Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The work reported here is concerned with the measurement of the spin-lattice relaxation of protons in water, acetone, a D₂O - acetone mixture and various aqueous solutions of acetone. The theory to account for the decay rates has been outlined for a general case and has been applied in particular to acetone-water mixtures. The NMR technique has been described briefly. Temperature dependences of T₁ for all solutions have been investigated. It has been found that the relaxation in mixtures are slower than predicted by the theory. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The performance of a spin echo spectrometer which is suitable for chemical exchange studies is described. Using the Carr-Purcell sequence of pulses, proton T₂ values were obtained from two experiments differing only in their method of eliminating accumulated error in the width of the 180° pulses. The Meiboom-Gill method of phase shifting the r.f. in the first pulse is more flexible in the range of pulse intervals. Following the theory of Bloom, Reeves and Wells, rate constants describing the exchange process in two molecules were measured from the dependence of T₂ upon the pulse interval. The values of the rate constants for the hindered internal rotation about the N-N bond in N, N-dimethylnitrosamine agree with previous high resolution studies. A similar spin echo study has been conducted in order to measure the rates of internal rotation about the C-N bond in N, N-dimethylcarbamyl chloride. The values for the entropy of activation are consistently low. The possibility of systematic errors in the spin echo method has been investigated. It is concluded that reported values of rate constants in magnetic resonance should be the result of a spin echo investigation extending over as wide a temperature range as possible in addition to a high resolution study which involves a complete theoretical line shape fit to the experimental data. / Science, Faculty of / Chemistry, Department of / Graduate

The magneto-optical Faraday effect has been used to observe the spin-bath relaxation at low temperatures in CeES and in Eu-doped CaF₂. The paramagnetic Faraday rotation ϩ is an instantaneous measure of the magnetization M and it is shown that in CeES and Eu²+ : CaF₂, ϩ∾ M at the light frequencies employed. The apparatus is the same as that previously described by Rieckoff and by Griffiths. Pulsed MW-power at X-band has been used to disturb the equilibrium between spin system and bath. In CeES, the observed relaxation time Շ is of the order of a few msec, which is several orders of magnitude longer than the theoretical estimate of T₁. This suggests a severe bottleneck in the energy transfer spin-bath. Շis found to be environment-dependent. In HeII, the relaxation is exponential. Շ is in good agreement with nonresonant relaxation measurements by Van den Broek and Van der Marel. It is explained as arising from the Kapitza boundary resistance at the CeES-HeII interface. In HeI, the relaxation is non-exponential and is slower than in He gas at the same temperature. This suggests that in this case the thermal diffusion in the helium around the crystal is the bottleneck. The same relaxation behaviour is found when the crystal is heated dielectrically with MW power far off resonance. This supports the assumption that the energy transfer spin-bath is limited by spatial diffusion. If the crystal is surrounded by a He film at a temperature below the λ-point, Շ is found to be the same as in HeII up to a well defined average MW power level. For higher powers the relaxation behaviour is similar to that of CeES immersed in HeI. In Eu²+ ; CaF₂, T₁ is expected to have the form T₁= AT + BT⁵. The observed relaxation time Շ , however, is found to be concentration dependent. All measurements have been done on the +½⇢ -½ transition with H II [100]. For the three lowest concentrations, the temperature dependence of Շ from 1.5 to 4.2°K can be fitted with the expression Շ ¯¹=CT with C = 2.75 (sec°K) ¯¹ for 0.02% Eu, C = 3.5for 0.8% and C = 5 for 0.2%, Շ is shorter and Շ ¯¹ ∾ T ² from 1.5°K to 7°K. The concentrations given correspond to the total Eu content. The Eu²+ concentration has been inferred from the magnitude of the saturation rotation. Շ(T) seems to depend on both Eu²+ and Eu³+ concentrations. It is suggested that exchange coupled pairs of Eu²+ and clusters involving Eu³+ may account for the concentration dependence of Շ. Upper limits of A = 2.5 and B = 5 x 10¯⁵ are found for T₁ by extrapolating the lowest concentrations investigated. These values are somewhat lower than both measured and calculated values found by Huang. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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Hoi-Yin Shik. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 92-94). / Text in English; abstracts in English and Chinese. / Hoi-Yin Shik. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Heisenberg Model --- p.1 / Chapter 1.2 --- Exactly Soluble Model --- p.3 / Chapter 1.3 --- This Project --- p.4 / Chapter 2 --- Spin-1 Net Spin Models --- p.6 / Chapter 2.1 --- Solution for the Four Spin Plaquette --- p.8 / Chapter 2.2 --- The Ground State and First Excited State Properties --- p.17 / Chapter 2.2.1 --- Spin Ladder Model --- p.18 / Chapter 2.2.2 --- Double Layer Model --- p.24 / Chapter 2.3 --- Excitation Spectrum for L Goes from One to Infinity --- p.27 / Chapter 2.4 --- General Spin S --- p.28 / Chapter 3 --- Constructing Exactly Soluble Quantum Spin Models --- p.29 / Chapter 3.1 --- Spin-1 Bond Operators --- p.29 / Chapter 3.1.1 --- Net Spin Ladder --- p.30 / Chapter 3.1.2 --- Spin Layer --- p.33 / Chapter 3.2 --- Other Two-dimensional Exactly Soluble Model --- p.35 / Chapter 3.3 --- Three-dimensional Model --- p.38 / Chapter 3.4 --- Spin-1 bond Operators --- p.56 / Chapter 3.5 --- Three-dimensional Spin-1 Model --- p.65 / Chapter 3.5.1 --- Other Exact Soluble Spin-1 Models --- p.68 / Chapter 3.6 --- General Spin-S --- p.68 / Chapter 4 --- Low Lying Excitations for the Net Spin Ladder --- p.72 / Chapter 4.1 --- Solutions of K-Rung Ladder --- p.74 / Chapter 4.1.1 --- K = 1 --- p.74 / Chapter 4.1.2 --- K = 2 --- p.75 / Chapter 4.1.3 --- K = 3 --- p.76 / Chapter 4.1.4 --- K = 4 --- p.78 / Chapter 4.1.5 --- K > 4 --- p.80 / Chapter 4.2 --- The Critical Point --- p.81 / Chapter 5 --- Conclusion --- p.90 / Bibliography --- p.92 / Chapter A --- The matrix represention of different Hamiltonians --- p.95 / Chapter A.1 --- p.95 / Chapter A.2 --- p.97 / Chapter A.3 --- p.99

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