Possible experiment for determination of the role of microscopic vortex rings in the λ-transition in He-II

It is suggested that microscopic vortex rings (MVR) play an important role in the \lambda-transition in helium-II and substantially determine the value of T_{\lambda}. For very thin films of He-II, with thickness d less than the size of the smallest MVR, the rings do not fit in and, therefore, do not exist in such films. Consequently, for superfluid films of He-II, a peculiarity in the form of a smoothed-out jump should be observed in the curve T_{m}(d) at the values of thickness approximately equal to the size of the smallest MVR, d= 3 - 9 A (T_{m} is the temperature of the maximum of the broad peak on the curve of the dependence of the specific heat on temperature). The absence of a similar peculiarity will be an evidence that MVR do not influence the values of T_{\lambda} and T_{m}, and do not play any key role in the \lambda-transition. The currently available experimental data are insufficient for revealing the predicted peculiarity.