Perturbation theory and spin temperature in the saturation of spins
type: CreativeWork
description: We have developed and experimentally_verifie~ a theory that displays the connection between the Bloembergen, Purcell, and Pound perturbation theory approach to nuclear resonance and Redfield's theory of spin temperature in the rotating frame. We show that, although Bloembergen, Purcell, and Pound's approach is correct for perturbations of short duration, for long lasting perturbations, the state of a system is significantly changed, perturbation theory fails, and a new calculational technique must be employed. For spins, placed in a static magnetic field and subjected to a strong magnetic field oscillating at -a. fte~ency near - \ the resonant frequency, Redfiel~s theory of spin temperature in the rotating frame can be used to calculate the thermodynamic equilibrium state of the system. Making the same assumpt-ions as previous workers, we find that a single rate equation governs the approach to equilibrium of the system, and by combining these two theories, we can easily find the state of the system at all intermediate times. Equations have been derived that predict the magnetization of the system as a function of the frequency and amplitude of the oscillating field, the strength of the static field, and the length of time for which the oscillating field is applied. Our experiments confirm the theoretical predictions. The technique of rotary saturation enabled US to carry out resonance experiments in I extr~mely weak effective static fields for which the Redfield approach should fail. The strong static field case is contrasted with the weak static case, and the large differences observed between the two are explained. Many-quanta transitions, which were observed during this work, are discussed, and the strength of the two-quanta line occurring at half the resonant frequency is calculated.
abstract: We have developed and experimentally_verifie~ a theory that displays the connection between the Bloembergen, Purcell, and Pound perturbation theory approach to nuclear resonance and Redfield's theory of spin temperature in the rotating frame. We show that, although Bloembergen, Purcell, and Pound's approach is correct for perturbations of short duration, for long lasting perturbations, the state of a system is significantly changed, perturbation theory fails, and a new calculational technique must be employed. For spins, placed in a static magnetic field and subjected to a strong magnetic field oscillating at -a. fte~ency near - \ the resonant frequency, Redfiel~s theory of spin temperature in the rotating frame can be used to calculate the thermodynamic equilibrium state of the system. Making the same assumpt-ions as previous workers, we find that a single rate equation governs the approach to equilibrium of the system, and by combining these two theories, we can easily find the state of the system at all intermediate times. Equations have been derived that predict the magnetization of the system as a function of the frequency and amplitude of the oscillating field, the strength of the static field, and the length of time for which the oscillating field is applied. Our experiments confirm the theoretical predictions. The technique of rotary saturation enabled US to carry out resonance experiments in I extr~mely weak effective static fields for which the Redfield approach should fail. The strong static field case is contrasted with the weak static case, and the large differences observed between the two are explained. Many-quanta transitions, which were observed during this work, are discussed, and the strength of the two-quanta line occurring at half the resonant frequency is calculated.
author: Franz, Judith Rosenbaum
language: en
keywords: perturbation theory, spin temperature, saturation of spins
date published: 2011-05-19T16:30:57Z
date modified: 2026-07-22T22:25:23Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois - Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/23970