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Fermi-liquid parameters

Argument of all these function is pressure in the range 0 -- 34.4 bar.

See also the source file: he3_fermi.f.

Examples

Library functions

Molar volume and heat capacity in normal $^3$He:

he3_vm(p) Molar volume $v_m$, [cm$^3$/mol], Graywall-86 (from Wheatley-75)
he3_gammaf(p) R-gas constant $\gamma_f = C_V/RT$, [1/K], Greywall-86

Derived values, $F_1^s$ parameter:

he3_c_n(t, p) Heat capacity $C/R = \gamma_f T$, $T$ [K], $P$[bar]
he3_rho(p) Density $\rho = \mu_3/v_m$, [g/cm$^3$]
he3_2n0(p) $2N(0) = \frac{\gamma_f}{v_m} \ \frac{3 N_A}{k_B \pi^2}$, [1/(erg cm$^3$)]
he3_pf(p) Fermi momentum $p_F = h \left(\frac{3}{8\pi} \ \frac{N_A}{v_m}\right)^{1/3}$, [g cm/s]
he3_meff(p) Effective mass $m^\star = \frac{h^3}{8\pi} \ \frac{2N(0)}{p_F}$, [g]
he3_mm(p) Effective mass ratio $m^\star/m_3$
he3_vf(p) Fermi velocity $v_F = p_F/m^\star$, [cm/s]
he3_f1s(p) $F_1^s = 3(m^\star/m_3 - 1)$
he3_a(p) Average atomic spacing, $a=(v_m/N_A)^{1/3}$, Å
he3_gdk(p) Average dipolar coupling enegy, $g_d/k_B = \frac{2\pi\gamma^2\hbar^2}{3 v_m k_B}$, [K]
he3_tfeff(p) Effective Fermi temperature, $T_{F_{eff}} = \frac{\pi^2}{2\gamma_f}$, [K]

Sound velocity in normal $^3$He and $F_0^s$ parameter:

he3_c1(p) First sound velocity, $c_1$, [cm/s], measured, Wheatley-75
he3_f0s(p) $F_0^s = 3\ m^\star m_3\ c_1^2 / p_F^2 - 1$

Magnetic susceptibility in normal $^3$He and $F_0^a$ parameter:

he3_f0a(p) $F_0^a$ (same as $Z_0/4$), from magnetic susceptibility measurements, Hensley-1993
he3_chi_n(p) $\chi_{N} = \frac{ 2N(0)(\gamma\hbar)^2}{4(1 + F_0^a)}$.

Other fermi-liquid parameters:

he3_f1a(p) $F_1^a$, calculated from spin-wave velocities in $^3$He-B, Zavjalov-2015
he3_f2a(p) $F_2^a$, currently is 0
he3_f2s(p) $F_2^s$, currently is 0

TODO: Greywall's F1a?