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We discuss how the new measurement of the $^{12}C+^{12}C$ fusion crosssection carried out with the Trojan Horse Method (Tumino, A., Spitaleri, C., LaCognata, M., et al., 2018, Nature 57, 687) affects the compactness of a star,i.e. basically the binding energy of the inner mantle, at the onset of the corecollapse. In particular, we find that this new cross section significantlychanges the dependence of the compactness on the initial mass with respect toprevious findings obtained in Chieffi & Limongi 2020 (ApJ 890, 43) by adoptingthe classical cross section provided by Caughlan, G.R., and Fowler, W.D. 1988(At. Data Nucl. Data Tables 40, 283). A non monotonic but well defined behavioris confirmed also in this case and no scatter of the compactness around themain trend is found. Such an occurrence could impact the possible explodabilityof the stars.

The impact of the new measurement of the $\rm ^{12}C+^{12}C$ fusion cross section on the final compactness of the massive stars