Liquid H e 4 H e 4 undergoes a superfluid transition at T 2.17 K T 2.17 K . The order

Liquid ${He}^4$ undergoes a superfluid transition at $T\simeq 2.17K$. The order parameter in this case is a complex number $\Psi$, which is related to the Bose condensate density ${\rho }_0$ as

$${\rho }_0\sim |\Psi {|}^2\sim |t{|}^{2\beta }(t\lesssim 0)$$

The superfluid density ${\rho }_s$, on the other hand, behaves as

$${\rho }_s\sim |t{|}^v(t\lesssim 0).$$

Show that the ratio ${}^{23}$

$$\left({\rho }_0/{\rho }_S\right)\sim |t{|}^{\eta v}(t\lesssim 0).$$