F. Zardi

Comparison of exact and approximate cross sections in relativistic Coulomb excitation

We present a new method of obtaining time-dependent matrix elements of the electromagnetic pulse produced by a highly-relativistic projectile. These matrix elements are used in a coupled-channel calculation to predict the cross-sections for population of 1- and 2-phonon states of the giant dipole resonance. Comparisons are made with the predictions of the long-wavelength and Born approximations.

Range of validity of the eikonal approximation within the coupled-channel description of heavy-ion scattering processes

The validity of the eikonal approximation in heavy-ion reactions is systematically investigated for both potential scattering and coupled-channel processes. Simple prescriptions are advanced to account for Coulomb and nuclear distortions of the trajectory within the eikonal description. The strong nuclear absorption characterizing heavy-ion collision favours the extension of the limit of validity of the eikonal approximation to larger angles and to lower energies than probably expected, i.e. of the order of 30–40 MeV per nucleon in the case of elastic scattering or inelastic processes with very low excitation energies. In the case of inelastic excitation to highlying modes, and in particular at the lowest bombarding energies, the agreement between the eikonal predictions and the exact ones is worsened by the finiteQ-values, but not invalidated if proper corrections for the momentum mismatch are accounted for. A similar argument also applies to the strong-coupling situations, where the discrepancies are amplified by the multistep nature of the process.

Equivalence of the long-wavelength approximation and the truncated Taylor expansion in relativistic Coulomb excitation

The long-wavelength approximation and the truncated Taylor expansion are frequently used in the theory of relativistic Coulomb excitation to obtain multipole expansions of the interaction. It is shown in this Brief Report that these two approximations are exactly equivalent.

Quantum derivation of the use of classical electromagnetic potentials in relativistic Coulomb excitation

We prove that a relativistic Coulomb excitation calculation in which the classical electromagnetic field of the projectile is used to induce transitions between target states gives the same target transition amplitudes, to all orders of perturbation theory, as would a calculation in which the interaction between projectile and target is mediated by a quantized electromagnetic field.