Theory of sound propagation in pair-correlated Fermi liquids: Application to /sup 3/He-B

Journal Article · Thu Jul 01 04:00:00 EDT 1976 · Phys. Rev., B; (United States)

DOI:https://doi.org/10.1103/PhysRevB.14.89· OSTI ID:7192886

Wolfle, P

On the basis of a set of kinetic equations for the matrix distribution function of a pair-correlated Fermi liquid derived previously, the dispersion law of sound is calculated for arbitrary values of ..omega..tau (tau is a collision time) and for all temperatures. The collision operator is approximated by a sum of energy-dependent relaxation-time expressions, such that the conservation laws are guaranteed and the important 1=2 component is preserved. The result agrees with exact solutions of the Boltzmann equation, wherever those are available, apart from irrelevant higher-order terms in the eigenvalue expansion. The principal results are (I) a simple relaxation-time expression is found to describe the attenuation and velocity of sound in the normal state at arbitrary ..omega..tau; (II) the relevant relaxation times in the superfluid are computed from the microscopic theory in the vicinity of the transition and for tempertures tending to zero; (III) the calculated attenuation and velocity of zero sound in the pseudoisotropic state are in good agreement with available data in the B phase of /sup 3/He. A value for the quasiparticle lifetime at the Fermi surface is obtained from the broadening of the collective-mode peak in the attenuation. It is found that the value of the 1 = 2 component of the collision integral near the polycritical point of /sup 3/He required to fit the data is smaller than theoretical predictions by a factor of 1.7, pointing to a possible source of the existing discrepancy between viscosity data theory (iv) The viscosity coefficient in the pseudoisotropic state is derived from the hydrodynamic sound attenuation for all temperatures. The change of the viscosity in the superfluid is found to be proportional to 1 - T/T/sub c/ near the transition due to a pair-breaking effect not included in previous theories. (AIP)

• Research Organization: Physik-Department der Technischen Universitat Munchen, D-8046 Garching, Germany
• OSTI ID: 7192886
• Journal Information: Phys. Rev., B; (United States), Journal Name: Phys. Rev., B; (United States) Vol. 14:1; ISSN PLRBA
• Country of Publication: United States
• Language: English

Related Subjects

640450* -- Fluid Physics-- Superfluidity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOLTZMANN EQUATION
COLLISIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVEN-ODD NUCLEI
FERMI GAS
FOURTH SOUND
HELIUM 3
HELIUM 3 B
HELIUM ISOTOPES
ISOTOPES
LIGHT NUCLEI
NUCLEI
RELAXATION
SECOND SOUND
SOUND WAVES
STABLE ISOTOPES
VISCOSITY
ZERO SOUND