jaxrts.models

This submodule contains high-level wrappers for the different Models implemented.

Functions

averagePlasmaState(state)

Create an average plasma state that shares the models of the original.

Classes

ArbitraryDegeneracyScreeningLength()

A screening length valid for arbitrary degeneracy [Baggott, 2017].

ArkhipovIonFeat()

Model for the ion feature of the scattering, presented in [Arkhipov and Davletov, 1998] and [Arkhipov et al., 2000].

AverageAtom_Sii([rmin, rmax, pot, mix, tmult])

This model performs a HNC calculation, assuming one average atom with a given, average charge state.

BM_V_eiSModel()

These models implement potentials which can be when calculating the Born collision frequencies in BornMermin and derived free-free scattering models.

BohmStaver()

The Bohm-Staver relation for the Debye temperature, valid for 'simple metals', as it is presented in Eqn (3) of [Gregori et al., 2006a].

BornMermin([no_of_freq, RPA_rewrite, KKT, ...])

Model for the free-free scattering, based on the Born Mermin Approximation ([Mermin, 1970]).

BornMermin_Fit([no_of_freq, RPA_rewrite, ...])

Model for the free-free scattering, based on the Born Mermin Approximation ([Mermin, 1970]).

BornMermin_Fortmann([no_of_freq, ...])

Model for the free-free scattering, based on the Born Mermin Approximation ([Mermin, 1970]).

BornMermin_Full([RPA_rewrite, KKT])

Model for the free-free scattering, based on the Born Mermin Approximation ([Mermin, 1970]).

CHSIonFeat()

Model for the ion feature of the scattering, presented in [Gregori et al., 2007].

ConstantChemPotential(value)

A model that returns a constant chemical potential, specified by a user.

ConstantDebyeTemp(value)

A model of constant Debye Temperature.

ConstantIPD(value)

A model that returns a constant value for the IPD, set by the user.

ConstantScreeningLength(value)

A model that returns a constant screening length, given by a user.

DebyeHueckelIPD([arb_deg])

Debye-Hückel IPD Model [Debye and Hückel, 1923].

DebyeHueckelScreening()

Debye Hückel screening as presented by [Chapman et al., 2015].

DebyeHueckelScreeningLength()

The standard Debye Hückel screening length.

DebyeHueckel_BM_V()

A Debye Hückel potential, using the jaxrts.plasmastate.PlasmaState.screening_length() method to get the screening length.

DebyeWallerSolid(S_plasma, b)

This model approximates the static structure factor (SSF) of a solid at finite temperature as suggested by [Gregori et al., 2006a].

DegenerateElectronChemPotential()

Chemical Potential of a fully degenerate electron gas, given by the Fermi energy.

DetailedBalance([sample_points])

Calculate the free-bound scattering by mirroring the free-bound scattering around the probing energy and applying a detailed balance factor to the intensity.

ESLFCDornheim2021()

Effective static approximation (ESA) of the local field correction model by Dornheim et al. [Dornheim et al., 2021].

EckerKroellIPD([C, arb_deg])

Ecker-Kröll IPD Model:[Ecker and Kröll, 1963].

EdgeModel()

Model class for edges as they appear, e.g., in the bound-free DSF.

Fermi()

Temperature dependent edge, where the edge is given by a Fermi-Dirac distribution with a slope dependent on the system's electron temperature:

FiniteWavelengthScreening()

Finite wavelength screening as presented by [Chapman et al., 2015], using a using a result from linear to calculate the screening density \(q\):

FiniteWavelength_BM_V()

Uses finite wavelength screening to screen the bare Coulomb potential, i.e., \(V_{s}=\frac{V_\mathrm{Coulomb}}{\varepsilon_\text{RPA}(k, E=0)}\)

FixedSii(Sii)

Model for the ion feature with a fixed value for \(S_{ii}\).

FormFactorLowering([Z_squared_correction])

Form factor lowering model as introduced by [Döppner et al., 2023].

FreeFreeModel([sample_points])

A class of models suitable for 'free-free scattering'.

Gericke2010ScreeningLength()

The Debye-Hückel screening length.

Gregori2003IonFeat()

Model for the ion feature of the scattering, presented in [Gregori et al., 2003].

Gregori2004Screening()

Calculating the screening from free electrons according to [Gregori et al., 2004].

Gregori2006IonFeat()

Model for the ion feature of the scattering, presented in [Gregori et al., 2006a].

GregoriCHSScreening()

Screening model to calculate the screening charge q based on expression for the static structure factors given in [Gregori et al., 2007].

GridInterpolation(interpolator, variable_names)

Interpolates an output from a grid from a grid.

GridInterpolationSii(interpolator, ...)

Interpolates \(S_{ab}\) from a grid.

Heaviside()

Hard cut of the edge at the binding energy, using a Heaviside function.

IPDModel()

A subset of Model's, to model the effect of ionization potential depression.

IPDSum(list_of_ipds)

A sum of several ipd Model s.

IchimaruChemPotential()

A fitting formula for the chemical potential of an ideal electron gas between the classical and the quantum regime, given by [Gregori et al., 2003].

IonFeatModel()

Abstract class of `Model`s, describing the scattering by electrons tightly bound to the ions, causing quasi-elastic scattering.

IonSphereIPD([C, arb_deg])

Ion Sphere IPD Model [Rozsnyai, 1972].

LFCConstant(value)

A constant local field correction which can be defined by the user.

LinearResponseScreening()

The screening density \(q\) is calculated using a result from linear response:

LinearResponseScreeningGericke2010()

The screening density \(q\) is calculated using a result from linear response:

Model()

Abstract definition of a Model in jaxrts.

Neglect()

Universal model to neglect a contribution and set it to zero.

NoEdge()

No edge, returns always one.

NonDegenerateElectronChemPotential()

Chemical Potential of a non-degenerate electron gas.

NonNegative()

Cuts at jaxrts.setup.Setup.measured_energy = 0 eV, independently of the edge_energy given, so that only energy transfer to the electrons (down-shifted photon energies) are permitted.

OnePotentialHNCIonFeat([rmin, rmax, pot, ...])

Calculates \(S_{ab}\) in the Hypernetted Chain approximation.

PauliBlockingIPD()

Pauli Blocking IPD Model [Röpke et al., 2019].

PaulingFormFactors()

Analytical functions for each electrons in quantum states defined by the quantum numbers n and l, assuming a hydrogen-like atom.

PeakCollection(k_pos, intensity, peak_function)

A model for approximating \(S_\text{ii}\) as a sum of peaks.

QCSalpeterApproximation([sample_points])

Quantum Corrected Salpeter Approximation for free-free scattering.

RPA([sample_points])

Model for free-free scattering based on the Random Phase Approximation.

RPA_DandreaFit([sample_points])

Model for free-free scattering based fitting to the Random Phase Approximation, as presented by [Dandrea et al., 1986].

SLFCFarid1993()

Static local field correction model by Farid at al.

SLFCGeldart1966()

Static local field correction model by Geldart and Vosko [Geldart and Vosko, 1966].

SLFCInterpFortmann2010()

Static local field correction model that interpolates between the zero temperature result by Farid [Farid et al., 1993] and the Geldart result [Geldart and Vosko, 1966] for high temperatures.

SLFCInterpGregori2007()

Static local field correction model that interpolates between the zero temperature result by Utsumi and Ichimaru [Utsumi and Ichimaru, 1982] and the Geldart result [Geldart and Vosko, 1966] for high temperatures.

SLFCUtsumi1982()

Static local field correction model by Utsumi and Ichimaru [Utsumi and Ichimaru, 1982].

ScatteringModel([sample_points])

A subset of Model's, used to provide some extra functionalities to (mainly elastic) scattering models.

SchumacherImpulse([r_k])

Bound-free scattering based on the Schumacher Impulse Approximation [Schumacher et al., 1975].

SchumacherImpulseColdEdges([r_k])

Bound-free scattering based on the Schumacher Impulse Approximation [Schumacher et al., 1975].

SchumacherImpulseFitRk()

Bound-free scattering based on the Schumacher Impulse Approximation [Schumacher et al., 1975].

SommerfeldChemPotential()

Interpolation function between the low and high temperature limit for the chemical potential of a non-interacting (ideal) fermi gas given in the paper of Cowan [Cowan, 2019].

StewartPyattIPD([arb_deg])

Stewart Pyatt IPD Model [Stewart and Pyatt, 1966].

StewartPyattPrestonIPD([arb_deg, ...])

Stewart Pyatt IPD Model [Stewart and Pyatt, 1966].

Sum_Sii()

This model sums up all \(S_{ab}\) from the HNC and multiplies it with \(\sqrt{x_{a}\cdot x_{b}}\).

ThreePotentialHNCIonFeat([rmin, rmax, pot, ...])

Calculates \(S_{ab}\) including electron-ion and electron-electron static structure factors using the Hypernetted Chain approximation.