Neutron skin thickness of ${}^{90}\mathrm{Zr}$ determined by charge exchange reactions

Charge exchange spin-dipole (SD) excitations of ${}^{90}\mathrm{Zr}$ are studied by the ${}^{90}\mathrm{Zr}$$(p,n)$ and ${}^{90}\mathrm{Zr}$$(n,p)$ reactions at 300 MeV. A multipole decomposition technique is employed to obtain the SD strength distributions in the cross-section spectra. For the first time, a model-independent SD sum rule value is obtained: $148\pm 12{\mathrm{fm}}^2$. The neutron skin thickness of ${}^{90}\mathrm{Zr}$ is determined to be $0.07\pm 0.04\mathrm{fm}$ from the SD sum rule value.

Figure 1

Charge exchange SD strength $\mathit{dB}({\mathrm{SD}}_{-})/\mathit{dE}$ (upper panel) and $\mathit{dB}({\mathrm{SD}}_{+})/\mathit{dE}$ (lower panel). The circles and squares are the experimental data. The $\mathit{dB}({\mathrm{SD}}_{+})/\mathit{dE}$ spectra are shifted by +17 MeV. The curve is the results of the second RPA calculation by Drożdż et al. [31].

Figure 2

Integrated charge exchange SD strengths. The upper panel shows the $S_{-}$ and $S_{+}$ spectra. The lower panel shows the $S_{-}-S_{+}$ spectrum.