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We theoretically investigate optical properties of II-VI core-shell distribution mixtures made of two type-I sized-nanoshells as a plausible negative dielectric function material. The nonlocal optical response of the semiconductor QD is described by using a resonant excitonic dielectric function, while the shell response is modeled with Demangeot formula. Achieving the zero loss at an optical frequency omega, i.e., epsilon(eff) = epsilon'(eff) + i epsilon ''(eff) with epsilon'(eff) < 0 and epsilon ''(eff) = 0, is of fundamental importance in nanophotonics. Resonant states in semiconductors provide a source for negative dielectric function provided that the dipole strength and the oscillator density are adequate to offset the background. Furthermore, the semiconductor offers the prospect of pumping, either optically or electrically, to achieve a gain mechanism that can offset the loss. We analyse optimal conditions that must be satisfied to achieve semiconductor-based negative index materials. By comparing with II-VI semiconductor quantum dots (QDs) previously reported in the literature, the inclusion of phonon and shell contributions in the epsilon(eff) along with the finite barrier Effective Mass Approximation (EMA) approach, we found similar qualitative behaviours for the epsilon(eff). The lossless optical condition along with epsilon'(eff) < 0 is discussed in terms of sizes, volume fractions and embedding medium of the mixtures' distributions. Furthermore, we estimated optical power to maintain nanocrystals density in excited states and this value is less than that previously obtained in II-VI semiconductor QDs. (C) 2014 Elsevier B.V. All rights reserved.