The talk presents the multipole expansion of the electron–nucleus scattering cross section at high energies within the framework of the unified electroweak theory. This expansion follows from that of the nuclear electroweak currents. To determine the multipole form factors, general formulas for calculating reduced matrix elements are derived using the shell model and the fractional parentage coefficient method. Calculation of form factors enables us to obtain more detailed information about nuclear structure and elucidate the role of the weak interaction in high-energy reactions.