Soft-x-ray appearance potential spectroscopy (SXAPS) has been developed for studying the elec- tronic configuration and composition of solid sur- faces. Briefly, one measures the derivative of the total x-ray fluorescence yield induced by electron bombardment of the surface of the sample. The theory most often cited to describe SXAPS line shapes was originally suggested by Dev and Brink- man, ' and further developed by Houston a, nd Park' to relate the mea. sured SXAPS signals to the self- convolution of the one-electron density of states above the Fermi level E~. This theory worked quite well for the 3d transition metals' and some of the simple As the technique became more popular, and the types of materials studied increased, discrepancies between theory and ex- periment appeared for rare earths, ' light ele- ments, and 4d transition metals. A recent review gives a thorough development of the one- electron theory for SXAPS and an extensive sum- mary of its successes and failures. The funda- mental reason for the breakdown of this theory is the inadequacy of the assumption that the excited core electron and the scattered projectile electron occupy spatially extended states in the conduction band. For the rare earths, the excited core elec- tron may occupy a 4f orbital which is quite local- ized about the excited ion. For such materials, Wendin has suggested a model for SXAPS incor- porating two densities of states, one for the scat- tered projectile electron and one for the excited ion with an electron-hole pair. Qne or both of these may contain highly localized states. We initially chose SXAPS as a means of studying evaporated I a films with the hope of locating the position of the 4f states above E~ using the one- electron theory cited above. This question had not been answered using other spectroscopic methods and is of interest particularly in superconductiv- ity. Measurements of the bremsstrahlung isochromat spectrum of La and Ce (Refs. 21, 22) have provided the best available estimate of the position of the 4f states relative to the Fermi level. These results did not completely clarify all the complexities of the SXAPS data. In Sec. II we describe the spectrometer used in this work and show typical I.a and Ce spectra ob- tained with this instrument. We found, as have other workers that our results were closely related to soft-x-ray absorption (SXA) data. For both La and Ce we find that portions of the individ- ual 3d and 4d core excitation line shapes are sim- ilar to du/dE, where n is the absorption coeffi- cient, while other models, such as the two-density- of-states model, are needed to explain other portions of the spectra. Sec. III presents our data and an interpretation based on the results from SXA and bremsstrahlung isochromat experiments. We point out some similarities between the SXA and SXAPS techniques which we feel are respon- sible for the rather simple relationship between the measured results of the two techniques. We also discuss the effects of contamination on the spectra of these reactive metals.