Fragmentation cross sections and binding energies of neutron-rich nuclei

An exponential dependence of the fragmentation cross section on the average binding energy is observed and reproduced with a statistical model. The observed functional dependence is robust and allows the extraction of binding energies from measured cross sections. From the systematics of Cu isotope cross sections, the binding energies of $^{76,77,78,79}\mathrm{Cu}$ have been extracted. They are $636.94\ifmmode\pm\else\textpm\fi{}0.4,647.1\ifmmode\pm\else\textpm\fi{}0.4,651.6\ifmmode\pm\else\textpm\fi{}0.4$, and $657.8\ifmmode\pm\else\textpm\fi{}0.5$ MeV, respectively. Specifically, the uncertainty of the binding energy of $^{75}\mathrm{Cu}$ is reduced from 980 keV, as listed in the 2003 mass table of Audi, Wapstra, and Thibault to 400 keV. The predicted cross sections of two near drip-line nuclei, $^{39}\mathrm{Na}$ and $^{40}\mathrm{Mg}$ from the fragmentation of $^{48}\mathrm{Ca}$ are discussed.