Two-step effects in 15-35 MeV proton scattering fromMg24low-lying states

Differential cross sections for proton scattering from the six lowest states of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ have been measured at eleven energies from 15 to 35 MeV. Optical model parameters with a constant geometry and with a linear dependence for the well depths have been deduced for the whole energy range. Coupled channel calculations and the asymmetric rotational model describe satisfactorily the inelastic scattering data of the $K^{\pi }=0^{+}$ rotational band while, in the fits relative to some members of the $K^{\pi }=2^{+}$ band, disagreements have been found. ($p$,$d$,$p^{\prime }$) and ($p$,$p^{\prime \prime }$,$p^{\prime }$) two-step effects have been considered; the contributions to the $3_2^{+}$(5.22 MeV) level data relative to the last process show an energy dependence in agreement with the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ giant resonance strength distributions.