BCS energy gap + trivial strong coupling correction + some values derived from energy gap.
See also the source file: he3_gap.f.
| he3_bcsgap(ttc) | BCS gap for 3He-B in $T_c$ units. |
| he3_bcsdgap2(ttc) | Derivative of the BCS gap $d(\Delta^2)/d(T/T_c)$. |
| he3_bcsgap_fast(ttc) | Einzel approximation for BCS gap (0.5% accuracy, 70 times faster).
(Einzel-1991, f.68) |
| he3_trivgap(ttc,p) | Trivial strong-coupling (or weak-couplig-plus, WCP) correction to the BCS gap. Tabulated values from Sirene-Rainer-1983 paper are used. Note that derivative of the gap squared in $T_c$ is not strictly proportional to the heat capacity jump. This probably shows that exact heat capacity calculation requires WCP energy terms, not just BCS calculations with modified gap... |
| he3_bcsdgap2(ttc, p) | Derivative of the WCP gap $d(\Delta^2)/d(T/T_c)$. |
| he3_todogap(ttc,p) | Gap based on Todoschenko's measurements: linear interpolation in density between BCS value at zero bar and measured value 1.99 at melting pressure. Temperature behaviour as in he3_trivgap. |
| he3_gap(ttc,p) | Wrapper for the gap used everywhere in the lib (trivgap by default). |
| he3_egap(ttc,p) | he3_gap expressed in energy units [erg] rather then $T_c$. |
| he3_yosida(ttc,gap,n) | Yosida functions $Y_n(T/T_c,\Delta) =
\int_{-\infty}^{\infty} \left(\frac{\xi_k}{E_k}\right)^n
\ \frac{1}{2T/T_c}\ \mbox{ch}^{-2}\left(\frac{E_k}{2T/T_c}\right)\ d\xi_k$
Note: type of n parameter should be real*8 (this is done for standard function handling). |
| he3_yosida_s(ttc,gap) | Entropy Yosida function $Y_s(T/T_c,\Delta) = \frac{3}{\pi^2} \int_{-\infty}^{\infty} \left(\frac{E_k}{T/T_c}\right)^2 \ \frac{1}{2T/T_c}\ \mbox{ch}^{-2}\left(\frac{E_k}{2T/T_c}\right)\ d\xi_k$ |
| he3_yosida_c(ttc,gap,dgap2) | Heat Capacity Yosida function
$Y_c(T/T_c,\Delta) = Y_s + T/T_c \frac{d}{dT/T_c} Y_s$
Gap derivative should be provided as a third argument. |
| he3_yosida_par(ttc,gap)
he3_yosida_perp(ttc,gap) he3_z3(ttc,gap) he3_z5(ttc,gap) he3_z7(ttc,gap) he3_lambda(ttc,gap) |
Various functions |
| he3_rho_nb(ttc, p) | B-phase normal component density: $\frac{\rho_B^n}{\rho_{N}} = \frac{(3 + F_1^s) Y_0}{3 + F_1^s Y_0}$ |
| he3_chi_b(ttc, p) | B-phase susceptibility (ratio of he3_chi_n): $\frac{\chi_B}{\chi_N} = \frac{(1+F_0^a)(2 + Y_0)}{3+F_0^a(2 + Y_0)}$ |
| he3_chi_bp(ttc, p) | B-phase Cooper pair susceptibility (ratio of he3_chi_b): $\frac{\chi^p_B}{\chi_B} = \frac{2 (1-Y_2)}{(2 + Y_0)}$ |
| he3_c_b(ttc, p) | B-phase heat capacity, $C/R$ |