Effective masses and surface-corrugation energies of bound-state levels in atom-surface scattering

We present simple formulas, in terms of band splittings, for surface-corrugation energies and for effective masses for bound-state levels in surface scattering of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms. Our calculations show that the lowest fundamental states for NaCl(001) and diamond (111) are associated with exceptionally large effective masses. These large effective masses may preclude the possibility of observing, at the expected positions, these states as resonances at the experimental energies, which is consistent with unexplained experimental data of Frankl et al. For a model of ${}_{}{}^4{}_{}{}^{}\mathrm{NaCl}$(001), we show, as an illustration, results of calculations of the dependence of the resonance structure in the specular beam on surface corrugation.