See also the source file:
he3_transp_b.f and doc_tech/spin_diff.pdf.
Values for he3_tau0, he3_tau_av, he3_diff_* are extended to
$T>T_c$ region using normal phase functions.
| he3_coll_int(xi,ttc,gap,g0,d0) | Full temperature range approximation.
(Einzel, Wolfle, Hirschfeld, JLTP80 (1990), p.66) |
| he3_coll_int_lt(xi,ttc,gap,g0,d0) | Collision integral for low temp (good for $T < 0.7 T_c$).
(Einzel, JLTP84 (1991), f.76) |
| he3_coll_int_ht(xi,ttc,gap,g0,d0) | Collision integral for high temp.
(Einzel, JLTP84 (1991), f.75) |
| he3_tau0(ttc,p) | Lifetime at the Fermi level, [s].
$\displaystyle\quad 1/\tau(0) = \frac{I (0,T)}{\tau_N(0,T)},$
(Einzel-1991, f.74,76. Einzel-1990 f.A1) |
| he3_tau0lt(ttc,p) | $1/\tau$ in the $T\rightarrow0$ limit (does not depend on energy). (Einzel-1978, f.79) |
| he3_tau_av(ttc,p) | Thermal average lifetime, [s].
$\displaystyle\quad 1/\bar\tau = \frac{1}{Y_0}
\int_{-\infty}^{\infty} \frac{\phi_k\ d\xi}{\tau}$
(Einzel-1991, f.77) |
| he3_fpath(ttc,p) | Mean free path, [cm]. (Einzel JLTP32 (1978) f.84) |
| he3_visc_fpath(ttc,p) | Viscous mean free path, [cm]. (Einzel 1990, eq.26) |
| he3_rmsv(ttc,p) | Rms velosity of Bogoliubov quasiparticles [cm/s] (Einzel JLTP32 (1990) f.28) |
| he3_tau_dperp(ttc,p)
he3_tau_dpar(ttc,p) |
Spin diff. transport time, [s].
\ $\tau_D^{\perp,\parallel} = \bar\tau
/(1-\lambda_1^a Y^{\perp,\parallel})$
(Einzel-1991, f.90,96) |
| he3_diff_hperp_zz(ttc,p)
he3_diff_hpar_zz(ttc,p) |
Spin diffusion in hydrodynamic limit ($\omega_L \tau \ll 1$),
$D^{\perp,\parallel}_{zz}(\omega_L=0)$, [cm$^2$/s].
Einzel JLTP84 (1991) f.102)
According to Einzel's paper (see f.105) nonhydrodynamic effects do not affect $D^\parallel$. In Mukharsky paper they do. |
| he3_diff_perp_xx(ttc,p,nu0)
he3_diff_perp_zz(ttc,p,nu0) he3_diff_perp_xx_im(ttc,p,nu0) he3_diff_perp_zz_im(ttc,p,nu0) he3_diff_par_xx(ttc,p,nu0) he3_diff_par_zz(ttc,p,nu0) |
Components of spin diffusion tenzor, [cm$^2$/s]
(Bunkov et al, 1990 f.3; Einzel, 1991, f.108; Markelov, Mukharsky, 1992, f.7,8) |
TODO:
Exchange coupling strength is in the $F_1^a = 0$ limit. (small difference from normal phase values)
How does he3_diff_perp_??_im extends to the normal phase?