Bethe-Salpeter-Approach to Relativistic Two-Fermion-Systems with a Separable Nonstatic Interaction

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 $\tilde{t}_{20}(k^2)$, $t_{20} (k^2,θ_e=70^{\circ})$ 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.