Elastic and inelastic scattering of 0.8 GeV protons fromMg24andMg26

Abstract

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from $^{24}\mathrm{Mg}$ and $^{26}\mathrm{Mg}$ are presented. Cross sections for protons exciting states of energy up to about 10 MeV are measured using a high resolution spectrometer. Coupled channels analyses of scattering data to the ${0}^{+}$, ${2}^{+}$, ${4}^{+}$, and ${6}^{+}$ states in the ground state rotational band, the ${2}^{+}$, ${3}^{+}$, ${4}^{+}$, and ${6}^{+}$ states in the $\ensuremath{\gamma}$-vibrational band, the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states in the $\ensuremath{\beta}$-vibrational band, and the ${3}^{\ensuremath{-}}$ and ${5}^{\ensuremath{-}}$ members of the ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}} \mathrm{and} {3}^{\ensuremath{-}}$ vibrational bands in $^{24}\mathrm{Mg}$ are presented. Also reported are coupled channels analyses of the experimental angular distributions in $^{26}\mathrm{Mg}$ for the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states in the ground state band, the possible ${2}^{+}$, ${3}^{+}$, and ${4}^{+}$, $\ensuremath{\gamma}$-band members, and several ${3}^{\ensuremath{-}}$ members of ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}} \mathrm{and} {3}^{\ensuremath{-}}$ bands. The data for the ${3}^{\ensuremath{-}}$ states in both $^{24}\mathrm{Mg}$ and $^{26}\mathrm{Mg}$ differ both in shape and angular positions of the maxima and minima. Coupled channels analyses are able to account for these differences in the ${3}^{\ensuremath{-}}$ experimental cross sections by selecting ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}} or {3}^{\ensuremath{-}}$. This is believed to be the first observation of "$K$ dependence" for $l=3$ excitations in inelastic scattering by $s\ensuremath{-}d$ shell nuclei. Distorted wave Born approximation analyses of the other states in $^{26}\mathrm{Mg}$ excited by $l$ transfers from 2 to 4 are also described. Several new assignments of ${J}^{\ensuremath{\pi}}$ for excited states in $^{26}\mathrm{Mg}$ are proposed based upon the distinctive $l$ transfer dependence found in the positions of the first maximum and in the general shapes of the angular distributions. Multipole moments extracted from the deformed optical potentials are related to those of the matter distributions by Satchler's theorem. These are compared to multipole moments obtained from analyses of hadronic scattering data, as well as with the moments of the charge distributions determined by electromagnetic measurements.NUCLEAR REACTIONS $^{24,26}\mathrm{Mg}$($p$,${p}^{\ensuremath{'}}$), $E=0.8$ GeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, enriched targets; resolution \ensuremath{\ge}80 keV, ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=5.49\ifmmode^\circ\else\textdegree\fi{} \mathrm{to} 31.66\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=0.1\ifmmode^\circ\else\textdegree\fi{}$. Optical model potential, DWBA analysis, coupled channels analysis, symmetric and asymmetric rotational model, coupling parameters, multipole moments, assigned ${J}^{\ensuremath{\pi}}$.