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Backward secondary-electron-emission yield ($\delta$) from plates of 0.1 mm-thick Cu and 1 mm Cr and Al have been measured by irradiation of a fully stripped Ne$^{10+}$ beam at 6 MeV/$n$ stopped within each plate. A difference between $\delta$s from Cr and Cu larger than the ambiguity of this measurement ($\pm$3%) has been observed, with the discrepancy of the predicted small difference by kinetic emission based on stopping power and work function of each metal. The measured $\delta$ from Cr is larger than that from Cu, and also than previous measurements of other transition metals of the 3$d$ series, not only for the process of potential emission but also for kinetic. The conduction-electron density of states around the Fermi level calculated for the metals shows that the number of electrons just below the Fermi level and excited over it to an empty level by many kinds of reaction with the beam irradiation has to be considered. The number involved in this emission from Cr thus seems to be much larger than from Cu, which explains the relation of magnitudes for $\delta$. The measured $\delta$ from Al is larger than previous results, but is still consistent due to the existence of Al$_2$O$_3$ on the Al.

Secondary electron emission measurement from Cr and Cu bombarded by an Ne10+ beam at 6 MeV/n