Quasi-bound resonances in electron scattering by small metal clusters

Abstract

Abstract.A quantal calculation to evaluate theoretically the elastic cross section of electrons scattered by metal clusters is presented. The method is applied to the elastic dispersion of low energy electrons (up to 5 eV) from the spherical sodium clusters Na 8 and Na2o. Strong resonances in the total cross sections are found for some energies which are closely related to the existence of quasibound states, i.e. states completely bound in the classical limit. PACS: 36.40.+d; It is known that the valence electrons in small metal clusters move independently in a central average field, like nucleons in nuclei or electrons in elemental atoms [1 ]. Different approximations, often based on the jellium model for the positive ionic background, were developed and have been successful in explaining a huge variety of cluster properties like relative abundance, ionization potentials, magic numbers, as a function of the number of free electrons in the system. These approximations give rise to a shell model description for the valence electrons of a cluster. Also optical properties and surface deformations can be qualitatively and, to a reasonable extend quantitatively, explained using the shell model for clusters.It is difficult, however, to gain direct or indirect experimental information on the fine details of the single particle potential. In nuclear physics, this kind of information about the nucleon mean field can be obtained through the analysis of some nuclear reactions, in particular studying the elastic and inelastic dispersion of neutrons and protons by nuclei. For low bombarding energies the resonances observed in the cross sections of these processes provide useful information about the nuclear structure and the mean field potential.* Fellow of the Consejo Nacional de Investigaciones Cientificas y T6cnicas, ArgentinaIn the present paper, considering the analogies between the shell structure of nucleons in nuclei and the valence electrons in clusters, we investigate the elastic scattering of electrons by small metallic particles. As was recently discussed [2], the total cross section should exhibit some structure when studied as a function of the incident electron energy. In the present work, we obtain the differential and total elastic cross sections with the same effective local interaction between the incoming electron and the cluster target used in [2]. However, we obtain exact quantum mechanical results by solving the Schr6dinger equation numerically, avoiding thereby the semiclassical approximations used in [2].The use of a fully quantal treatment in order to study the scattering problem seems to be necessary for two reasons:i) for the range of energies we are dealing wdth, around 0.01 to 5 eV, the wavelength for the relative motion ranges approximately between 200 and 10 Bohrs, a magnitude which is larger or comparable than the cluster size;ii) the centrifugal potential together with the electroncluster interaction gives rise to a potential barrier which in turn may generate resonances when the incident ele...

Response of metal clusters to elastic electron impact

“…Recently we carried out a fully quantum mechanical study [9] of the neutral clusters Nas and Na2o by solving the scattering Schrodinger equation. Pure quantum mechanical effects, such as the appearance of resonances in the elastic cross sections (when studied as a function of the incident electron energy) have been obtained.…”

“…In this paper we apply the quantum mechanical treatment of Ref. [9] to the scattering of electrons by larger sodium clusters, not only neutral but also positively ionized. In this way, we treat systems which are easier to produce experimentally.…”

Photoionization of a strongly polarizable target

“…The model potential, which was used to describe the interaction between the photoelectron and the neutral residue, accounted for the following three terms: (a) the short-range potential due to the Coulomb interaction with the core's electrons and the ionic jellium core, (b) the exchange-correlation term, which was treated within the Gunnarsson-Lundqvist approximation [21], (c) the polarization potential was considered in the form U pol (r) = −α(0)/2(r 2 +R 2 ) 2 for r > R and U pol (r) = 0 if otherwise. Inclusion of the polarization term is important for an adequate description the low-energy electron scattering from metallic clusters (e.g., [22]). A more rigorous treatment accounts for the many-body correlations, which may be considered, for example, within the Dyson equation scheme [23].…”

“…To justify the use of ( 19) we refer to the analysis of the exchange effects in elastic electroncluster scattering carried out in [8,9]. From these papers it follows that for electron energies about 1 eV and higher the results obtained within the LDA (local density approximation) [10,11] do not differ much from the calculations within the many-body perturbation theory.…”

Measuring the Raman spectrum of water with a smartphone, laser diodes and diffraction grating

“…Also fluorecence photons irradiated on the substance cause the transition of electrons when they have a sufficient amount of energy (right blue and violet photons in figure 1) in molecular orbitals from the quantum ground state to an excited state with higher energy by the absorption process. Subsequently, the energy can be emitted through photons, with a lesser energy than the absorbed ones (green photons from the final excited to the ground state), and converted in thermal energy by lattice quantum vibrations (phonons) with the mechanism labelled as internal conversion and vibrational relaxation, a mechanism which involves excited states [18].…”