Deformation effects on isoscalar giant resonances in Mg 24

Strength distributions for isoscalar giant resonances with multipolarity $L\ensuremath{\le}2$ have been determined in $^{24}\mathrm{Mg}$ from ``instrumental background-free'' inelastic scattering of 386-MeV $\ensuremath{\alpha}$ particles at extreme forward angles, including ${0}^{\ensuremath{\circ}}$. The isoscalar $E0, E1$, and $E2$ strengths are observed to be $57\ifmmode\pm\else\textpm\fi{}7%, 111.{1}_{\ensuremath{-}7.2}^{+10.9}%$, and $148.6\ifmmode\pm\else\textpm\fi{}7.3%$, respectively, of their energy-weighted sum rules in the excitation energy range of 6 to 35 MeV. The isoscalar giant monopole (ISGMR) and quadrupole (ISGQR) resonances exhibit a prominent $K$ splitting which is consistent with microscopic theory for a prolate-deformed ground state of $^{24}\mathrm{Mg}$. For the ISGQR it is due to splitting of the three $K$ components, whereas for the ISGMR it is due to its coupling to the $K=0$ component of the ISGQR. Deformation effects on the isoscalar giant dipole resonance are less pronounced, however.