The longitudinal relaxation time T$\sb1$ is calculated for a dilute Fermi gas. We include the possibility of arbitrary degrees of polarization P, and uniform external magnetic fields. At low temperatures T$\sb1$ is proportional to T$\sp{-2}$ for the unpolarized gas in agreement with earlier calculations. For a polarized system in zero applied field the separation between up and down Fermi spheres provides an open channel in phase space for spin flipping processes. As temperature is reduced to zero T$\sb1$ levels off and approaches a constant value which depends sensitively on P, leading to much smaller values of T$\sb1$ than in the unpolarized case. For relaxation in a uniform external field H, Zeeman energy conservation during spin flipping interactions essentially shifts the location of the T$\sp{-2}$ behavior from zero polarization to the polarization P(H) which would be produced in equilibrium with the external field H. When the initial polarization of the system is different from P(H), T$\sb1$ again approaches a constant value which is equally sensitive to the initial polarization as temperature is reduced to zero. We apply our calculations to the case of dilute $\sp3$He-HeII solutions. We also consider the calculation of density dependent corrections to T$\sb1$ for unpolarized, or weakly polarized $\sp3$He-HeII using the long wavelength limit of the Bardeen-Baym-Pines interaction as a form for the spin independent part of the $\sp3$He-$\sp3$He interaction. Owing to the positive sign of the antisymmetric Landau parameter $\rm F\sbsp{o}{a}$ in dilute $\sp3$He-HeII Fermi Liquid interactions act to screen the magnetic dipole interactions which cause relaxation. To lowest order in density we find that the relaxation rate 1/T$\sb1$ is reduced by factor $\rm (1 - 3F\sbsp{o}{a})$ which compares favorably with recent calculations of T$\sb1$ for pure $\sp3$He.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-8652 |
| Date | 01 January 1993 |
| Creators | Nelson, Erik D |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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