and clusters of the form M:He$_N$ (where $N = 1, 2, 3, ...$ is the number of He atoms) have been extensively investigated. While, in a break through work, Grebenov [*et.al.*]{} [@grebe] found that OCS molecule embedded in $^4$He droplets, isolated in the normal phase of liquid $^3$He, rotates almost like a free rotor if the droplet has about 60 or more $^4$He atoms, systematic experimental study of M:He$_N$ clusters have demonstrated non-trivial dependence of their rotational constant $B$ (or moment of inertia, $I$) and vibrational frequency shift $\Delta\nu$ (of select modes of vibrations) with $N$ which concludes that superfluidity of $^4$He atoms has observable impact on $B$ of such small clusters as well [@mcke2; @mcke3; @mcke4; @surin; @topic]. A number of theoretical models, such as, (i) super-molecule model [@hartm], (ii) two fluid model [@grebe; @kwon], (iii) quantum hydrodynamic model [@calth], [*etc.*]{}, have been used to explain the initial observations. Simulation techniques have also been used, recently, to explain the phenomenon but with limited success at quantitative scale [@moron; @paesa; @paoli; @paes2; @blino; @zilli; @miur2; @miura]. It is not surprising because all these models associate the phenomenon with the superfluidity of $^4$He atoms which by itself is not clearly understood 