Application of Boltzmann Equation on Spin Diffusion of Ferromagnetic Superfluid 3He: Near Critical Temperature

Abstract

Different scattering processes of quasiparticles containing a binary process, a coalescence process and a decay process in transition probabilities are taken into account. In the meantime, interaction between Bogoliubov quasiparticles as well as that between normal and superfluid components (spin up-spin down quasiparticles) of ferromagnetic superfluid 3 He-A 1 are considered. Pfitzner procedure is used in the calculation of triplet and singlet quasiparticle scattering amplitude existing in transition probabilities of the collision integral of standard Boltzmann equation at melting pressure. Pfitzner procedure is extended beyond s-p approximation by adding higher angular momentum components. Then, using the results of Boltzmann equation and considering smallness of the gap close to T c↑ , the change of the spin diffusion coefficients tensor of the A 1 -phase of superfluid 3 He close to critical temperature and melting pressure is calculated. Temperature dependence of the spin diffusion coefficient change, i.e., δD xyxy /D = (3/2)(δD xzxz /D) , is −0.71(1 − (T /T c↑ )) 1/2 . It is also shown that interaction between normal and Bogoliubov quasiparticles (normalsuperfluid components interaction) is very important to transport properties such as spin diffusion close to critical temperature. Furthermore, using s-p approximation, the prefactor of δD xyxy /D is plotted in terms of pressure; hence, the pressure dependence of δD xyxy /D is also determined.