The Role of Gluon Depletion in J/$\psi$ Suppression

The depletion of gluons as the parton flux traverses a nucleus in a heavy-ion collision can influence the production rate of heavy-quark states. Thus the suppression of $J/\psi$ can be due to gluon depletion in the initial state in addition to nuclear and hadronic absorption in the final state. A formalism is developed to describe the depletion effect. It is shown that, without constraints from other experimental facts beside the $J/\psi$ suppression data in $pA$ and $AB$ collisions, it is not possible to determine the relative importance of depletion vs absorption. Possible relevance to the enhanced suppression seen in the $Pb - Pb$ data is mentioned but not studied