dorsal/arxiv
View SchemaBethe-Salpeter-Approach to Relativistic Two-Fermion-Systems with a Separable Nonstatic Interaction
| Authors | Frieder Kleefeld, Manfred Dillig |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9806058 |
| URL | https://arxiv.org/abs/nucl-th/9806058 |
| Journal | Few-Body Systems 15 (1993) N24 |
Abstract
To study the characteristic features of relativistic bound systems, the Bethe-Salpeter equation (BSE) for two equal mass spin 1/2 particles (like the deuteron) is solved in the cm-frame for a covariant separable interaction kernel. For that purpose the BSE is transformed to an eigenvalue problem which is diagonalized numerically. The Bethe--Salpeter amplitudes (BSAs) are obtained straightforwardly from the resulting eigenvectors. Only positive parity solutions of the eigenvalue problem are considered. To correlate the BSAs to standard quantum mechanical wavefunctions, the corresponding equal-time-wavefunctions (ETWs) are calculated. A decomposition of BSAs and ETWs in partial waves in angular momenta and parity is performed. As a first application elastic electron-deuteron-scattering in the impulse approximation (IA) is considered. The charge, magnetic and quadrupole formfactors $F_C(k^2)$, $F_M(k^2)$, $F_Q(k^2)$ and tensor polarizations $\tilde{t}_{20}(k^2)$, $t_{20} (k^2,\theta_e=70^{\circ})$ are obtained from three independent matrix elements of the deuteron current in the Breit-frame of elastic electron-deuteron-scattering. Additionally, the formfactors $A(k^2)$ and $B(k^2)$ of the Rosenbluth formula are calculated.
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"abstract": "To study the characteristic features of relativistic bound systems, the\nBethe-Salpeter equation (BSE) for two equal mass spin 1/2 particles (like the\ndeuteron) is solved in the cm-frame for a covariant separable interaction\nkernel. For that purpose the BSE is transformed to an eigenvalue problem which\nis diagonalized numerically. The Bethe--Salpeter amplitudes (BSAs) are obtained\nstraightforwardly from the resulting eigenvectors. Only positive parity\nsolutions of the eigenvalue problem are considered. To correlate the BSAs to\nstandard quantum mechanical wavefunctions, the corresponding\nequal-time-wavefunctions (ETWs) are calculated. A decomposition of BSAs and\nETWs in partial waves in angular momenta and parity is performed. As a first\napplication elastic electron-deuteron-scattering in the impulse approximation\n(IA) is considered. The charge, magnetic and quadrupole formfactors $F_C(k^2)$,\n$F_M(k^2)$, $F_Q(k^2)$ and tensor polarizations $\\tilde{t}_{20}(k^2)$, $t_{20}\n(k^2,\\theta_e=70^{\\circ})$ are obtained from three independent matrix elements\nof the deuteron current in the Breit-frame of elastic\nelectron-deuteron-scattering. Additionally, the formfactors $A(k^2)$ and\n$B(k^2)$ of the Rosenbluth formula are calculated.",
"arxiv_id": "nucl-th/9806058",
"authors": [
"Frieder Kleefeld",
"Manfred Dillig"
],
"categories": [
"nucl-th"
],
"journal_ref": "Few-Body Systems 15 (1993) N24",
"title": "Bethe-Salpeter-Approach to Relativistic Two-Fermion-Systems with a Separable Nonstatic Interaction",
"url": "https://arxiv.org/abs/nucl-th/9806058"
},
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