the rotor part of the cluster in CPA-WP type arrangement of $^4$He atoms may in certain cases experience a kind of low energy potential barrier with an axial symmetry of the order $n$ (as shown in Fig.5). A theoretical analysis for such a case [@jain3] reveals that the effective $I$ of the rotor has a lower value that depends on the height and symmetry of $V_n$ ([*cf.*]{}, Fig. 5). This renders an additional reason for a small decrease in $I$.

As concluded by Jain’s NCMT of a system of interacting bosons such as liquid $^4$He [@jain1], atoms in He-II not only move coherently in order of their locations but also have identically equal angular momentum when they move on different concentric paths around the axis of a quantum vortex; in fact this theory for the first time answers a question raised by Wilks [@wilks] in relation to Feynman’s account for the origin of quantized circulation [@feyn1]. Wilks has rightly argued that Feynman’s basis for quantum vortices in He-II is equally valid for He-I but the latter does not show any quantum vortex. Using a basic aspect of quantum vortices observed in He-II, we discover a model which has enough potential 