Elastic and Inelastic Scattering ofαParticles fromBa138

Differential cross sections for the elastic scattering and inelastic scattering to the low-lying states in ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ have been measured using 50-MeV $\alpha$ particles. The angular distributions are analyzed in the distorted-wave Born approximation, employing collective-model form factors. Spin and parity assignments of $2^{+}$, $4^{+}$, and $3^{-}$ are verified for states at 1.436, 1.898, and 2.880 MeV. Assignments of $2^{+}$ and $4^{+}$ are made for states at 2.19 and 2.27 MeV. Tentative assignments of $2^{+}$ and $4^{+}$ are made for members of unresolved multiplets at 3.34 and 3.50 MeV. Values of ${\beta }_l{R}^{\prime }$ are obtained for all observed levels. Reasonable agreement for excitation energies and $J^{\pi }$ assignments has been obtained between the present results and previous experimental measurements and with recent theoretical calculations. A comparison of available isoscalar and electromagnetic transition rates in the mass region $115<A<\mathrm{}150\mathrm{}$ indicates that, for the lowest $2^{+}$ states, the ratio of the neutron-to-proton contributions to the isoscalar matrix elements is in the ratio $\frac{N}{Z}$ as predicted by the collective vibrational model, except for the $N=82\mathrm{}$ region. A similar result has previously been observed at the $N=28\mathrm{}$ shell closure.