Superfluidity in He^{3}: Inhibition by Polarization
Abstract
We summarize the previous treatments of the question of superfluidity in He^{3}, which have not shown conclusively whether this phase should or should not occur. The most promising calculation was by Pitaevskii, whose determination of the screened quasiparticle transition amplitude T~_{j} was carried out in the limiting case of large angular momentum j. In estimating T_{c} this was extrapolated to j=2 by Gor'kov and Pitaevskii (GP). The work of GP was found to contain an inadequate approximation (the Dwave Born approximation) plus also an algebraic error. When these corrections are made, their formula for T_{c} then yields the unattainably low value T_{c}~10^{100} deg. We have projected precisely T~_{j}(0<=j<=10) in secondorder perturbation theory. We used as the bare vertex function the offenergyshell K matrix, the particular form of which was chosen so that K would satisfy two exact identities (Ward identities). It was found that GP's extrapolation underestimates the effective Dwave interaction. In fact, the polarization (particlehole) diagram is an attractive correction to K_{j}, for j=2 and j>=6, in contrast to Pitaevskii's result that the secondorder diagram for T~_{j} is repulsive. We study carefully the three approximations involved in Pitaevskii's largej calculation. Theoretical arguments are given, and numerical evidence is furnished, which indicate that as j increases, Pitaevskii's limit is being approached asymptotically, but so slowly that his analytical result does not hold for angular momenta of interest (i.e., for j<20). The possibility of Dstate superfluidity is discussed. The transition temperature is such a sensitive function of the calculated theoretical parameters that it is difficult to furnish a precise estimate for T_{c}.
 Publication:

Physical Review A
 Pub Date:
 January 1971
 DOI:
 10.1103/PhysRevA.3.372
 Bibcode:
 1971PhRvA...3..372B