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If we first consider Helium-4 we can calculate the critical velocity via

[itex]\frac{d\epsilon(p)}{dp}=\frac{\epsilon(p)}{p}[/itex] where [itex]\epsilon(p)=\frac{(p-p_0)^2}{2\mu}+\Delta[/itex] is the dispersion relation for roton excitations in Helium-4.

Putting in the constants [itex]\mu=0.164 m_4[/itex] is the effective mass, [itex]\Delta/k_B=8.64[/itex]K, [itex]p_0/\hbar=19.1[/itex]nm you get roughly [itex]v_c=59.3[/itex]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

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# Landau critical velocity in Helium-3

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