Direct Boundary Matching: A Bound-State Technique for Nuclear Scattering with Lagrange-Legendre Functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909948066136064 |
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| author | Lei, Jin |
| author_facet | Lei, Jin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Direct Boundary Matching: A Bound-State Technique for Nuclear Scattering with Lagrange-Legendre Functions Lei, Jin Nuclear Theory 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. |
| title | Direct Boundary Matching: A Bound-State Technique for Nuclear Scattering with Lagrange-Legendre Functions |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2512.07111 |