AI 中文总结
本研究将人工约束策略应用于$^4$He两集团道模型，通过三种几何构型提取耦合道可观测量，为基于约束的散射方法提供了可控基准并明确其优缺
AI 中文摘要
人工约束将连续谱散射信息编码为类束缚态的离散谱，使得可通过有限基或有限域方法提取反应可观测量。我们将该策略应用于$^4$He的两集团道模型，包含开放道$^3$H+p与$^3$He+n。我们从简谐子（HO）势阱、球形硬壁，以及单分波截断下的周期性立方盒生成的谱中提取耦合道可观测量。三种几何构型被纳入统一的量子化条件框架，并与连续谱R矩阵计算进行基准比对。在第二道阈值之上，将共同散射能处的多个受限能级组合为超定拟合，以确定两个相移与一个非弹性度。在无库仑相互作用时，三种构型对$^1S_0$与$^3P_1$分波给出一致结果；在带电$^3$H+p道引入库仑相互作用后，HO与球形壁结果也与连续谱参考吻合良好。蒙特卡洛传播研究表明，谱不确定性在阱函数极点附近及与非弹性度、相移差相关的病态方向被放大，而相移和则保持相对稳健。这些结果为基于约束的散射方法提供了可控基准，并明确了其在未来少体与从头算反应计算中的优势与局限。
英文摘要
Artificial confinement encodes continuum scattering information in discrete, bound-state-like spectra, allowing reaction observables to be extracted with finite-basis or finite-domain methods. We apply this strategy to a two-channel cluster model of $^4$He with open $^3$H+p and $^3$He+n channels. We extract coupled-channel observables from spectra generated by a harmonic-oscillator (HO) trap, a spherical hard wall, and, within a single-partial-wave truncation, a periodic cubic box. The three geometries are formulated in a unified quantization-condition framework and benchmarked against a continuum $R$-matrix calculation. Above the second-channel threshold, several confined levels at a common scattering energy are combined in an overdetermined fit to determine two phase shifts and an inelasticity. Without Coulomb interactions, all three geometries yield consistent results for the $^1S_0$ and $^3P_1$ partial waves. With Coulomb interactions in the charged $^3$H+p channel, the HO and spherical-wall results also agree closely with the continuum reference. A Monte Carlo propagation study shows that spectral uncertainties are amplified near trap-function poles and along poorly conditioned directions associated with the inelasticity and phase-shift difference, whereas the phase-shift sum remains comparatively robust. These results provide a controlled benchmark for confinement-based scattering methods and delineate their strengths and limitations for future few-body and ab initio reaction calculations.
