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Published February 15, 1967 | Published
Journal Article Open

Theory of Collision-Broadened Ion Cyclotron Resonance Spectra


A formalism for calculating collision-broadened ion cyclotron resonance spectra is developed in detail. The Boltzmann transport equation describing the time variation of the arbitrary function of ion velocity X(v) is extended to include resonant charge transfer. Then with X(v) = v and X(v) = v^2, equations describing, respectively, the velocity and energy of an average particle are developed. The solution of these equations is used to obtain the power absorption of the ions from the observing radio-frequency electric field.The effects of collisions are treated in terms of specific ion—molecule interactions. The equations of motion for a mixture of ions, A and B, are coupled by the collision term which accounts for the charge-transfer process A+ + B ⇌ A + B+. As numerical examples the collision frequencies are evaluated for the rare gases and used to calculate absorption spectra for Ar+ in Ar and mixtures of He and Ne isotopes. The formalism permits the straightforward examination of the effects of electric-field strength, pressure, and temperature on the line shapes.

Additional Information

© 1967 American Institute of Physics. Received 24 June 1966. The author wishes to acknowledge the assistance and encouragement of Professor John D. Baldeschwieler with the above work. Also helpful were L.R. Anders and Professor D.R. Herschbach who read the manuscript and provided useful comments. The support of the National Science Foundation under grant GP-4924 is gratefully acknowledged. The computations were supported in part by the Stanford University Computation Center and the Department of Chemistry, Harvard University. [J.L.B. was a] National Science Foundation Predoctoral Fellow, Harvard University [and a] Travelling Guidance Fellow, Harvard University.

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August 19, 2023
August 19, 2023