Isoscalar transition rates viaCa40,Pb208(α,α′)at 79 MeV

The inelastic scattering of $\alpha$ particles from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been studied at a bombarding energy of 79.1 MeV. Isoscalar transition rates have been extracted for the $2^{+}$ level at 3.90 MeV, the $3^{-}$ levels at 3.73, 6.29, and 6.58 MeV, and the $5^{-}$ level at 4.48 MeV in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. These have been compared with previous results, and a slight energy dependence is evident. In the case of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, the isoscalar transition rates have been extracted for the $2^{+}$ level at 4.09 MeV, the $3^{-}$ level at 2.62, and the $5^{-}$ levels at 3.22 and 3.73 MeV. The analysis of the Coulomb and nuclear interference for the $2^{+}$ level at 4.09 MeV indicates that ${\beta }_{\mathrm{Coulomb}}=1.2\mathrm{}{\beta }_{\mathrm{nuclear}}$. A folding model analysis has been made for the 3.73-MeV ($3^{-}$) and 3.90-MeV ($2^{+}$) levels in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and the 2.62-MeV ($3^{-}$) and 4.09-MeV ($2^{+}$) levels in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. This analysis, using an effective $\alpha$ particle, bound nucleon interaction determined from 79-MeV elastic α-scattering data, is compared with a standard deformed optical potential analysis. Agreement between the two analyses is best for the $2^{+}$ state in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and worst for the $3^{-}$ state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. The explicit inclusion of exchange effects tends to reduce the discrepancy between the two reaction models.