  We have attempted to develop here tentatively a model for $J/\Psi$ production
in p+p, d+Au, Cu + Cu and Au + Au collisions at RHIC energies on the basic
ansatz that the results of nucleus-nucleus collisions could be arrived at from
the nucleon-nucleon (p + p)-interactions with induction of some additional
specific features of high energy nuclear collisions. Based on the proposed new
and somewhat unfamiliar model, we have tried (i) to capture the properties of
invariant $p_T$ -spectra for $J/\Psi$ meson production; (ii) to study the
nature of centrality dependence of the $p_T$ -spectra; (iii) to understand the
rapidity distributions; (iv) to obtain the characteristics of the average
transverse momentum $< p_T >$ and the values of $< p_T^2 >$ as well and (v) to
trace the nature of nuclear modification factor. The alternative approach
adopted here describes the data-sets on the above-mentioned various observables
in a fairly satisfactory manner. And, finally, the nature of
$J/\Psi$-production at Large Hadron Collider(LHC)-energies deduced on the basis
of our chosen model has been presented in a predictive way against the
RHIC-yields, both calculated for the most central collisions and on the same
model.
