Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength

Abstract

The electron and photon excitation of confined and compressed atoms is discussed. It is shown that the optical oscillator strength, the inelastic X-ray and electron impact cross-sections are all density-dependent. Ab-initio electronic structure calculations are presented for the 1 s 2 → 1 s 2 p ( 1 P ) transition in helium, which predict that the amplitudes for the inelastic scattering of electrons, optical absorption and the excitation energy are all significantly increased in bulk condensed phases of pure helium compared to those of an isolated atom. The enhancements increase with atomic density but are very similar for bcc and fcc structured bulk phases of the same density. These enhancements need to be incorporated into the analysis of scanning transmission electron microscope studies of helium nano bubbles embedded in different materials. The excitation energy and cross-section enhancements with increasing density arise from the contraction of the 2 p orbital on entering a condensed phase. For the bulk phases, but not the bubbles, the close agreement between the experimental and computed values of the energy shifts can be well described by a simple relationship.

The density and pressure of helium nano-bubbles encapsulated in silicon

“…The computed helium atom wave functions were also used [25,32] to calculate the atomic form factor which enters the expression for the scattering cross sections σ 2p (n). In atomic units, the first Born cross section for the excitation of the target atom from the ground state to first excited state by an electron with an impact energy, E i , is given by [25,34]…”

“…where q min and q max are the minimum and maximum values of the momentum transfer, q, as given in [25] and ε 2p (q) is the atomic form factor. In the microscope experiments considered here E i is 200 keV for which (2.1) is certainly valid.…”

“…However, in all previous attempts [9,14,18–23] to deduce the density by this method it was assumed that the scattering cross section of an atom in the bubbles was essentially the same as that of a free helium atom. However, since we have previously shown [24,25] by ab initio electronic structure computations that this cross section is itself significantly sensitive to the density, the densities reported in the literature using this method must be questionable. In neither of the two methods just described is the density explicitly measured, rather it is deduced from other measured quantities.…”

“…For the bulk condensed phases, the energy shifts have been investigated theoretically [24,25,31,32] and compared with the IXS and VUV experiments. For each of the densities examined experimentally, the corresponding energy shifts normalΔEfalse(nfalse) have been calculated using an entirely non-empirical approach [31,32].…”

“…The energy shifts, E(n), are in eV and Σ in 10 −3 atoms Å −1 , citations are to the experimental measurements. All calculations, except the quasi-free atom cross sections, in the fcce model[25,32]. computed energy shifts, scattering cross sections and…”