To obtain the neutron spectroscopic amplitudes for \begin{document}${}^{90-96}$\end{document} Zr overlaps, experimental data of elastic scattering with small experimental errors and precise optical potentials were analyzed. In this study, the elastic scattering angular distributions of \begin{document}${}^{12,13}$\end{document} C + \begin{document}${}^{A} {\rm{Zr}}$\end{document} (A = 90, 91, 92, 94, 96) were measured using the high-precision Q3D magnetic spectrometer in the Tandem accelerator. The Sao Paulo potential was used for the optical potential. The optical model and coupled channel calculations were compared with the experimental data. The theoretical results were found to be very close to the experimental data. In addition, the possible effects of the couplings to the inelastic channels of the \begin{document}${}^A {\rm{Zr}}$\end{document} targets and \begin{document}${}^{12, 13}$\end{document} C projectiles on the elastic scattering were studied. It was observed that the couplings to the inelastic channels of the \begin{document}${}^{12,13}$\end{document} C projectiles could improve the agreement with the experimental data, while the inelastic couplings to the target states are of minor importance. The effect of the one-neutron stripping in the \begin{document}${}^{13}$\end{document} C+ \begin{document}${}^A {\rm{Zr}}$\end{document} elastic scattering was also studied. The one-neutron stripping channel in \begin{document}${}^{13}$\end{document} C + \begin{document}${}^A {\rm{Zr}}$\end{document} was found to be not relevant and did not affect the elastic scattering angular distributions. Our results also show that in the reactions with the considered zirconium isotopes, the presence of the extra neutron in \begin{document}${}^{13}$\end{document} C does not influence the reaction mechanism, which is governed by the collective excitation of the \begin{document}${}^{12}$\end{document} C core.

中文翻译：

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12,13C+Zr的弹性散射角分布

为了获得\begin{document}${}^{90-96}$\end{document} Zr 重叠的中子光谱振幅，分析了具有小实验误差和精确光势的弹性散射实验数据。在本研究中，\begin{document}${}^{12,13}$\end{document} C + \begin{document}${}^{A} {\rm{Zr} 的弹性散射角分布}$\end{document} (A = 90, 91, 92, 94, 96) 使用串联加速器中的高精度 Q3D 磁谱仪测量。圣保罗势被用于光学势。将光学模型和耦合通道计算与实验数据进行了比较。发现理论结果与实验数据非常接近。此外，耦合到 \begin{document}${}^A {\rm{Zr}}$\end{document} 目标和 \begin{document}${}^{12, 13 的非弹性通道的可能影响}$\end{document} C 弹丸在弹性散射上的研究。观察到\begin{document}${}^{12,13}$\end{document} C 弹丸与非弹性通道的耦合可以提高与实验数据的一致性，而与目标的非弹性耦合状态是次要的。\begin{document}${}^{13}$\end{document} C+ \begin{document}${}^A {\rm{Zr}}$\end{ 单中子剥离的效果还研究了弹性散射。\begin{document}${}^{13}$\end{document} C + \begin{document}${}^A {\rm{Zr}}$\end{document} 中的单中子剥离通道发现不相关并且不影响弹性散射角分布。我们的结果还表明，在与考虑的锆同位素的反应中，\begin{document}${}^{13}$\end{document} C 中额外中子的存在不会影响反应机制，这是受控制的由 \begin{document}${}^{12}$\end{document} C 核心的集体激发。