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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12827 |
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| _version_ | 1866916372542390272 |
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| author | Arellano, H. F. Adriazola, N. A. |
| author_facet | Arellano, H. F. Adriazola, N. A. |
| contents | We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the construction of non-overlapping multi-rank separable potentials, whose form factors are obtained by solving linear equations on intervals where the $K$ matrix does have zeros. Applications are made to nucleon-nucleon $NN$ interactions constrained to the SAID-SP07 phase-shift analysis up to 2.5 GeV lab energy. The inversion potentials are channel dependent with rank dictated by the number of zeros of the $K$ matrix, reproducing the data up to a selected upper momentum. The account for absorption yields complex separable form factors, resulting in a non-Hermitian potential. Applications are restricted to $NN$ spin-uncoupled states considering a Schrödinger-like wave equation with minimal relativity. Its extension to spin-coupled states and relativistic kernels are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse-scattering separable NN potential constrained to phase-shift data up to 2.5 GeV. I.- Uncoupled states Arellano, H. F. Adriazola, N. A. Nuclear Theory We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the construction of non-overlapping multi-rank separable potentials, whose form factors are obtained by solving linear equations on intervals where the $K$ matrix does have zeros. Applications are made to nucleon-nucleon $NN$ interactions constrained to the SAID-SP07 phase-shift analysis up to 2.5 GeV lab energy. The inversion potentials are channel dependent with rank dictated by the number of zeros of the $K$ matrix, reproducing the data up to a selected upper momentum. The account for absorption yields complex separable form factors, resulting in a non-Hermitian potential. Applications are restricted to $NN$ spin-uncoupled states considering a Schrödinger-like wave equation with minimal relativity. Its extension to spin-coupled states and relativistic kernels are discussed. |
| title | Inverse-scattering separable NN potential constrained to phase-shift data up to 2.5 GeV. I.- Uncoupled states |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2406.12827 |