dorsal/arxiv
View SchemaThe energy dependence of the $\pi N$ amplitude and the three-nucleon interaction
| Authors | T-Y Saito, I. R. Afnan |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9412004 |
| URL | https://arxiv.org/abs/nucl-th/9412004 |
| DOI | 10.1007/s006010050006 |
| Journal | Few Body Syst. 18 (1995) 101-132 |
Abstract
By calculating the contribution of the $\pi-\pi$ three-body force to the three-nucleon binding energy in terms of the $\pi N$ amplitude using perturbation theory, we are able to determine the importance of the energy dependence and the contribution of the different partial waves of the $\pi N$ amplitude to the three-nucleon force. A separable representation of the non-pole $\pi N$ amplitude allows us to write the three-nucleon force in terms of the amplitude for $NN\rightarrow NN^*$, propagation of the $NNN^*$ system, and the amplitude for $NN^*\rightarrow NN$, with $N^*$ being the $\pi N$ quasi-particle amplitude in a given state. The division of the $\pi N$ amplitude into a pole and non-pole gives a procedure for the determination of the $\pi NN$ form factor within the model. The total contribution of the three-body force to the binding energy of the triton for the separable approximation to the Paris nucleon-nucleon potential (PEST) is found to be very small mainly as a result of the energy dependence of the $\pi N$ amplitude, the cancellation between the $S$- and $P$-wave $\pi N$ amplitudes, and the soft $\pi NN$ form factor.
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"abstract": "By calculating the contribution of the $\\pi-\\pi$ three-body force to the\nthree-nucleon binding energy in terms of the $\\pi N$ amplitude using\nperturbation theory, we are able to determine the importance of the energy\ndependence and the contribution of the different partial waves of the $\\pi N$\namplitude to the three-nucleon force. A separable representation of the\nnon-pole $\\pi N$ amplitude allows us to write the three-nucleon force in terms\nof the amplitude for $NN\\rightarrow NN^*$, propagation of the $NNN^*$ system,\nand the amplitude for $NN^*\\rightarrow NN$, with $N^*$ being the $\\pi N$\nquasi-particle amplitude in a given state. The division of the $\\pi N$\namplitude into a pole and non-pole gives a procedure for the determination of\nthe $\\pi NN$ form factor within the model. The total contribution of the\nthree-body force to the binding energy of the triton for the separable\napproximation to the Paris nucleon-nucleon potential (PEST) is found to be very\nsmall mainly as a result of the energy dependence of the $\\pi N$ amplitude, the\ncancellation between the $S$- and $P$-wave $\\pi N$ amplitudes, and the soft\n$\\pi NN$ form factor.",
"arxiv_id": "nucl-th/9412004",
"authors": [
"T-Y Saito",
"I. R. Afnan"
],
"categories": [
"nucl-th"
],
"doi": "10.1007/s006010050006",
"journal_ref": "Few Body Syst. 18 (1995) 101-132",
"title": "The energy dependence of the $\\pi N$ amplitude and the three-nucleon interaction",
"url": "https://arxiv.org/abs/nucl-th/9412004"
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