# Landau critical velocity in Helium-3

1. ### andbe

1
Hello,

If we first consider Helium-4 we can calculate the critical velocity via
$\frac{d\epsilon(p)}{dp}=\frac{\epsilon(p)}{p}$ where $\epsilon(p)=\frac{(p-p_0)^2}{2\mu}+\Delta$ is the dispersion relation for roton excitations in Helium-4.
Putting in the constants $\mu=0.164 m_4$ is the effective mass, $\Delta/k_B=8.64$K, $p_0/\hbar=19.1$nm you get roughly $v_c=59.3$m/s.

Now I want to do the same calculation for Helium-3 but can't find the values of the constants for Helium-3, if rotons even exists for Helium-3?

What is the dispersion relation for Helium-3? Taking inspiration from superconductivity and the BCS-theory I'm thinking that there will be an energy gap here as well, i.e. no phonon region as for Helium-4, but it's hard to find information about this. Can anyone point me in the correct direction? I'm mostly interested in drawing some conclusions about the critical velocity of Helium-3 from the calculation above, if it is even possible...

Regards,
Andreas