High-Energy-Resolution Inelastic Electron and Proton Scattering and the Multiphonon Nature of Mixed-Symmetry $2^{+}$ States in ${}^{94}\mathrm{Mo}$

High-energy-resolution inelastic electron scattering (at the S-DALINAC) and proton scattering (at iThemba LABS) experiments permit a thorough test of the nature of proposed one- and two-phonon symmetric and mixed-symmetric $2^{+}$ states of the nucleus ${}^{94}\mathrm{Mo}$. The combined analysis reveals the one-phonon content of the mixed-symmetry state and its isovector character suggested by microscopic nuclear model calculations. The purity of two-phonon $2^{+}$ states is extracted.

Figure 1

Top: Spectrum of the ${}^{94}\mathrm{Mo}(e,e^{\prime })$ reaction at $E_e=70\mathrm{MeV}$ and ${\Theta }_e=141°$. Bottom: Spectrum of the ${}^{94}\mathrm{Mo}(p,p^{\prime })$ reaction at $E_p=200\mathrm{MeV}$ and ${\Theta }_p=9°$. Insets: zoom on the $E_x=1.5–4\mathrm{MeV}$ region of the respective spectra.

Figure 2

Momentum-transfer dependence of the one-phonon FSS (top) and MSS (bottom) excitation cross sections in ${}^{94}\mathrm{Mo}$. Left: electron scattering. Right: proton scattering. The data (full squares) are compared to QPM (solid lines), SM (dashed lines), and IBA-2 (dotted lines) predictions described in the text.

Figure 3

Momentum-transfer dependence of the two-phonon FSS (top) and MSS (bottom) excitation strengths in ${}^{94}\mathrm{Mo}$. Left: electron scattering. Right: proton scattering. The data (full squares) are compared to full QPM (solid lines), SM (dashed lines), and simplified (pure) QPM (dashed-dotted line) calculations described in the text.

Figure 4

Coupled-channel analysis for the excitation of the two-phonon states in the ${}^{94}\mathrm{Mo}(p,p^{\prime })$ experiment. Left: Coupling scheme. Right: Best fits to the data using the indicated coupling strengths (uncertainty of about 5%) for the transitions to the FSS (top) and to the MSS (bottom), respectively.