Resonant Photoemission in Barium and Cerium

Abstract

Recent experiments using synchrotron radiation have revealed giant enhancements in the valence-level photoemission from rare-earth metals and compounds which are associated with the large broad maximum observed in photoabsorption above the Ad-ionization threshold. 1 * 2 For example, the resonant 4/ emission is now being used as a "fingerprint'' technique to study valence changes in these interesting materials. 3 ' 4 In this work we report the first calculations which exhibit this resonant 4/ emission in cerium and illustrate how this effect is common to all the valence levels. In addition, we show that a close connection exists between this and similar behavior observed in the well-studied case of barium photoemission. 5 " 7 An important aspect of our work is that all the above-mentioned phenomena may be very simply understood within the "local field" framework of our theoretical methods.Our calculations are based upon a generalization of the Hohenberg-Kohn-Sham density-functional formalism 8 recently introduced in a study of rare gas photoabsorption. 9 The method is essentially a time-dependent local density approximation (TDLDA) in which the external radiation field is replaced by an effective local field, c/? SCF (r, co), which self-consistently takes account of the response of the electronic charge density to the external perturbation. Since the total photoabsorption in the vapor and that in the condensed phase are practically identical for both barium and cerium in the photon energy range of interest, 10 * n we have performed all of our calcula-7 N.tions for the case of the free atom.In the manner of a typical self-consistent field theory, the complex frequency-dependent local field is related to the Fourier components of the time-dependent density disturbance 6n(r,t), by the equations Mr, co) = Jd V Xoft ?'; coV SCF (r', co), cp SC¥ (r, co) = <p ext (f, co) + fd 3 r'K(f, r')6n(?', co).We exactly calculate the retarded density-density response function in the independent-particle approximation, x 0 (r,r';to); and the time-independent kernel function is taken to be ^(? > f') = I|^F 7 I + 6(r-?')£7 xc {n}U n(r) .Vxdnffi} i s * ne exchange-correlation potential commonly employed in a local density approximation (LDA) to density-functional formalism. 12 We wish to emphasize that the structure of our calculation is identical to the random-phase approximation with exchange (RPAE) 5 ' 6 ; however, we replace the Hartree-Fock orbitals, eigenvalues, and Coulomb matrix elements by LDA orbitals, eigenvalues, and linearized potentials, respectively. The crucial replacement of the nonlocal Hartree-Fock exchange operator by the local exchange-correlation potential is responsible for the spatially local character of c£ SCF (r, co) = <^e xt (r, co) + <p lnd (r, co). In the long-wavelength limit, photoemission cross sections are computed by simply replacing the usual dipole opera-In this Letter, a theoretical discussion of resonant photoemission in barium and cerium is presented. Calculations are performed using a time-depe...

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