Gauge dependence of calculations in relativistic Coulomb excitation

Abstract

Before a quantum-mechanical calculation involving electromagnetic interactions is performed, a choice must be made of the gauge to be used in expressing the potentials. If the calculation is done exactly, the observable results it predicts will be independent of the choice of gauge. However, in most practical calculations approximations are made, which can destroy the gauge invariance of the predictions.We compare here the results of coupled-channel time-dependent relativistic Coulomb excitation calculations, as performed in either Lorentz or Coulomb gauges. We find significant differences when the bombarding energy per nucleon is ≥ 2 GeV, which indicates that the common practice of relying completely on the Lorentz gauge can be dangerous.

Time-dependent aspects of the semiclassical approach in the analysis of heavy ion reactions

“…2 and 3 mean that there is a sustained "exchange" of probability between the ground state and the GDR (also observed by the authors of Ref. [17]) that keeps taking place long after there is any apparent justification for such trade-off to occur.…”

“…Explicit expressions for are known that allow the particular transformation from Lorentz to Coulomb gauges [17].…”

Gauge dependence of spontaneous radiation spectrum in a time-dependent relativistic non-perturbative Coulomb field

“…These elements have been encountered individually in some studies. For example, Coulomb excitation [13,14] may also utilize a relativistic projectile, but in a perturbative and/or non-adiabatic way.…”

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

“…The reason for this apparent restriction is that ABHMW used the Coulomb gauge for the calculation of the quantized-field version of ṽγα (t), but they used the Lorentz gauge for the calculation of the classical field version. It is shown in Reference [19] that the versions of ṽγα (t) calculated in the two gauges agree in their on-shell Fourier components, but are generally different when ω = ω γα . In Sections III, IV, and V, we have shown that the quantized field and classical field treatments agree for all t, and so for all ω, if both are calculated in the same gauge.…”