A method is described to calculate the heavy ion reaction cross section σ R when one of the two nuclei is deformed. This method is based on both the double folding model and the optical limit approximation to Glauber theory. Both finite range of the nucleon-nucleon (NN) interaction and in-medium effects of NN cross section are included. The interacting pair 12C -238U is taken to study orientation, energy, and deformation dependence of σ R. The finite range force increases the value of σ R by about 5%. In-medium NN cross section decreases σ R by about 1.9% compared to the free NN cross section.

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