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The J/Psi cross section ratios of p-A/p-p under different collision energy is calculated with cold nuclear matter effects redefined in this paper. The advantage of these new definitions is that all cold nuclear matter effects have clear physical origins.The radios are compared with the corresponding experiment data and that calculated with classic nuclear effects. The ratios calculated with new definitions can reproduce almost all existing J/Psi measurements in p-A collisions more accuratly than that calculated with classic nuclear effects. Hence, this paper presents a new approach to explain cold nuclear effects in the hardproduction of quarkonium.

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