Final-state symmetry of Na 1s core-shell excitons in NaCl and NaF K. P. Nagle, 1 G. T. Seidler, 1, * E. L. Shirley, 2 T. T. Fister, 1,3 J. A. Bradley, 1 and F. C. Brown 1 1 Department of Physics, University of Washington, Seattle, Washington 98105, USA 2 Optical Technology Division, NIST, Gaithersburg, Maryland 20899-8441, USA 3 Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA Received 27 February 2009; revised manuscript received 26 May 2009; published 8 July 2009 We report measurements of the Na 1s contribution to the nonresonant inelastic x-ray scattering NRIXS from NaCl and NaF. Prior x-ray absorption studies have observed two pre-edge excitons in both materials. The momentum-transfer dependence q dependence of the measured NRIXS cross section and of real-space full multiple scattering and Bethe-Salpeter calculations determine that the higher-energy core excitons are s type for each material. The lower-energy core excitons contribute at most weakly to the NRIXS signal and we propose that these may be surface core excitons, as have been observed in several other alkali halides. The analysis of the orbital angular momentum of these features leads to a discussion of the limited sensitivity of NRIXS measurements to d-type final states when investigating 1s initial states. In this case the s- and p-type final density of states can be characterized by measurements at a small number of momentum transfers. This is in contrast to the case of more complex initial states for which measurements at a large number of momentum transfers are needed to separate the rich admixture of accessible and contributing final-state symmetries. DOI: 10.1103/PhysRevB.80.045105 PACS numbers: 71.35.-y, 78.70.Ck, 71.20.Ps, 61.05.cj I. INTRODUCTION The interaction between the photoelectron and the con- comitant hole which is present in electronic excited-state spectroscopies plays an important role in the optical and electronic properties of both condensed and molecular phases. 1–4 This interaction is responsible for so-called final- state effects, wherein the photoelectron wave function in the excited state does not correspond to an unoccupied state for the ground state of the system; the interaction with the core hole results in a fundamental modification of the density of states DOS. The prototypical case in point is the formation of core-hole excitons, as is frequently observed in x-ray ab- sorption spectroscopy XAS and related experimental methods. 2–5 Recent progress in both real-space and reciprocal-space treatments of XAS incorporates the interac- tion between the photoelectron and core hole to account for final-state effects, resulting in significant improvements in calculations of XAS in the near-edge region. 1,6–11 Measurements of nonresonant x-ray Raman scattering XRS, the core-shell contribution to nonresonant inelastic x-ray scattering NRIXS, are blossoming as an alternative to and extension of XAS. In the limit of low momentum trans- fer q, XRS provides a bulk-sensitive measurement whose transition matrix element is closely related to that for the absorption coefficient in XAS. 9,12–16 However, as q in- creases, XRS becomes sensitive to dipole-forbidden final states, thus allowing a more complete investigation of the spectrum of possible excited states. 2,17 XRS measurements have been used to determine the orbital angular momentum of excitons and other resonances in several materials. 2,3,18–21 Here, we report new XRS measurements of the q depen- dence of excitonic features associated with the Na 1s initial states of NaCl and NaF. The optical and electronic properties of alkali halides have seen several decades of work and they serve as important test cases for understanding final-state ef- fects in insulators. Most relevant for the present paper, there have been recent XAS and resonant Auger studies of the Na 1s initial state in both compounds which found demon- strably excitonic pre-edge features. 22,23 While it has been dif- ficult to explain the origin of two dipole-forbidden excitons in NaF, 23 there is good reason to believe that all of the ob- served pre-edge features are dipole forbidden for XAS from the Na 1s initial state. 22,23 Their weak presence in the XAS measurements where they should nominally be absent be- cause of the dipole selection rule is made possible by the symmetry-breaking effects of vibrational disorder. 24 Our q-dependent XRS measurements directly demonstrate that the underlying DOS in the pre-edge region is indeed predominantly dipole forbidden and new real-space full mul- tiple scattering RSFMS and Bethe-Salpeter equation BSE calculations identify the DOS as being overwhelmingly s type. However, the XRS spectra find that this DOS is asso- ciated with the higher-energy pre-edge feature in NaCl and most clearly in NaF with little or no signal from the lower- energy features. We discuss possible explanations for this behavior, including the small probability of 1s → d transi- tions even at high-momentum transfer and the weakness of spin-flip scattering in XRS, but are unable to find a model for two bulk excitons for the Na 1s initial state which is consis- tent with both theory and experiment. Given the experimen- tal details of the prior XAS measurements, we propose that the lower-energy excitons in both materials may be surface core excitons, as have been observed in several other alkali halides. Further measurements will be necessary to test this hypothesis. II. THEORY A. Nonresonant inelastic x-ray scattering The double-differential cross section for NRIXS is PHYSICAL REVIEW B 80, 045105 2009 1098-0121/2009/804/0451059 ©2009 The American Physical Society 045105-1