Production of excitons in grazing collisions of protons with LiF surfaces: An onion model

Abstract

In this work we evaluate the production of excitons of a lithium fluoride crystal induced by proton impact in the intermediate and high energy regime (from 100 keV to 1 MeV). A simple model is proposed to account for the influence of the Coulomb grid of the target by dressing crystal ions to transform them in what we call onions. The excited states of these onions can be interpreted as excitons. Within this model, total cross section and stopping power are calculated by using the first Born and the continuum distorted-wave (CDW) eikonal initial-state (EIS) approximations. We found that between 7 and 30 excitons per incident proton are produced in grazing collisions with LiF surfaces, becoming a relevant mechanism of inelastic transitions.

Reexamination of the interaction of atoms with a LiF(001) surface

“…(6) and (11) of Ref. [19] V + G was approximated by a radial onion potential produced by a series of charged shells. But these discrete charged layers introduce structures in the potential, which are difficult to handle.…”

“…But these discrete charged layers introduce structures in the potential, which are difficult to handle. Therefore, in this work we fit the previous grid potential [19] by means of a smooth potential, here named Madelung potential, defined as…”

“…represents the proper Madelung potential at the origin [25] and the parameter λ is chosen to verify that the spacial integral of V + M (r) in the range (0, +∞) coincides with the one of the grid potential of Ref. [19], finding λ 0.3 a/2 , with a = 7.60 a.u. being the lattice constant.…”

“…In all the cases, the kinetic, exchange and correlation terms of the binary potentials are evaluated from well established non-local functionals, which depend on first-and second-order derivatives of the electron density. The electron density corresponding to each ionic center of the LiF crystal is obtained from an onion model that takes into account the influence of the whole crystal lattice, i.e., the Madelung potential [19]. Long-range contributions associated with polarization and van der Waals (vdW) forces, produced by the rearrangement of the atom and surface densities as a result of the mutual interaction, are determined within a similar pairwise additive scheme.…”

Neonization method for stopping, mean excitation energy, straggling, and for total and differential ionization cross sections of CH4, NH3, H2O and FH by impact of heavy projectiles

“…Numerical integrations were carried out in these grids with the cubic spline technique. With the stopping power in mind, we have extended the CDW-EIS for excitation as well, which involves the numerical solution of the Schrödinger equation for the initial and final excited state in the same potential V nl (see appendix of [70] for details of the algebra involved). Transitions to 3s, 3p, 3d, 4s, 4p and 4d, including all the magnetic sub-states, were calculated.…”