Spectroscopic Strength of1f72Transitions Deduced from the ReactionV51(e,e′p)Ti50

The spectral function for the knockout of $1f$ protons from ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ leading to the ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^2$ quadruplet in ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ has been measured in a high-resolution ($e,e^{\prime }p$) experiment. In the distorted-wave impulse approximation the $1f$ spectroscopic strength observed in the $0^{+}$, $2^{+}$, $4^{+}$, $6^{+}$ quadruplet of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ is 1.11(14). This is considerably lower than predicted by shell-model calculations. In addition the rms radius of the $1f_{\frac{7}{2}}$ orbit, 4.20(14) fm, is deduced. With this rms radius, recent ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}\left(d{}_{}{}^3{}_{}{}^{}\mathrm{He}\right){}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ data yield a similar low value of the $1f$ strength.