Comparison between radial sensitivity of different strongly interacting probes

Abstract

We investigate the radial sensitivity of different strongly interacting probes to neutron density distributions in nuclei. The experiments considered are elastic scattering of 104 MeV $\ensuremath{\alpha}$ particles, 1 GeV protons, 130 MeV pions, and also shifts and widths of pionic atom levels. The Fourier-Bessel method is used, thus avoiding any prior assumption on the neutron densities. To enable statistically meaningful comparisons between the different experiments, "pseudodata" are used, which are based on the real data. Although the region of most sensitivity is near the surface and is similar for each case, the $\ensuremath{\alpha}$ particles probe better the extreme surface and the protons probe better the interior. Pion scattering appears to be inferior to the other two scattering experiments because of the gradient terms in the potential. Surprisingly, there are some indications that ${\ensuremath{\pi}}^{+}$ could be better than ${\ensuremath{\pi}}^{\ensuremath{-}}$ in determining neutron densities. Pionic atom data are sensitive mostly to the surface region. A critical discussion of error analyses is presented.NUCLEAR REACTIONS Radial sensitivity to neutron density within optical model calculations of elastic $\ensuremath{\sigma}(\ensuremath{\theta})$ data analyzed for $\ensuremath{\alpha}$, $p$, ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$+$^{48}\mathrm{Ca}$ for 100-1000 MeV and of pionic atoms of $^{48}\mathrm{Ca}$.