  A low-energy shape-independent expansion is suggested for the function
$[tan(2\epsilon_{BB})/(2k^2)]$, where $\epsilon_{BB}$ is the Blatt-Biedenharn
mixing parameter for the $^3S_1 -$ $^3D_1$ channel. This expansion allows an
evaluation of the mixing parameter $\epsilon_{BB}$ from a knowledge of the
deuteron asymptotic $D$ to $S$ ratio, pion mass and other low-energy
observables, such as the scattering lengths, deuteron binding etc., of the
nucleon-nucleon system. We demonstrate that the correct long range behavior of
the tensor potential is essential for a realistic reproduction of
$\epsilon_{BB}$.
