Effect of elasticity on torsional oscillator experiments probing the possible supersolidity of helium

We consider the effect of elasticity on torsional oscillator experiments to investigate the possible supersolidity of helium. We show that in most, and possibly all torsional oscillators there is a significant and hitherto unconsidered contribution to the torsional period from the helium elasticity. This effect needs to be carefully considered before it can be concluded that a supersolid component is indeed present.

Figure 1

Schematic diagram showing the cross section of a typical torsional oscillator.

Figure 2

The tangential displacement $u_{\phi }$ and the angular rotation $\phi$ of the top surface of the disk as a function of the distance $r$ from the axis. The lower end of the torsion rod has been rotated by a unit angle. These results were obtained using the finite-difference relaxation method.

Figure 3

Contour plot of the tangential displacement $u_{\phi }$ in solid helium resulting from the displacement of the top surface of the disk as shown in Fig. 2. In the right-hand part of the figure the contours are equally spaced between 0.000 05 and 0.0006 cm, and in the left-hand part of the figure between −0.0006 and 0.000 05 cm. The magnitude of the displacements is based on a rotation of the lower end of the torsion rod of 1 radian.