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

TL;DR

This paper extends the calculable R-matrix theory to include incoming wave boundary conditions, enhancing its application to low-energy heavy-ion fusion reactions and enabling the extension of eigenvector continuation to fusion observables.

Contribution

The authors generalize the calculable R-matrix theory to IWBC and adapt eigenvector continuation for fusion studies, broadening the theoretical tools for nuclear reaction analysis.

Findings

The generalized R-matrix theory works well with IWBC.

Eigenvector continuation can be extended to fusion observables.

Numerical validation with N-12+C-14 fusion reaction.

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 ${}^{14}\text{N}+{}^{12}\text{C}$ 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.