Shear Viscosity of Superfluid 3He using Collision Integral Model Kinetic Equation

Abstract

Helium is an inert gas and it has two isotopes 4He and 3He. 4He is abundant in nature where as 3He is rarely found. 4He is a Bose particle and it follows Bose Einstein Statistics. Whereas 3He is a Fermi particles and it follows Fermi Dirac Statistics and also Pauli Exclusion Principal. Both these particles are well separated out and at low temperature they are in liquid form. Liquid 4He is a normal Bose liquid whereas liquid 3He is a Fermi liquid. These two liquids are also called Quantum liquids. At T = 2.17 K liquid 4He goes into famous phase transition called λ-transition. Above λ Temperature i.e. Tλ = 2.17 K 4He is a normal liquid also called He-I and below λ Temperature it is a superfluid also called He-II. In liquid 3He, phase transition occurs at very low temperature, about 2.7 mK. Between 3 mK to 100 mK liquid 3He is a normal liquid and below 3mK they are in a superfluid phase and these phases are also mesophase called 3He-A phase and 3He-B phase. These phases are observed through NMR experiments. These phases are also spin polarised phase. It is generally belief that superfluidity is a flow of liquid without viscosity. In case of superfluid He-II the value of viscosity is almost negligible. Where in two phase of superfluid 3He, He – A phase is almost negligible viscosity whereas He-B phase has finite value of viscosity which is in Tensor form having first order (shear) and second order viscosity.