Systematics of the giant monopole resonance from inelastic alpha scattering

The properties of the isoscalar giant monopole resonance have been studied with inelastic $\alpha$ scattering between $0°\le {\theta }_L\le 8°$, 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 $E_{\alpha }=129\mathrm{}$ MeV; some data were taken at $E_{\alpha }=99\mathrm{}$ MeV and $E_{\alpha }=117\mathrm{}$ MeV. A monopole resonance was identified in all the nuclei with $A\ge 64$ at $E_x\approx \frac{76}{A^{\frac{1}{3}}}$ MeV. In nuclei with $A\ge 90$, 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 $A\le 58$.