$E2\mathrm{}$ Transition Strengths Between ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^{\pm 2}$ States of ${\mathrm{Ca}}^{42}$, ${\mathrm{Ti}}^{50}$, and ${\mathrm{Fe}}^{54}$

The lifetimes of the $6^{+}$ states at 3.20 MeV in ${\mathrm{Ti}}^{50}$ and 2.95 MeV in ${\mathrm{Fe}}^{54}$ have been measured by a $\beta -\gamma$ delayed-coincidence technique using accelerator-produced 1.72-min ${\mathrm{Sc}}^{50}$ and 1.5-min ${\mathrm{Co}}^{54}$ activities, respectively. Mean lifetimes of $\tau =630\mathrm{}\pm 30$ psec for the 3.20-MeV state in ${\mathrm{Ti}}^{50}$ and $\tau =1.71\mathrm{}\pm 0.04$ nsec for the 2.95-MeV state in ${\mathrm{Fe}}^{54}$ were obtained. The $4^{+}$ 2.75-MeV state in ${\mathrm{Ca}}^{42}$ was determined to have a mean lifetime of $\tau =11.5\mathrm{}\pm 2.5$ psec by a recoil-distance measurement with the ${\mathrm{K}}^{39}(\alpha , p){\mathrm{Ca}}^{42}$ reaction. The resulting $6^{+}$→$4^{+}$ and $4^{+}$→$2^{+}$ $E2\mathrm{}$ transition strengths are compared with Coulomb-excitation $2^{+}$→$0^{+}$ results and theoretical predictions. The $E2\mathrm{}$ strengths in ${\mathrm{Ti}}^{50}$ and ${\mathrm{Fe}}^{54}$ are consistent with ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^{\pm 2}$ configurations for the $0^{+}$, $2^{+}$, $4^{+}$, and $6^{+}$ group of states, and do not indicate deformed-core components such as are required in the lower members of the ${\mathrm{Ca}}^{42}$ group.