Isospin distribution of quadrupole strength inSn118: Comparison with pion, nucleon, and electron scattering

The isospin structure of the quadrupole strength in ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$ is examined by a variety of means in an attempt to understand the surprisingly large amount of isovector strength extracted from some recent ${\pi }^{\mathrm{-}}$/${\pi }^{+}$ experiments in the excitation-energy region (below 2ħω) expected for the isoscalar giant-quadrupole resonance. The ratio of the giant-quadrupole resonance neutron and proton multipole matrix elements for ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$ determined from ${\pi }^{\mathrm{-}}$/${\pi }^{+}$ data is $M_{\mathrm{n}/M_{\mathrm{p}=1.9\mathrm{}\pm 0.4}}$ compared to calculations which range from 1.1 to about N/Z (1.36). It is demonstrated that this large ratio has unrealistic consequences in random-phase approximation mixing of the giant states into the first $2^{+}$ state transition (core polarization), which has been independently studied by other probes and is in rather good agreement with quasiparticle random-phase approximation calculations, which have $M_{\mathrm{n}/M_{\mathrm{p}\mathrm{\le }\mathrm{N}/\mathrm{Z}}}$ for the isoscalar giant-quadrupole resonance. Quasiparticle random-phase approximation transition densities are used to calculate pion, proton, and neutron cross sections to the isoscalar giant-quadrupole resonance and the first $2^{+}$ state using microscopic reaction models. A comparison of B(E2) from the same structure model is made to the various data for the first $2^{+}$ transition and to the ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$(e,e’) data on the isoscalar giant-quadrupole resonance. Although not completely conclusive because of the lack of reliable (e,e’) data, the evidence from all these comparisons is that the ${\pi }^{\mathrm{-}}$/${\pi }^{+}$ results are at odds with the results of other probes and with nuclear structure theory and that the problem seems to be with the ${\pi }^{+}$ scattering results.