Electronic Transitions Between an Inner Shell and the Virtual Outer Shells of the Ions of the Rare Earths in Crystals

In the rare earths, the inner $4f$ shell is incomplete and its electrons are much less stable than those in the outer complete $5s$ and $5p$ electronic shells. The rare earths possess sharp absorption lines which are ascribed to initial and final quantum states arising from different orientations of the spin and orbital moments of the electrons within the $4f$ shell. ${\mathrm{Ce}}^{+++}$ has only one electron in this shell giving rise to only one term ${}_{}{}^2{}_{}{}^{}F$, a doublet, with an interval of about 1000 ${\mathrm{cm}}^{-1\mathrm{}}$. Absorption in the ultraviolet must correspond, then, to a transition from the $4f$ shell to virtual outer shells such as $5d$ or $6s$, or to the lattice. The ultraviolet absorption spectra were taken of single crystals of hydrated cerium chloride and cerium ethylsulfate at room temperatures, at that of liquid nitrogen, and of liquid hydrogen. The crystals varied in thickness from about 0.2 mm to 3 mm; about the same thickness as has been employed in studying the line spectra of other rare earths. Aside from the very faint diffuse band at about 3020A found in one of the chloride crystals and which doubtless exists in the ethylsulfate also, the crystals were completely transparent from the visible to about 2700A and there, absorption set in and occupied the rest of the ultraviolet (to 2000A). To discover whether this continuum was caused by the overlapping of several regions of selective absorption, the cerium ions were diluted in the isomorphous lanthanum crystals which are transparent and possess practically the same electric fields as the cerium crystals. The ratio of ${\mathrm{Ce}}^{+++}$ to ${\mathrm{La}}^{+++}$ in the solution from which the crystals were grown varied from about 1 to 10 to about 1 to 5000. Three new diffuse bands were discovered which remained structureless even at great dilution and at the temperature of liquid hydrogen. The bands were recognized as transitions from a rather sharp inner quantum state ${}_{}{}^2{}_{}{}^{}F$ (the electron in the $4f$ shell) to a diffuse outer quantum state ${}_{}{}^2{}_{}{}^{}D$ (the electron in the virtual $5d$ shell). The electron of the activated ${\mathrm{Ce}}^{+++}$ is subject to enormous inhomogeneous electric fields because it is very close to the water molecules (and the negative ions) in the lattice. The ${}_{}{}^2{}_{}{}^{}D$ term is decomposed by these fields into sublevels of wide separation which are extremely sensitive to all the variations in electric fields. The substitution of one negative ion for another or a change in the fields accompanying thermal contraction displaces the bands in some instances by a hundred times as much as the lines of ${\mathrm{Gd}}^{+++}$ are displaced under similar conditions. Whence, we return to the conclusion that the lines of the rare earths in general are associated with inner quantum states. It was predicated that transitions from the $4f$ electron to the outer shells would occur in other rare earths ${\mathrm{Pr}}^{+++}$, ${\mathrm{Nd}}^{+++}$ etc., but the bands would begin further in the ultraviolet than they do in ${\mathrm{Ce}}^{+++}$. A band extending from 2280A to 2100A was found in undiluted neodymium chloride which also remained without structure at the temperature of liquid hydrogen. ${\mathrm{Pr}}^{+++}$ exhibited no absorption band within the range of the spectrograph although the existence of one beginning at about 2100A would not have been determined. It is expected that the first band of ${\mathrm{Pr}}^{+++}$ begins somewhere in this region. The breadth of the bands has been discussed.