将可计算的$R$ -矩阵理论和特征向量延拓推广到入射波边界条件
Generalizing the calculable $R$-matrix theory and eigenvector continuation to the incoming wave boundary condition
摘要：
可计算的$R$ -矩阵理论已成功地用于在坐标原点处径向波函数为零的正则边界条件[P. Descouvemont和D.贝耶，报告。Prog. 73，036301（2010）]。本文将可计算的$R$ -矩阵理论推广到低能重离子聚变理论研究中广泛使用的入射波边界条件（IWBC），以模拟库仑势垒对入射通量的强吸收。广义可计算$R$ -矩阵理论也为特征向量延拓（EC）[D. Frame等人，物理修订版信函121，032501（2018）]到融合观测。以${}^{14}\text{N}+{}^{12}\text{C}$聚变反应为例验证了这些新的理论工具。在数值计算中考虑了局部势和非局部势。我们的推广的可计算的$R$ -矩阵理论和EC被发现工作良好的IWBC。
英文摘要：
The calculable $R$-matrix theory has been formulated successfully for regular boundary conditions with vanishing radial wave functions at the coordinate origins [P. Descouvemont and D. Baye, Rept. Prog. Phys. 73, 036301 (2010)]. We generalize the calculable $R$-matrix theory to the incoming wave boundary condition (IWBC), which is widely used in theoretical studies of low-energy heavy-ion fusion reactions to simulate the strong absorption of incoming flux inside the Coulomb barriers. The generalized calculable $R$-matrix theory also provides a natural starting point to extend eigenvector continuation (EC) [D. Frame et al., Phys. Rev. Lett. 121, 032501 (2018)] to fusion observables. The ${}^{14}\text{N}+{}^{12}\text{C}$ fusion reaction is taken as an example to validate these new theoretical tools. Both local and nonlocal potentials are considered in numerical calculations. Our generalizations of the calculable $R$-matrix theory and EC are found to work well for IWBC.
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