*2.1. First-Order Effects*

If the interaction between the colliding nuclei is weak, i.e., the excitation probability is 1, Coulomb-excitation amplitudes can be calculated within the first-order perturbation theory. In the first order, the cross section for the excitation of a final state *If* from the ground state *I*g.s. is proportional to the square of the transitional matrix element *If* ||*EL*||*I*g.s. , where *L* = 2, 3. Therefore, from the measured *I*g.s. → *If* Coulomb-excitation cross section, it is possible to extract the reduced transition probability *B*(*EL*; *I*g.s. → *If*).

The excitation process strongly depends on the kinematics and the mass es *A* and atomic numbers *Z* of the target and projectile nuclei. The first-order approximation is usually sufficiently accurate to describe the population of excited states from the ground state in experiments employing a light beam or a light target, or when small centre-of-mass scattering angles are used; examples of such recent studies are presented in Section 3.4. Larger kinetic energy, larger atomic numbers of the collision partners, and lower excitation energies enhance the excitation probability, leading to the appearance of higher-order effects in the excitation process.
