标题： 核变形测定的高能重离子散射研究 显示英文标题

标题： Investigation of the determination of nuclear deformation using high-energy heavy-ion scattering

摘要： 背景：核变形是核结构的一个关键特征。通常，核的四极形变长度$\delta_{2}$通常是通过一个形变核势能来确定的，该势能具有形变长度$\delta^{\rm (pot)}_{2}$，该长度被确定以重现核散射数据。这种方法假设了$\delta_{2}=\delta^{\rm (pot)}_{2}$，尽管没有理论基础。目的：我们系统地阐明高能重离子散射中$\delta_{2}$和$\delta^{\rm (pot)}_{2}$之间的关系，以评估传统方法确定核形变的有效性。 方法：在$E/A$ = 50--400 MeV下，研究了$^{12}$C通过$^{12}$C、$^{16}$O、$^{40}$Ca和$^{208}$Pb靶的非弹性散射的形变长度。首先，我们进行微观耦合通道（CC）计算，将变形密度的$\delta_{2}$与非弹性散射截面相关联。 其次，我们使用变形势模型来确定$\delta^{\rm (pot)}_{2}$，以重现微观 CC 结果。 然后我们将$\delta^{\rm (pot)}_{2}$与$\delta_{2}$进行比较。 结果：我们发现$\delta^{\rm (pot)}_{2}$比假设的$\delta_{2}$小约 20--40%，显示出强烈的能量和靶核依赖性。 进一步分析考虑了超越微分模型的高阶变形效应，结果表明$\delta^{\rm (pot)}_{2}$仍然比$\delta_{2}$小约 15--35%。 结论：我们的结果表明，在使用变形势模型研究高能重离子散射以提取核变形时需要格外谨慎。 传统的方法可能系统性地低估变形长度$\delta_2$。 显示英文摘要

摘要： Background: Nuclear deformation provides a crucial characteristic of nuclear structure. Conventionally, the quadrupole deformation length of a nucleus, $\delta_{2}$, has often been determined based on a macroscopic model through a deformed nuclear potential with the deformation length $\delta^{\rm (pot)}_{2}$, which is determined to reproduce the nuclear scattering data. This approach assumes $\delta_{2}=\delta^{\rm (pot)}_{2}$ although there is no theoretical foundation. Purpose: We clarify the relationship between $\delta_{2}$ and $\delta^{\rm (pot)}_{2}$ for high-energy heavy-ion scattering systematically to evaluate the validity of the conventional approach to determine the nuclear deformation. Method: The deformation lengths for the $^{12}$C inelastic scattering by $^{12}$C, $^{16}$O, $^{40}$Ca, and $^{208}$Pb targets at $E/A$ = 50--400 MeV are examined. First, we perform microscopic coupled-channel (CC) calculations to relate $\delta_{2}$ of the deformed density into the inelastic scattering cross section. Second, we use the deformed potential model to determine $\delta^{\rm (pot)}_{2}$ so as to reproduce the microscopic CC result. We then compare $\delta^{\rm (pot)}_{2}$ with $\delta_{2}$. Results: We find that $\delta^{\rm (pot)}_{2}$ is about 20--40 \% smaller than presumed $\delta_{2}$, showing strong energy and target dependence. Further analysis, which considers higher-order deformation effects beyond the derivative model, reveals that $\delta^{\rm (pot)}_{2}$ is still about 15--35 \% smaller than $\delta_{2}$. Conclusion: Our results suggest that one needs to be careful when the deformed potential model for the high-energy heavy-ion scattering is used to extract the nuclear deformation. The conventional approach may underestimate the deformation length $\delta_2$ systematically.