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Modern Applied Science

Scattering Properties of Spin-polarized 3He-HeII Mixtures at Low Temperature

Ayman S. Sandouqa

Published Jul 20, 2012• 3 citations
Publisher

Abstract

The cross sections and the man free path of 3He? atoms in HeII background are calculated. The Ramsauer-Townsend effect in the cross sections is found in these mixtures at low temperatures. In the low energy limit the cross sections are dominated by the S-wave scattering. The influence of S-scattering decreases with increasing magnetic field. With increasing k, S-wave scattering tends to decrease; whereas the contribution of the higher angular-momentum waves (especially P-wave) to the scattering increases. Our results of the mean free path exhibit the 3He? atoms propagate through the HeII background with an exceedingly long mean free path and without friction.

DOI
10.5539/mas.v6n8p32

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The cross sections and the man free path of 3He? atoms in HeII background are calculated. The Ramsauer-Townsend effect in the cross sections is found in these mixtures at low temperatures. In the low energy limit the cross sections are dominated by the S-wave scattering. The influence of S-scattering decreases with increasing magnetic field. With increasing k, S-wave scattering tends to decrease; whereas the contribution of the higher angular-momentum waves (especially P-wave) to the scattering increases. Our results of the mean free path exhibit the 3He? atoms propagate through the HeII background with an exceedingly long mean free path and without friction.
In this paper, the Lippmann-Schwinger (LS) formalism is applied to spin-polarized atomic tritium (T↓). The total and viscosity cross sections of T↓- T↓ collisions are calculated, using two triplet-state potentials: a Morse- and a Silvera- type potentials. Also, the scattering length and the binding energy of T↓ atoms are calculated. Our results are found to be in good agreement with previous calculations. Our results for the Morse potential are smaller in magnitude than those for the Silvera potential, because the Morse-potential well is shallower than that of the Silvera potential. In the low-energy limit, the cross sections are dominated by S-wave scattering. In this limit, the S-wave scattering length a0< 0 for both potentials. This means that the interaction between the T↓ atoms is attractive. The Ramsauer-Townsend (RT) effect and phase transitions in the cross sections are found at low temperatures. The effect of the D-wave scattering appears as a resonance-like behavior in the total cross section. This peak corresponds to a quasi-bound state.
In this paper the Galitskii–Migdal–Feynman (GMF) formalism is applied to spin-polarized 3 He–HeII mixtures with special emphasis on the effect of the magnetic field on hole–hole scattering. For comparison purposes, the relative phase shifts for S- and P-waves, in both GMF and Brueckner–Bethe–Goldstone (BBG) formalisms, are calculated and analysed. Also, the corresponding scattering lengths are evaluated. In polarized mixtures, the S-wave pairing decreases because of the flip of one spin in the pair; whereas the magnetic field has no effect on P-wave pairing.
Low-energy properties of spin-polarized electron-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) and spin-polarized positronium-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that He(23S)\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)He(23S) may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the SSS-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium(23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.
Total cross sections for the scattering of low-energy electrons and positrons by atomic beryllium in the energy range below the first inelastic thresholds are calculated. A Ramsauer–Townsend minimum is seen in the electron scattering cross sections, while no such effect is found in the case of positron scattering. A minimum total cross section of 0.016 a 0 2 at 0.0029 eV is observed for the electron case. In the limit of zero energy, the cross sections yield a scattering length of −0.61 a 0 for electron and a 0 for positron scattering.
We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.
A theory of magnetotransport phenomena in low-density paramagnetic systems at low temperature is proposed. The main contentions are based on considering a dissipation mechanism due to the inelastic scattering of paramagnetic particles with transverse collective spin fluctuations. In the presence of an external magnetic field and in the low-momentum limit the corresponding cross section may be very large. Theoretical estimates are in good agreement with recent indirect measurements of intrabeam scattering for cooled H atoms. The extra scattering channel results in a drastic reduction in the mean free path and, consequently, a decrease in the thermal conductivity and viscosity, in contrast to previous theories. In the case of degenerate Fermi systems, the calculations yield quite different temperature dependencies compared with those given by the Fermi-liquid approach. Application of the theory to gaseous H\ensuremath{\downarrow}, $^{3}\mathrm{\ensuremath{\uparrow}}$, and dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures are briefly discussed, and it is shown that the thermal conductivity and viscosity of gaseous H\ensuremath{\downarrow} under common conditions are expected to be roughly 102{10}^{2}102 times less than the normal gas-kinetic values.