Coulomb excitation at intermediate energies

TL;DR

This paper develops a model for Coulomb excitation at intermediate energies that incorporates relativistic effects, improving the accuracy of cross section calculations and aligning well with experimental data.

Contribution

A new model that includes relativistic effects in Coulomb excitation calculations, bridging non-relativistic and relativistic regimes with good experimental agreement.

Findings

Model converges to relativistic straight-line approximation at high energies.

Model agrees well with experimental measurements between 30 and 70 MeV/nucleon.

Relativistic and Coulomb distortion effects are significant and discussed in detail.

Abstract

Straight line trajectories are commonly used in semi-classical calculations of the first-order Coulomb excitation cross section at intermediate energies, and simple corrections are often made for the distortion of the trajectories that is caused by the Coulomb field. These approximations are tested by comparing to numerical calculations that use exact Coulomb trajectories. In this paper a model is devised for including relativistic effects in the calculations. It converges at high energies towards the relativistic straight-line trajectory approximation and approaches the non-relativistic Coulomb trajectory calculation at low energies. The model is tested against a number of measurements and analyses that have been performed at beam energies between 30 and 70 MeV/nucleon, primarily of quadrupole excitations. Remarkably good agreement is achieved with the previous analyses, and good agreement is also achieved in the few cases, where the B(E$\lambda$) value is known from other methods. The magnitudes of the relativistic and Coulomb distortion effects are discussed.