Systematics of the giant monopole resonance from inelastic alpha scattering

Abstract

The properties of the isoscalar giant monopole resonance have been studied with inelastic $\ensuremath{\alpha}$ scattering between $0\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}{\ensuremath{\theta}}_{L}\ensuremath{\le}8\ifmmode^\circ\else\textdegree\fi{}$, where the quadrupole and monopole states can be distinguished by their angular distributions. Data were taken for $^{12}\mathrm{C}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ti}$, $^{58}\mathrm{Ni}$, $^{64,66}\mathrm{Zn}$, $^{90}\mathrm{Zr}$, $^{116,118,120,124}\mathrm{Sn}$, $^{144,154}\mathrm{Sm}$, and $^{208}\mathrm{Pb}$ mostly at ${E}_{\ensuremath{\alpha}}=129$ MeV; some data were taken at ${E}_{\ensuremath{\alpha}}=99$ MeV and ${E}_{\ensuremath{\alpha}}=117$ MeV. A monopole resonance was identified in all the nuclei with $A\ensuremath{\ge}64$ at ${E}_{x}\ensuremath{\approx}\frac{76}{{A}^{\frac{1}{3}}}$ MeV. In nuclei with $A\ensuremath{\ge}90$, most of the energy weighted sum rule was located in this state; in $^{64,66}\mathrm{Zn}$, less than one-third of the energy weighted sum rule was located. No evidence for a monopole resonance was found in nuclei with $A\ensuremath{\le}58$.NUCLEAR REACTIONS $^{12}\mathrm{C}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ti}$, $^{58}\mathrm{Ni}$, $^{64,66}\mathrm{Zn}$, $^{90}\mathrm{Zr}$, $^{116,118,120,124}\mathrm{Sn}$, $^{144,154}\mathrm{Sm}$, $^{208}\mathrm{Pb}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$; ${E}_{\ensuremath{\alpha}}=99,117,129$ MeV. Measured ${E}_{x}$, $\ensuremath{\sigma}(\ensuremath{\theta})$, giant resonances; deduced $L$, nuclear incompressibility.