基于波函数的耦合通道散射仿真实现：非仿射参数化相互作用
Wavefunction-Based Emulation of Coupled-Channels Scattering with Non-Affinely Parametrized Interactions
AI总结：
本研究提出了一种基于波函数的耦合通道散射仿真实现方法，通过减少基组和经验插值法提高计算效率，适用于核反应中不同耦合通道的散射问题。
摘要：
基于物理的仿真实现为核物理中散射问题的精确解提供了一种快速且可靠的替代方案。先前的工作开发了一种减少基组的仿真实现用于单通道弹性散射，使用了光学势。由于许多感兴趣的反应可以被表示为耦合通道问题，本工作的目的是将RBM扩展到耦合通道框架（CC-RBM）。尽管所推导的框架是通用的，但在本工作中，我们将其应用于那些哈密顿耦合项来自于假设靶核具有旋转结构模型的反应。从一组训练耦合通道波函数中，我们执行奇异值分解以获得一组减少的基波函数，并然后求解扩展的（Petrov-）伽辽金方程。此外，经验插值法被用来扩展势能。我们将CC-RBM方法应用于中子对48Ca的弹性及非弹性散射，包括四极耦合以填充第一个2+态，以及中子对208Pb的散射，包括八极耦合以填充其第一个3-态。我们证明CC-RBM计算的截面与传统有限差分方法得到的截面一致。我们展示了CC-RBM的结果能够可靠地再现不同能量区域的核散射截面。计算精度与时间的图示表明，CC-RBM方法在增加基组大小时能有效提高精度。最重要的是，对于反应计算所需的精度（截面百分比级别），我们发现CC-RBM方法在计算速度上比传统耦合通道求解器快约一个数量级。然而，我们也讨论了这种缩放在耦合通道集合中包含的通道数越大时变得不如人意。
英文摘要：
Physics based emulators offer a fast and reliable replacement for an exact solution of the scattering problem in nuclear physics. Previous work developed a reduced-basis emulator for single-channel elastic scattering using an optical potential. Since many reactions of interest can be cast as a coupled-channel problem, the purpose of this work is to extend the RBM to a coupled-channel framework (CC-RBM). Although the framework derived is general, in this work we apply it to reactions where the Hamiltonian coupling term comes from assuming a rotational structure model for the target. From a set of training coupled-channel wavefunctions, we perform a singular value decomposition to obtain a reduced set of basis wavefunctions, and then solve the extended (Petrov-)Galerkin equations. In addition, the empirical interpolation method is used to expand the potentials. We apply the CC-RBM method to elastic and inelastic scattering of neutrons on 48Ca including a quadrupole coupling to populate the first 2+ state, and neutrons on 208Pb, including an octupole coupling to populate its first 3- state. We demonstrate that the CC-RBM calculated cross sections match those obtained using traditional finite-difference methods. We show that the CC-RBM results can reliably reproduce the nuclear scattering cross sections at different energy regimes. The computational accuracy versus time plots demonstrate that the CC-RBM method efficiently increases precision with increasing basis size. Most importantly, for the precisions required in reaction calculations (a percent on the cross section), we find the CC-RBM method offers roughly one and a half orders of magnitude gain in computational speed compared to the traditional coupled-channels solver. However, we also discuss how this scaling becomes less favorable, the larger the number of channels included in the coupled-channel set.
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