Electric dipole strength in $sd$-shell nuclei from small-angle proton scattering

The present work reports new total photoabsorption cross sections for the $N=Z$ nuclei in the $sd$-shell $^{20}$Ne, $^{24}$Mg, $^{28}$Si, $^{32}$S, $^{36}$Ar, and for $^{26}$Mg. The results are compared to predictions of a data-driven artificial neural network application and to configuration-interaction shell-model calculations covering the excitation energy region of the isovector giant dipole resonance. Double-differential cross sections of the $(p,p^\prime)$ reaction at 295 MeV have been measured between $0^\circ$ and $14^\circ$. The angular distributions of the $E1$ parts due to Coulomb excitation have been extracted with a multipole decomposition analysis for excitation energies 12 to 24 MeV and converted to equivalent photoabsorption cross sections with the virtual photon method. Reasonable agreement of the photoabsorption cross sections with previous experiments is found for $^{24}$Mg and $^{28}$Si, while the present results diverge for $^{32}$S. For the first time, data are presented for $^{20}$Ne, $^{26}$Mg and $^{36}$Ar. Configuration-interaction shell-model calculations provide an overall satisfactory description of the fragmented $E1$ strength distributions. The same holds for absolute cross sections except for $^{26}$Mg and $^{36}$Ar, where the experimental results significantly exceed the expected exhaustion of the Thomas-Reiche-Kuhn energy-weighted sum rule. Fot light nuclei, there is a larger model dependence compared to previous analyses in heavy nuclei, in particular for excitation energies above 20 MeV, due to the need to constrain the continuum background with additional assumptions. The overall success of the shell-model approach to describe the features of the experimental photoabsorption cross sections motivates its application in large-scale reaction network calculations aiming at an understanding of the mass composition of ultrahigh-energy cosmic rays.