Isoscalar breathing mode state inZr90andSn116

Beams of 96- and 129-MeV $\alpha$ particles were used to excite the giant resonance region in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$. From the analysis of data obtained from 0° to 8°, two distinct components of the giant resonance peak were resolved in each nucleus. The upper component is well described by a distorted-wave Born-approximation calculation for $L=0\mathrm{}$ exhausting 90% (180%) of the energy weighted sum rule and has $E_x=16.2\mathrm{}$ MeV (15.6 MeV), $\Gamma =3.5\mathrm{}$ MeV (4.1 MeV) for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ (${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$). The nuclear incompressibility is extracted from these data and from that available for ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The lower component is the giant quadrupole resonance exhausting 66% (84%) of the isoscalar quadrupole sum rule and has $E_x=14.0\mathrm{}$ MeV (13.2 MeV), $\Gamma =3.4\mathrm{}$ MeV (3.3 MeV) for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ (${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$).