MeV. The deduced $B(E2, 6^{+}\to 4^{+})$ values result in proton and neutron effective charges which are in good agreement with other ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^{\pm 2}$ nuclei. However, the present lifetime result for ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ti}$ is in disagreement with another measurement for this nucleus. A comparison of $E2\mathrm{}$ effective charges extracted from all presently available $B\left(E2\mathrm{}\right)\mathrm{}$ data on the $6^{+}$→$4^{+}$→$2^{+}$→$0^{+}$ transitions in ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^{\pm 2}$ nuclei is presented.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^3{}_{}{}^{}\mathrm{He}, n\gamma )$, $E=12\mathrm{}$ MeV, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(\alpha , \alpha 2n\gamma )$, $E=50\mathrm{}$ MeV; measured pulsed beam electronic timing; deduced $T_{\frac{1}{2}}$, $B\left(E2\mathrm{}\right)\mathrm{}$, effective charges. Natural and enriched targets, Ge(Li) detectors.