Struct SinglePolePenn 

pub struct SinglePolePenn { /* private fields */ }

The single-pole Penn model built from one optical ELF. See the module docs for the equations, the units and the integration tolerance.

Implementations

impl SinglePolePenn

pub fn new(elf: OpticalElf) -> Self

The model for elf, with Fermi energy zero and the default tolerance.

pub fn with_exchange(self, exchange: ExchangeCorrection) -> Self

Switch the exchange correction on (it is off by default).

pub fn exchange(&self) -> Option<ExchangeCorrection>

The exchange correction, if enabled.

pub fn exchange_applies_at(&self, energy_ev: f64) -> bool

Whether the exchange correction applies at kinetic energy energy_ev.

pub fn with_fermi_energy_ev( self, fermi_ev: f64, ) -> Result<Self, ElectronDataError>

Set the Fermi energy (eV, finite and non-negative). Energies passed to the model are then kinetic energies above the Fermi level, and the kinematics use T' = T + E_F (S2017 eq. (2)).

pub fn with_relative_tolerance( self, rel_tol: f64, ) -> Result<Self, ElectronDataError>

Set the relative integration tolerance, in [1e-12, 1e-2].

pub fn optical_elf(&self) -> &OpticalElf

The optical ELF the model is built from.

pub fn fermi_energy_ev(&self) -> f64

The Fermi energy, eV.

pub fn relative_tolerance(&self) -> f64

The relative integration tolerance.

pub fn loss_function(&self, q_per_m: f64, loss_ev: f64) -> f64

Im[-1/ε(q, ω)] in the SPA (S2017 eq. (13)), at momentum transfer q (as a wavenumber, m⁻¹, so the momentum is ħq) and energy loss ω (eV). Zero where S2017 eq. (11) has no root (ħ²q²/2m >= ω) and where ω₀ falls outside the tabulated range. At q = 0 it is the optical ELF.

pub fn diimfp_per_m_ev( &self, energy_ev: f64, loss_ev: f64, ) -> Result<f64, ElectronDataError>

The DIIMFP p(T, ω) (S2017 eq. (2), nonrelativistic) at kinetic energy energy_ev above the Fermi level and energy loss loss_ev, in m⁻¹ eV⁻¹. Zero for ω <= 0 or ω > T, and, with the exchange correction applying at this energy, for ω > T'/2 (module docs; no binding energy, B = 0).

pub fn diimfp_with_binding_per_m_ev( &self, energy_ev: f64, loss_ev: f64, binding_ev: f64, ) -> Result<f64, ElectronDataError>

The DIIMFP at kinetic energy energy_ev above the Fermi level and energy loss loss_ev, m⁻¹ eV⁻¹, for a loss that ionises a shell of binding energy binding_ev (finite, non-negative) and so emits an electron of kinetic energy W = ω - B. B enters only through the exchange correction, where it applies: the Born-Ochkur denominator is T' - W = T' - ω + B and the loss is limited to ω <= (T' + B)/2 (dV2022 eqs. (32), (34), (35); module docs). Without exchange the result does not depend on B; with B = 0 it is Self::diimfp_per_m_ev.

pub fn imfp_and_stopping( &self, energy_ev: f64, ) -> Result<InelasticPoint, ElectronDataError>

The inverse IMFP (m⁻¹) and the stopping power (eV/m) at kinetic energy energy_ev above the Fermi level. Both are zero where no loss is allowed (below the first energy at which a pole of the tabulated range fits inside the kinematic limits).

pub fn imfp_and_stopping_with_binding( &self, energy_ev: f64, binding_ev: f64, ) -> Result<InelasticPoint, ElectronDataError>

As Self::imfp_and_stopping, for losses that ionise a shell of binding energy binding_ev (finite, non-negative): with the exchange correction applying, the Born-Ochkur denominator is T' - ω + B and the losses run up to min((T' + B)/2, T) (Self::diimfp_with_binding_per_m_ev). Without exchange it does not depend on B. The loss range is not cut at B from below: an ELF that should only act above the edge must start there (the model is zero below the first tabulated energy).

pub fn imfp_m(&self, energy_ev: f64) -> Result<f64, ElectronDataError>

The inelastic mean free path λ(E), m; infinite where no loss is allowed.

pub fn stopping_power_ev_per_m( &self, energy_ev: f64, ) -> Result<f64, ElectronDataError>

The stopping power S(E), eV/m.

pub fn tabulate( &self, energies_ev: &[f64], ) -> Result<Vec<InelasticPoint>, ElectronDataError>

IMFP and stopping power on a grid of energies (eV above the Fermi level), in order. Sequential and deterministic.

pub fn bethe_inverse_imfp_per_m( &self, energy_ev: f64, ) -> Result<f64, ElectronDataError>

The model’s own high-energy (Bethe) limit of the inverse IMFP, m⁻¹ (see the module docs): (1/(2π T')) ∫ dω_p ELF(ω_p) ln(8T'/(ω_p + k_F²/3)), over the whole table.

pub fn bethe_stopping_ev_per_m( &self, energy_ev: f64, ) -> Result<f64, ElectronDataError>

The nonrelativistic Bethe stopping power with W_max = T, the electron density from the f-sum of the same ELF and the mean excitation energy I of the same ELF (SumRuleReport, bethe::stopping_power_ev_per_m), eV/m. With a Fermi energy, the kinematic energy is T' = T + E_F and W_max = T.

Trait Implementations

impl Clone for SinglePolePenn

fn clone(&self) -> SinglePolePenn

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SinglePolePenn

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.