Landau critical velocity in Helium-3


by andbe
Tags: critical, helium3, landau, velocity
andbe
andbe is offline
#1
Feb22-14, 06:48 AM
P: 1
Hello,

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
Phys.Org News Partner Physics news on Phys.org
Vacuum ultraviolet lamp of the future created in Japan
Understanding the energy and charge transfer of ions passing through membranes
High-temperature plasmonics eyed for solar, computer innovation

Register to reply

Related Discussions
Landau Lifshitz's statement on Coordinates, velocity & acceleration Classical Physics 2
critical velocity, pantograph & mechanics forums Mechanical Engineering 4
Helium Gas: Pressure, root-mean-square velocity, and more Advanced Physics Homework 6
Critical Velocity Problem Introductory Physics Homework 9
Critical Velocity??? Aerospace Engineering 3