Mobility of negative ions in superfluid 3He-B

Abstract

We calculate the mobility of negative ions in superfluid 3He-B. We first derive the general formula for the mobility, and show that to a good approximation the scattering of quasiparticles from an ion may be treated as elastic, both in the superfluid for temperatures not too far below the transition temperature and also in the normal state. The scattering cross section in the superfluid is then calculated in terms of normal state properties; as we show, it is vital to include the effects of superfluid correlations on intermediate states in the scattering process. We find that for quasiparticles near the gap edge, the quasiparticle-ion scattering amplitude has a resonant behavior, and that as a result of interference among many partial waves, the differential scattering cross section is strongly peaked in the forward direction and reduced at larger angles, in much the same way as in diffraction. The transport cross section for such a quasiparticle is strongly reduced compared to that for a normal state quasiparticle, and the mobility is consequently strongly enhanced. Detailed calculations of the mobility which contain essentially no free parameters, agree well with the experimental data.

Mobility tensor of negative ions in superfluid 3He-A

“…It is convenient to work with the Fourier transform of (26). We write the energy-dependent single-particle propagator G(p, E) in the unperturbed superfluid as 22 1 G(P' E) = E2-~Z--~p \-A* (/~) E-,~p/ (27) where A(/~)= A(iG + i/~y)l is the energy gap matrix (4).…”

“…4 The ,it and nl are spherical Bessel and Neumann functions of order L The differential quasiparticle-ion scattering cross section in the normal state is illustrated in a polar plot in units of zrR 2 in Fig. 3, with p~R = 8.45.…”

“…In Ref. 4 (hereafter referred to as I) we showed that in the B phase the latter effect leads to a resonant structure in the quasiparticle-ion scattering amplitude. This causes a strong modification in the cross section for low-energy excitations and is crucial for an understanding of the experimental mobility.…”

“…of superfluid coherence factors, we may express (53) by the compact formula where we have defined the matrix which is the projection operator onto states of energy E and momentum in the direction/~ on both branches of the spectrum 4. The O a reduces to the unit matrix in the normal limit (A/E --> 0).…”

Mobility Tensor of the Electron Bubble in SuperfluidHe3-A

“…Recently we showed 1 that the rapid mobility increase of negative ions in 3 He-£ just below T c is due to a novel scattering phenomenon. 2 Here we evaluate the mobility of negative ions in 3 He-A where the important new feature is the anisotropy of the spectrum of elementary excitations, which leads to the observed tensor structure for the mobility. 3 The striking constancy of the normal-state mobility throughout the Fermi-liquid regime 1 is explained by the large size of the ion, a cavity of radius R = 10-20 A enclosing an electron.…”