Perturbation theory and spin temperature in the saturation of spins
Franz, Judith Rosenbaum
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https://hdl.handle.net/2142/23970
Description
Title
Perturbation theory and spin temperature in the saturation of spins
Author(s)
Franz, Judith Rosenbaum
Issue Date
1965
Doctoral Committee Chair(s)
Slichter, C.P.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
perturbation theory
spin temperature
saturation of spins
Language
en
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.
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