Relaxation and spectral line shape in Fourier transform ion resonance spectroscopy

Analytical expressions for Fourier transform ion cyclotron resonance (FT-ICR) line shape absorption mode, dispersion mode, and magnitude (absolute value) mode are derived for coherently excited ions that undergo both reactive and nonreactive ion–molecule collisions. The expressions are valid at arbitrary sample pressure, and reduce to particularly simple form in the ’’zero-pressure’’ limit (essentially no ion–molecule collisions during the data acquisition period) or ’’high-pressure’’ limit (many ion–molecule collisions during the data acquisition period). The zero-pressure line shape has been analyzed in earlier papers; in this paper, various useful properties of the high-pressure line shape (e.g., linewidth, mass resolution, and upper mass limit) are tabulated for various choices of the fraction of maximal absorption (or magnitude) peak height at which linewidth is to be measured. Absorption, dispersion, and magnitude spectra are plotted for zero-pressure and high-pressure limits, and also for an intermediate pressure. Convenient reference graphs of high-pressure FT-ICR linewidth, mass resolution, and upper mass limit as functions of ionic mass and time-domain ICR half-life for singly charged ions at magnetic field strength of 2 T are included. Finally, the intermediate-pressure resolution is calculated as a function of acquisition period at fixed pressure, to shown that near-optimal mass resolution (to within 90% of maximal absorption-mode resolution, or 95% of maximal magnitude-mode resolution) is achieved by truncating the FT-ICR time-domain signal after just three relaxation times. The particularly simple trade-off between signal-to-noise ratio and mass resolution in FT-ICR spectroscopy is noted and explained. Good agreement between experimental and theoretical line shape (and thus mass resolution) is demonstrated.