A Study of the Space-Time Trajectory Approach to Relativistic Coulomb Excitation of Giant Dipole Resonance States in Nuclei

In the standard semi-classical approach to relativistic Coulomb excitation, the relative motion of the colliding nuclei is treated classically while the excitation of the internal degrees of freedom is treated quantum-mechanically. Specifically, Winther and Alder [1] make a multipole expansion of the interacting potentials in terms of the Fourier transforms of the retarded electromagnetic potentials. This approach, while valid and accurate, entails severe numerical difficulties in practice. Recently, Dasso et al. [2, 3] have proposed a method which bypasses the complications of the standard approach. They model the excitation as a collective oscillation between the charged and the neutral components of the nucleus. With this simplification, the relativistic Coulomb excitation process can be treated completely in space and time coordinates without the need to Fourier-transform. In this work, we implement the space-time trajectory approach of Dasso et al. to compute the excitation probability and cross section for the relativistic Coulomb excitations of double giant dipole resonances in l36Xe and 208Pb nuclei. We demonstrate that the cross section depends critically on the distance of closest approach parameter. We show that the formula of Bayman and Zardi yields cross sections in better agreement with experimental results.