Relativistic Effects in Quasielastic Electron Scattering

Electron scattering is known to be one of the most powerful means to study both the structure of nuclei and the internal structure of the nucleon, especially the less known strange and axial form factors. In particular, inclusive (e,e′) processes at or near quasielastic peak kinematics have attracted attention in the last two decades and several experiments have been performed with the aim of disentangling the longitudinal and trans-verse contributions to the quasielastic cross section. These are linked to the hadronic tensor $$ {W^{\mu \nu }} = \mathop {\bar \sum }\limits_i \mathop \sum \limits_f \langle f\mid \mathop {{J^\mu }}\limits^ \wedge \mid i\rangle *\langle f\mid \mathop {{J^v}}\limits^ \wedge \mid i\rangle \delta ({E_i} + \omega -{E_f}) $$ (1) via the relations $$ {R^L}(q,\omega ) = {\left( {{{{q^2}} \over {{Q^2}}}} \right)^2}\left[ {{W^{00}} -{\omega \over q}({W^{03}} + {W^{30}}) + {{{\omega ^2}} \over {{q^2}}}{W^{33}}} \right] $$ (2) $$ {R^T}(q,\omega ) = {W^{11}} + {W^{22}}, $$ (3) where Q µ = (ω, q) is the four-momentum carried by the virtual photon, Ĵ µ is the nuclear many-body current operator and the nuclear states |i〉 and |f〉 are exact eigenstates of the nuclear Hamiltonian with definite fourmomentum. The general form (1) includes all possible final states that can be reached through the action of the current operator Ĵ µ on the exact ground state; here we focus on the one-particle one-hole (1p–1h) excitations.