Influence of Multiple Virtual Transitions on the Reorientation Effect in Coulomb Excitation

Calculations of the reorientation effect in Coulomb excitation of the first $2^{+}$ state of even-even nuclei are extended by employing the semiclassical approximation to take into account second- and third-order virtual $E2\mathrm{}$ transitions to higher excited states. Deviations from first-order perturbation theory in the excitation probability are investigated numerically as a function of the bombarding energy and the scattering angle for heavy-ion projectiles. Results are presented for rotational and vibrational nuclei as a guide in the selection of conditions suitable for the determination of the static quadrupole moment of the lowest $2^{+}$ state. Conditions for the practical convergence of the perturbation expansion are discussed.