Broadening of atomic levels near metal surfaces: first-order model versus coupled-angular-mode method

Many-body theory of the neutralization of strontium ions on gold surfaces

“…(11) by setting s(t) to Su(t) and So(t'), respectively, and using the material parameters given in Table I. To demonstrate that the widths we get are of the correct order of magnitude, we also plot the width of a rubidium 5 s level in front of an aluminum surface and compare it with the width obtained by Nordlander and Tully using a complex scaling technique [56], In qualitative agreement with Borisov and Wille's investigation [57] of Gadzuk's approach, our rubidium width is a factor 2-3 too small for z > lap and a factor 2 too large for z = 5ab-Between lap and 9a B, however, the widths fortuitously agree with each other. The same trend we found for the other alkaline-metal combinations investigated by Nordlander and Tully [56].…”

“…Only for shorter distances chemical interactions lead to a substantial deviation between the two. Borisov and Wille [57], on the other hand, found the level width of hydrogen ions approaching an aluminum surface to be for distances larger than five Bohr radii also not too far off the widths obtained from Gadzuk's golden rule calculation, that is, the widths are perhaps off by a factor 2. The reason most probably is Gadzuk's ingenious choice of the tunneling matrix element (see below) which takes care of the nonorthogonality of the projectile and target states [44], Since the turning point of the strontium ion is sufficiently far away from the first atomic layer, we estimate it to be around five Bohr radii, we expect Gadzuk's semiempirical approach to also provide a reasonable parametrization of the Sr: Au system investigated by He and Yarmoff [30,31].…”

“…Within the adiabatic approximation, which treats the center-of-mass motion of the projectile along the collision trajectory classically [8], it leads to a position-and hence time-dependent broadening and shifting of the projectile's energy levels. The adiabatic modification of the atomic energy levels as a function of distance can be calculated from first principles [55][56][57][58][59]. As in our previous work on secondary electron emission from metallic [60] and dielectric [61,62] surfaces, we employ, however, Gadzuk's semiempirical approach [43,44], based on classical image shifts and a golden rule calculation of the level widths, which not only provides a very appealing physical picture of the interaction process [45], but produces for distances larger than a few Bohr radii also reasonable level widths and shifts [57][58][59].…”

“…From this comparison we expect the widths of the strontium levels to be of the correct order of magnitude for intermediate distances between 5ab and 12ab-This is the range required for the description of the collision process we are interested in. For smaller and larger distances, the semiempirical approach breaks down and should be replaced by quantum-chemical methods [55][56][57][58][59], With the single-particle matrix elements at hand, the Anderson-Newns Hamiltonian [5-8, [35][36][37][38][39][40][41] describing the charge transfer between the strontium ion and the gold surface Atomic units are used, that is, energy is measured in hartrees and length in Bohr radii. Data are shown only for distances larger than 5 Bohr radii, which is the turning point of the collision trajectory.…”

“…The adiabatic modification of the atomic energy levels as a function of distance can be calculated from first principles. [55][56][57][58][59] As in our previous work on secondary electron emission from metallic 60 and dielectric 61,62 surfaces, we employ however Gadzuk's semi-empirical approach 43,44 based on classical image shifts and a golden rule calculation of the level widths-which not only provides a very appealing physical picture of the interaction process 45 but produces for distances larger than a few Bohr radii also reasonable level widths and shifts. [57][58][59] Indeed, first-principle investigations of Auger neutralization of helium ions on aluminum surfaces by Monreal and coworkers 58,59 showed that for distances larger than five Bohr radii the level shift follows the classical image shift.…”