Scattering Length

Functions to calculate the electronic and nuclear scattering lengths E and N and set the computation method.

nexus.GetAtomicScatteringFactorCXRO()

Get the calculation method of the atomic scattering factors. If False the scattering factors are calculated from Klein-Nishina cross sections and tabulated photo-effect cross sections. If True the tabulated scattering factors from the Center of X-ray Optics are used.

Returns:

atomic_scattering_factor_cxro.

Return type:

bool

nexus.SetAtomicScatteringFactorCXRO(cxro)

Set the calculation method of the atomic scattering factors.

Parameters:

cxro (bool) – Determines the calculation of the atomic scattering factors. If False the scattering factors are calculated from Klein-Nishina scattering and tabulated photo-effect cross sections. If True the tabulated scattering factors from the Center of X-ray Optics are used.

nexus.ElectronicScatteringLength(element, energy, cxro)

Calculates the electronic scattering length as given in Eq.(4.11) [Roehlsberger]. Note that the definition differs by a factor of \(1/(2\pi)\) from the one given in Eq. (4, 16) [Sturhahn]. The Debye-Waller factor is one here, because only forward and grazing incidence scattering are considered. An additional relativistic correction is applied to the real part, after Eq. (78) [Henke].

Parameters:

  • element (Element) – Element for which the scattering length is calculated.

  • energy (float) – X-ray energy (eV).

  • cxro (bool) – Determines the calculation of the atomic scattering factors. If False the scattering factors are calculated from Klein-Nishina cross sections and tabulated photo-effect cross sections (as in CONUSS). If True the tabulated scattering factors from the Center of X-ray Optics are used (as in GenX).

Returns:

Electronic scattering length (m).

Return type:

complex

nexus.ElectronicScatteringLengthTheory(element, energy)

Calculates the electronic scattering length as defined in Eq.(4.11) [Roehlsberger]. Note that the definition differs by a factor of \(1/(2\pi)\) from the one given in Eq. (4, 16) [Sturhahn]. Klein Nishina cross sections are calculated after [KleinNishina]. Photoeffect cross sections are calculated after [Smith]. The Debye-Waller factor is one here, because only forward and grazing incidence scattering are considered. An additional relativistic correction is applied to the real part, after Eq. (78) [Henke].

Parameters:

  • element (Element) – Element for which the scattering length is calculated.

  • energy (float) – X-ray energy (eV).

Returns:

Electronic scattering length (m).

Return type:

complex

nexus.ElectronicScatteringLengthCXRO(element, energy)

Calculates the electronic scattering length as defined in Eq.(4.11) [Roehlsberger] but with the atomic scattering factors from the CXRO database [Henke]. Note that the definition differs by a factor of \(1/(2\pi)\) from the one given in Eq. (4, 16) [Sturhahn]. The complex correction to the refractive index in [Roehlsberger] and [Henke] are defined differently. The factor \(E_i\) from [Roehlsberger] is \(E_i = -r_e (f_1 - i f_2)\). The Debye-Waller factor is one here, because only forward and grazing incidence scattering are considered. An additional relativistic correction is applied to the real part, after Eq. (78) [Henke].

See also

https://henke.lbl.gov/optical_constants/asf.html

Parameters:

  • element (Element) – Element for which the scattering length is calculated.

  • energy (float) – X-ray energy (eV).

Returns:

Electronic scattering length (m).

Return type:

complex

nexus.ElectronicScatteringLengthMatrix(*args)

Overload 1:

Electronic scattering length in the base of \(\sigma\) and \(\pi\) polarization, Eq. (4.11), [Roehlsberger]. Note that the definition differs by a factor of \(1/(2\pi)\) from the one given in Eq. (4, 16) [Sturhahn]. The Debye-Waller factor is one here, because only forward and grazing incidence scattering are considered. An additional relativistic correction is applied to the real part, after Eq. (78) [Henke].

Parameters:

  • element (Element) – Element for the calculation.

  • energy (float) – X-ray energy (eV).

  • cxro (bool) – Determines the calculation of the atomic scattering factors. If False the scattering factors are calculated from Klein-Nishina cross sections and tabulated photo-effect cross sections (as in CONUSS). If True the tabulated scattering factors from the Center of X-ray Optics are used (as in GenX).

Returns:

2x2 matrix of the electronic scattering length (m).

Return type:

ndarray


Overload 2:

Electronic scattering length in the base of \(\sigma\) and \(\pi\) polarization, Eq. (4.11), [Roehlsberger]. Note that the definition differs by a factor of \(1/(2\pi)\) from the one given in Eq. (4, 16) [Sturhahn]. The Debye Waller factor is one here, because only forward and grazing incidence scattering are considered. An additional relativistic correction is applied to the real part, after Eq. (78) [Henke]. The electronic scattering length is calculated around the transition energy of MoessbauerIsotope.

Parameters:

  • element (Element) – Element for the calculation.

  • isotope (MoessbauerIsotope) – The MoessbauerIsotope for which the electronic scattering length should be calculated.

  • detuning (list or ndarray) – Detuning values around the isotope transition energy.

  • cxro (bool) – Determines the calculation of the atomic scattering factors. If False the scattering factors are calculated from Klein-Nishina cross sections and tabulated photo-effect cross sections (as in CONUSS). If True the tabulated scattering factors from the Center of X-ray Optics are used (as in GenX).

Returns:

Array of 2x2 matrices of the electronic scattering length (m).

Return type:

array

nexus.NuclearScatteringLength(material, isotope, detuning, calc_transitions=True)

Nuclear scattering length in the base of \(\sigma\) and \(\pi\) polarization. Eq. (11), [Sturhahn]. Note that the definition differs by a factor of \(1/(2\pi)\) from the one given in Eq. (11, 16) [Sturhahn]. The nuclear scattering length is calculated around the transition energy of MoessbauerIsotope.

Parameters:

  • material (Material) – Material for the X-ray interaction.

  • isotope (MoessbauerIsotope) – The MoessbauerIsotope for which the nuclear scattering length should be calculated.

  • detuning (list or ndarray) – Detuning values around the isotope transition energy.

  • calc_transition (bool) – Specifies if the nuclear transitions of the material are calculated before the nuclear scattering length is determined.

Returns:

Array of 2x2 matrices of the nuclear scattering length (m).

Return type:

array

nexus.MaterialWeightedScatteringLength(material, energy)

Electronic scattering length for a material. Calculation mode is defined by the function SetAtomicScatteringFactorCXRO().

Parameters:

  • material (Material) – Material for the calculation.

  • energy (float) – Energy for the calculation in eV.

Returns:

Electronic scattering length (1/m^2).

Return type:

complex

nexus.MaterialWeightedScatteringLengthMatrix(*args)

Overload 1:

Electronic scattering length for a material in the base of \(\sigma\) and \(\pi\) polarization. Calculation mode is defined by the function SetAtomicScatteringFactorCXRO(). See ElectronicScatteringLength().

Parameters:

  • material (Material) – Material for the calculation.

  • energy (float) – Energy for the calculation in eV.

Returns:

2x2 matrix electronic scattering length (1/m^2).

Return type:

array


Overload 2:

Electronic scattering length for a material in the base of \(\sigma\) and \(\pi\) polarization for a detuning range. Calculation mode is defined by the function SetAtomicScatteringFactorCXRO(). See ElectronicScatteringLength().

Parameters:

  • material (Material) – Material for the calculation.

  • ( (isotope) – class:MoessbauerIsotope): The MoessbauerIsotope for the calcuaiton.

  • detuning (list or ndarray) – Detuning values around the isotope transition energy.

Returns:

Array of 2x2 matrices of the electronic scattering length (1/m^2).

Return type:

array

nexus.MaterialWeightedNuclearScatteringLength(material, isotope, detuning_grid, calc_transitions)

Nuclear scattering length in the base of \(\sigma\) and \(\pi\) polarization already weighted by the isotope density.

Parameters:

  • material (Material) – Material for the X-ray interaction.

  • isotope (MoessbauerIsotope) – The MoessbauerIsotope for which the nuclear scattering length should be calculated.

  • detuning (list or ndarray) – Detuning values around the isotope transition energy.

  • calc_transition (bool) – Specifies if the nuclear transitions of the material are calculated before the nuclear scattering length is determined.

Returns:

Array of 2x2 matrices of the nuclear scattering length (1/m^2).

Return type:

array

nexus.MaterialWeightedCoherentScatteringLength(material, isotope, detuning_grid, calc_transitions)

Coherent (electronic + nuclear) scattering length in the base of \(\sigma\) and \(\pi\) polarization already weighted by the material properties.

Parameters:

  • material (Material) – Material for the X-ray interaction.

  • isotope (MoessbauerIsotope) – The MoessbauerIsotope for which the nuclear scattering length should be calculated.

  • detuning (list or ndarray) – Detuning values around the isotope transition energy.

  • calc_transition (bool) – Specifies if the nuclear transitions of the material are calculated before the nuclear scattering length is determined.

Returns:

Array of 2x2 matrices of the nuclear scattering length (1/m^2).

Return type:

array

Examples

# electronic scattering length of 20 keV photons in iron
Fe = nx.Element(element = "Fe")

scattering_length = nx.ElectronicScatteringLength(Fe, 20e3, cxro = True)
print(scattering_length)

# nuclear scattering length at 57-Fe transition energy
mat_Fe = nx.Material.Template(nx.lib.material.Fe_enriched)

site1 = nx.Hyperfine(magnetic_field = 33)

mat_Fe.hyperfinesites = [site1]

detuning = np.linspace(-200, 200, 201)

scattering_length = nx.NuclearScatteringLength(mat_Fe, nx.lib.moessbauer.Fe57, detuning)
print(scattering_length)