Image Potential Eigenstates and Resonances on the (110) Surfaces of Noble Metals: Energies and Lifetimes

摘要

The energies and lifetimes of the image potential resonances at the point on the Cu(110), Ag(110), and Au(110) surfaces are studied, and the energies of the image potential states on the Pd(110) surface are analyzed. It is shown that every quantum number n corresponds to a pair of image potential states (resonances) n~+ and n~- at the Y-bar point. The average energy of a pair of eigenstates (resonances) at n ≥ 2 is well described by the formula E-bar_n= (E_n+ + E_(n-)) = E_0 - (0.85 eV)/(n + δ)~2, where δ is the quantum defect, E_0 = (1/2m_e)(?π/a)~2, and a is the lattice parameter. The splitting energy of a pair of eigenstates (resonances) obeys the law ΔE_n = E_(n+) - E_(n-) ∝ n~(-3). The lifetimes τn± of image potential resonances are proportional to n3.