Module inner_shell 

Inner-shell ionization channels from shell-resolved loss functions.

Source

P. de Vera, S. Taioli, P. E. Trevisanutto, M. Dapor, I. Abril, S. Simonucci and R. Garcia-Molina, “Energy Deposition around Swift Carbon-Ion Tracks in Liquid Water”, Int. J. Mol. Sci. 23, 6121 (2022), doi:10.3390/ijms23116121 (open access, PMC9181504; “dV2022”, as in super::penn):

• eq. (1) splits the ELF into an outer-shell and an inner-shell part, and eq. (2) writes the inner part as a sum over elements j (weighted by the atoms per molecule ν_j) and subshells nℓ of atomic generalised oscillator strengths, each multiplied by the step Θ(E - B_nℓ^j): an inner shell contributes only to losses above its binding energy;
• eqs. (32) and (35) write the secondary-electron spectrum and the ionization cross section as a sum of one outer-shell (valence) term and one term per inner shell j, each built from that shell’s own loss function Im[-1/ε(k, W + B_j)]_j, where W is the kinetic energy of the emitted electron. So a loss ω = W + B_j in shell j hands the secondary W = ω - B_j (ShellResolvedChannels::secondary_energy_ev).

The model here

ShellResolvedChannels takes what those equations take: a valence optical ELF and one optical ELF per inner shell. The shell ELFs are either supplied by the caller or built from atomic oscillator strengths as in dV2022 eq. (2) by super::shell_elf (the hydrogenic K-, L1-, L2- and L3-subshell formulas, with binding energies and occupancies from a SubshellBindingTable; other subshells are not built there). A single total ELF is never split: no partition rule of ours is applied. Each shell’s ELF must start at or above its binding energy (the step of eq. (2)). Each channel’s DIIMFP is the single-pole Penn DIIMFP (SinglePolePenn) of its own ELF; with the exchange correction applying, shell j uses its binding energy in the Born-Ochkur denominator T' - W = T' - ω + B_j and is limited to ω <= (T' + B_j)/2, and the valence channel has B = 0 (dV2022 eqs. (32), (34), (35); see the super::penn module docs for the terms of eq. (32) not followed: the Coulomb-field correction of the direct term, and the energy-dependent valence binding energy B(T)).

Our choices, not from dV2022: the momentum dependence of every channel’s loss function is the Penn SPA of S2017 applied to that channel’s optical ELF (dV2022 uses Mermin functions for the outer shells and hydrogenic GOS for the inner ones); and the channel models share the valence model’s Fermi energy, tolerance and exchange setting. The SPA is linear in the optical ELF, so without exchange the channel inverse mean free paths add up to that of one model built from the sum of the ELFs (when the sum is representable on one grid; tested).

The binding energies come from a SubshellBindingTable (InnerShell::from_table) or are given directly.

In the transport

super::table::build_shell_channel_tables tabulates every channel (one ShellChannelTable per shell, beside the valence table), and crate::electron::transport::Transport::with_inner_shells samples them: a channel is chosen first, with probability proportional to its inverse IMFP, and the loss is then drawn from that channel’s own table. That is a different construction from ShellResolvedChannels::sample_channel (channel conditional on a loss already drawn from the total DIIMFP), which the transport does not use. The secondary-energy convention on the transport’s band-bottom axis is in crate::electron::secondary, “Inner-shell events”.

Structs

ChannelDiimfp

DIIMFP by channel at one loss, m⁻¹ eV⁻¹.

ChannelInverseImfp

Inverse mean free path by channel, m⁻¹.

InnerShell

An inner-shell channel: one subshell of one element.

ShellResolvedChannels

A valence channel and inner-shell channels, each with its own optical ELF (module docs).

Enums

Channel

A loss channel.