Direct Boundary Matching: A Bound-State Technique for Nuclear Scattering with Lagrange-Legendre Functions

TL;DR

This paper introduces a direct boundary matching method (DBMM) for nuclear scattering that simplifies boundary conditions, operates in real space, and shows excellent agreement with traditional methods in benchmark tests.

Contribution

The paper presents a novel DBMM approach that incorporates outgoing wave boundary conditions directly into the matrix, avoiding complex scaling and Bloch operators, and extends to coupled-channel problems.

Findings

Accurate results for p+12C scattering benchmark tests.

Elimination of Bloch operators and complex scaling in boundary matching.

Effective handling of coupled-channel nuclear scattering problems.

Abstract

I present a direct boundary matching method (DBMM) for solving nuclear scattering problems using Lagrange-Legendre basis functions. This approach belongs to the family of bound-state techniques for the continuum, reformulating scattering problems into a localized, square-integrable ($L^2$) representation. The key feature is the direct incorporation of the outgoing wave boundary condition into the last row of the matrix equation, eliminating the need for Bloch operators and two-step matching procedures required in traditional R-matrix methods. Unlike the complex scaling method that rotates coordinates into the complex plane, DBMM operates entirely in real coordinate space. The formalism is extended to coupled-channel problems, where the wave function decomposition naturally leads to an effective source potential that distinguishes between the entrance channel and other channels. Benchmark calculations for p~+~$^{12}$C scattering demonstrate excellent agreement with the Numerov integration method.