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UBC Theses and Dissertations

Theory of the magnetic resonance spectrum of spin-polarized hydrogen gas Zhou, Haosheng


The Green's function method is applied to investigate the magnetic spin resonance spectra of three-dimensional and two-dimensional spin-polarized quantum gases. The Hartree-Fock approximation is employed to calculate the one-particle Green's function of the atoms, then this one-particle Green's function is used for the calculation of the vertex part of the Green's function. Such a combination yields a self-consistent result. The absorption spectra are obtained from the calculation of the susceptibility in terms of the two-particle Green's function (bubble diagram). Some general expressions for the dispersion relation, for the effective mass of a spin wave, and for the dipolar frequency shift are given in the calculation. In order to estimate the shift of the electron-spin-resonance (ESR) frequency, the effective dipole-dipole interactions among the hydrogen atoms are included in the calculation. These effective interactions are deduced from the ladder approximation, and hence are characterized by the scattering amplitude. The scattering amplitude is calculated numerically. The result shows that the theoretical value of the shift is smaller than the experimentally observed value by about 35%.

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