Quasi-Elastic (p,n) Scattering from Scandium and Titanium Isotopes

The differential cross sections have been measured for quasi-elastic ($p,n$) scattering on a sequence of targets ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$ and ${}_{}{}^{46,47,48,49,50}{}_{}{}^{}\mathrm{Ti}$ which have neutron excesses from 2 to 6. Except for ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ti}$, the cross sections are proportional to the neutron excess. The measured $Q$ values for the reaction are interpreted as measurements of the Coulomb energy difference for the isobars. The results show that the effective charge radius increases less rapidly than $A^{\frac{1}{3}}$ as neutrons are added to the titanium isotopes.