SIMPLE PHYSICAL MODELS FOR COULOMB-INDUCED FREQUENCY-SHIFTS AND COULOMB-INDUCED INHOMOGENEOUS BROADENING FOR LIKE AND UNLIKE IONS IN FOURIER-TRANSFORM ION-CYCLOTRON RESONANCE MASS-SPECTROMETRY

Two simple models which correspond more closely to physical reality than some prior models are proposed to account for the Coulomb-induced frequency shifts to lower frequency, which have been observed in Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. The first model consists of two different-mass point charges which undergo cyclotron orbits with the same orbit centers at their respective cyclotron frequencies. The model predicts that each excited cyclotron motion should induce a negative frequency shift in the other's cyclotron motion. The model predicts a zero frequency shift for ions of the same mass. The physical basis for the Coulomb-induced shift is most easily seen in a coordinate frame which rotates at the cyclotron motion of the ion whose frequency is shifted. It is noted that a prior model for Coulomb-induced frequency shifts is more appropriate for scanning ICR than FT-ICR and the reason is described for the correctness of the predictions of this less appropriate model. A second model, the line model, is created by extension of the point model. The line model gives rise to a position-dependent frequency shift which is synonymous with inhomogeneous Coulomb broadening. When a non-quadrupolar electrostatic trapping field is included in the model, 'like' ions become 'unlike' and Coulomb-shifting and Coulomb-broadening apply, as for 'like' ions. The analysis predicts that ICR cells which are designed to have negligible trapping fields over most of their volume will be less sensitive to Coulomb shifting/broadening than ordinary ICR cells.