dorsal/arxiv
View SchemaDetermination of low energy parameters for NN-scattering at $N^4 LO$ in all partial waves with $j\le 5$
| Authors | M. Pavon Valderrama, E. Ruiz Arriola |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0407113 |
| URL | https://arxiv.org/abs/nucl-th/0407113 |
Abstract
The Variable S-matrix approach offers a unique way to extract low energy threshold parameters for a given NN potential. We extract those parameters for the np system from the NijmII and Reid93 potentials, to all partial waves with total angular momentum $j \le m5 $, using the generalized effective range expansion % $$ ({\bf f}^{sj})_{l,l'} k^l k^{l'} = -({{\bf a}^{sj}}^{-1})_{l,l'} + \frac12 ({\bf r}^{sj})_{l,l'} k^2 + ({\bf v_2}^{sj})_{l,l'} k^4 + + ({\bf v_3}^{sj})_{l,l'} k^6 + + ({\bf v_4}^{sj})_{l,l'} k^8 + ... - {\rm i} k^{l+l'+1} $$ % where $ {\bf f}^{sj} = ({\bf S}^{sj} - {\bf 1}) / (2 {\rm i} k) $ is the scattering amplitude and ${\bf S}^{sj}$ is the unitary S-matrix in coupled channel space with total spin $s$ and total angular momentum $j$. Our calculation includes all the relevant contributions of the full amplitude to order ${\cal O} (k^8) $ in the CM momentum. We also discuss the validity of the generalized effective range expansion in the region of analyticity $ k \le m_\pi /2$.
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"date_created": "2026-03-02T18:00:01.186000Z",
"date_modified": "2026-03-02T18:00:01.186000Z",
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"abstract": "The Variable S-matrix approach offers a unique way to extract low energy\nthreshold parameters for a given NN potential. We extract those parameters for\nthe np system from the NijmII and Reid93 potentials, to all partial waves with\ntotal angular momentum $j \\le m5 $, using the generalized effective range\nexpansion % $$ ({\\bf f}^{sj})_{l,l\u0027} k^l k^{l\u0027} = -({{\\bf a}^{sj}}^{-1})_{l,l\u0027}\n+ \\frac12 ({\\bf r}^{sj})_{l,l\u0027} k^2 + ({\\bf v_2}^{sj})_{l,l\u0027} k^4 + + ({\\bf\nv_3}^{sj})_{l,l\u0027} k^6 + + ({\\bf v_4}^{sj})_{l,l\u0027} k^8 + ... - {\\rm i}\nk^{l+l\u0027+1} $$ % where $ {\\bf f}^{sj} = ({\\bf S}^{sj} - {\\bf 1}) / (2 {\\rm i} k)\n$ is the scattering amplitude and ${\\bf S}^{sj}$ is the unitary S-matrix in\ncoupled channel space with total spin $s$ and total angular momentum $j$. Our\ncalculation includes all the relevant contributions of the full amplitude to\norder ${\\cal O} (k^8) $ in the CM momentum. We also discuss the validity of the\ngeneralized effective range expansion in the region of analyticity $ k \\le\nm_\\pi /2$.",
"arxiv_id": "nucl-th/0407113",
"authors": [
"M. Pavon Valderrama",
"E. Ruiz Arriola"
],
"categories": [
"nucl-th"
],
"title": "Determination of low energy parameters for NN-scattering at $N^4 LO$ in all partial waves with $j\\le 5$",
"url": "https://arxiv.org/abs/nucl-th/0407113"
},
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