Generalizing the calculable $R$-matrix theory and eigenvector continuation to the incoming wave boundary condition

Abstract

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 N + 12 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.