dorsal/arxiv
View SchemaMedium Effects on Binary Collisions with the Delta Resonance
| Authors | T. -S. H. Lee |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9602021 |
| URL | https://arxiv.org/abs/nucl-th/9602021 |
| DOI | 10.1103/PhysRevC.54.1350 |
| Journal | Phys.Rev.C54:1350-1359,1996 |
Abstract
To facilitate the relativistic heavy-ion calculations based on transport equations, the binary collisions involving a $\Delta$ resonance in either the entrance channel or the exit channel are investigated within a Hamiltonian formulation of $\pi NN$ interactions. An averaging procedure is developed to define a quasi-particle $\Delta^*$ and to express the experimentally measured $NN\rightarrow \pi NN$ cross section in terms of an effective $NN\rightarrow N\Delta^\ast$ cross section. In contrast to previous works, the main feature of the present approach is that the mass and the momentum of the produced $\Delta^*$'s are calculated dynamically from the bare $\Delta \leftrightarrow \pi N$ vertex interaction of the model Hamiltonian and are constrained by the unitarity condition. The procedure is then extended to define the effective cross sections for the experimentally inaccessible $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions. The predicted cross sections are significantly different from what are commonly assumed in relativistic heavy-ion calculations. The $\Delta$ potential in nuclear matter has been calculated by using a Bruckner-Hartree-Fock approximation. By including the mean-field effects on the $\Delta$ propagation, the effective cross sections of the $NN\rightarrow N\Delta^\ast$, $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions in nuclear matter are predicted. It is demonstrated that the density dependence is most dramatic in the energy region close to the pion production threshold.
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"abstract": "To facilitate the relativistic heavy-ion calculations based on transport\nequations, the binary collisions involving a $\\Delta$ resonance in either the\nentrance channel or the exit channel are investigated within a Hamiltonian\nformulation of $\\pi NN$ interactions. An averaging procedure is developed to\ndefine a quasi-particle $\\Delta^*$ and to express the experimentally measured\n$NN\\rightarrow \\pi NN$ cross section in terms of an effective $NN\\rightarrow\nN\\Delta^\\ast$ cross section. In contrast to previous works, the main feature of\nthe present approach is that the mass and the momentum of the produced\n$\\Delta^*$\u0027s are calculated dynamically from the bare $\\Delta \\leftrightarrow\n\\pi N$ vertex interaction of the model Hamiltonian and are constrained by the\nunitarity condition. The procedure is then extended to define the effective\ncross sections for the experimentally inaccessible $N\\Delta^\\ast \\rightarrow\nNN$ and $N\\Delta^\\ast \\rightarrow N\\Delta^\\ast$ reactions. The predicted cross\nsections are significantly different from what are commonly assumed in\nrelativistic heavy-ion calculations. The $\\Delta$ potential in nuclear matter\nhas been calculated by using a Bruckner-Hartree-Fock approximation. By\nincluding the mean-field effects on the $\\Delta$ propagation, the effective\ncross sections of the $NN\\rightarrow N\\Delta^\\ast$, $N\\Delta^\\ast \\rightarrow\nNN$ and $N\\Delta^\\ast \\rightarrow N\\Delta^\\ast$ reactions in nuclear matter are\npredicted. It is demonstrated that the density dependence is most dramatic in\nthe energy region close to the pion production threshold.",
"arxiv_id": "nucl-th/9602021",
"authors": [
"T. -S. H. Lee"
],
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"doi": "10.1103/PhysRevC.54.1350",
"journal_ref": "Phys.Rev.C54:1350-1359,1996",
"title": "Medium Effects on Binary Collisions with the Delta Resonance",
"url": "https://arxiv.org/abs/nucl-th/9602021"
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