Electron-induced one-nucleon knock-out observables are computed for moderate to high momentum transfer making use of semi-relativistic expressions for the one-body and two-body meson-exchange current matrix elements. Emphasis is placed on the semi-relativistic form of the $Delta$-isobar exchange current and several prescriptions for the dynamical-equivalent form of the $Delta$-propagator are analyzed. To this end, the inclusive transverse response function, evaluated within the context of the semi-relativistic approach and using different prescriptions for the $Delta$-propagator, is compared with the fully relativistic calculation performed within the scheme of the relativistic Fermi gas model. It is found that the best approximation corresponds to using the traditional static $Delta$-propagator. These semi-relativistic approaches, which contain important aspects of relativity, are implemented in a distorted wave analysis of quasielastic $(e,ep)$ reactions. Final state interactions are incorporated through a phenomenological optical potential model and relativistic kinematics is assumed when calculating the energy of the ejected nucleon. The results indicate that meson exchange currents may modify substantially the $TL$ asymmetry for high missing momentum.
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