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B-phase dipole energy and Legget frequency

Values are given according to Thuneberg's paper JLTP 122, p657 (2001). Temperature independent $g_d$ parameter is restored from experimental data for $\Omega_B$, measured in transverse and longitudinal NMR.

See also the source file: he3_dipole.f. Dipolar energy: $$ F_D = \lambda_D \int (R_{ii}R_{jj}+R_{ij}R_{ji})\ d^3r \quad =\quad 4 \lambda_D \int \cos\theta(1+2\cos\theta)\ d^3r $$ $$ \lambda_D = \Delta^2 g_d, \qquad \Omega_B = \gamma \sqrt{15 \lambda_D/\chi_B} $$ Note: In old papers (Leggett, ...) $g_D/5$ is used instead of $\lambda_G$.

Examples

Library functions

he3_gd(p) $g_d$, [1/(erg cm$^3$)]
he3_ld(p) $\lambda_D = \Delta^2 g_d$, [erg/cm$^3$]
he3_nu_b(ttc, p) B-phase Leggett frequency $\nu_B = \frac{\gamma}{2\pi} \sqrt{15 \Delta^2 g_d/\chi_B}$ [Hz]
he3_nu_b1(ttc, p) Less accurate formula without using $g_d$
$\nu_B =\frac{1}{2\pi}\sqrt{\frac{3\pi}{2\chi}} \ \frac{\gamma^2\hbar}{2}\ N(0)\ \Delta \log\frac{e_f}{\Delta}$ [Hz]