hertz/history damping coefficients coherency

Hello.

I have some question about the mutual consistency of the damping coefficients for Hertz's contact model.
From doc for gran/hertz/history (I use liggghts-1.5.1) I got:

gamma_n / gamma_t = 1/2 * (Y/G)^(1/2)

From my own solution for Hertz and Mindlin equations I got:

c_n / c_t = (5/6)^(1/2) * 1/2 * (Y/G)^(1/2)

Comparing my solution with liggghts I see that,

gamma_n = c_n
gamma_t = (5/6)^(1/2) * c_t

Then I got the all expression exactly as they appear in the documentation. I conclude that gamma_t is a modified dissipation coefficient for a linear contact model by multiplication by (5/6)^(1/2). I guess this is done to ensure an isotropic viscosity for the contact model. But why multiplied only (5/6)^(1/2), not (5/6)^(1/2) * 1/2? (I guess intuitively that the proportionality to Y/G should remain as it is elastic properties rather than viscosity).

p.s. I have found a mistake in doc for gran/hertz/history: in the expression for G should be (2-nu)(1+nu) instead (2+nu)(1-nu). In the source code (liggghts-1.5.1/src/pair_gran_hooke_history.cpp:450) it is written correctly.