Size-dependent valence change in small Pr, Nd, and Sm clusters isolated in solid Ar

The $L_{\mathrm{III}}$ absorption thresholds of Pr, Nd, and Sm clusters isolated in solid Ar are marked by prominent white lines. The lines ascribed to divalent and trivalent rare-earth metals are well separated in energy. From the relative intensities of these lines an average valence of the rare-earth atoms in the cluster has been determined. For dimers and trimers the average valence is close to 2, the value for free atoms. For clusters consisting of more than 20 atoms the average valence approaches 3, the value for bulk metals. In between the valence changes abruptly, indicating the existence of a critical cluster size of approximately 5 atoms for Pr and Nd and of 13 atoms for Sm.