Parameter Overview

NuMagSANS simulations are configured using the Python function

NuMagSANS.write_config(...)

This function generates a configuration file that is passed to the NuMagSANS backend executable. The parameters listed below correspond directly to entries in the generated configuration file and control the physical model and numerical settings of the simulation.

Example Script

The following script demonstrates a minimal NuMagSANS workflow.

from NuMagSANS import NuMagSANS
from pathlib import Path

BASE_DIR = Path(__file__).resolve().parent

# Create NuMagSANS object
sim = NuMagSANS()

# Temporary configuration file
config = BASE_DIR / "NuMagSANSInput_temp.conf"

# Write configuration file
sim.write_config(
    config,
    MagData_activate=1,
    MagDataPath=str(BASE_DIR / "RealSpaceData" / "MagData"),
    foldernameSANSData=str(BASE_DIR / "NuMagSANS_Output"),
    Fourier_Approach="atomistic",
    User_Selection=[1, 2, 3],
    Scattering_Volume_V=2.618e-24,
    enable_outputs=["SpinFlip_2D", "SpinFlip_1D"]
)

# Run NuMagSANS simulation
sim.run(config)

# Remove temporary configuration file
sim.config_clear(config)

Data Paths and Data Selection

These parameters define where the simulation reads input data and where results are written.

NucDataPath

Default path RealSpaceData/NucData

NucData_activate

Default value 0

MagDataPath

Default path RealSpaceData/MagData

MagData_activate

Default value 0

StructDataFilename

Default path RealSpaceData/StructData.csv

StructData_activate

Default value 0

foldernameSANSData

Default NuMagSANS_Output

Exclude_Zero_Moments

Fourier Approach

Defines how the Fourier transform from real space to reciprocal space is performed.

Fourier_Approach

Default atomistic Options: atomistic, micromagnetic

Loop Control

These parameters control batch simulations or repeated calculations.

Loop_Modus

Description: Enable looping over simulation indices Default 0

Loop_From

Description: First index used in loop simulations Default 1

Loop_To

Description: Last index used in loop simulations Default 20

User_Selection

Description: Explicit list of selected indices Default [1]

Constant Parameters

XYZ_Unit_Factor

Conversion factors for coordinate units. Scaling factor applied to spatial coordinates. This parameter is equal to 1, if the positional input data is in units of \(\mathrm{nm}\). Default value 1

Scattering_Volume_V

Effective scattering volume in units of \(\mathrm{m}^3\) Default value 2.618e-24

RotMat_alpha

Rotation angle in degree. Rotates the sample Default value 0.0

RotMat_beta

Rotation angle in degree. Rotates the sample in the \(x-y\)-plane. Default value 0.0

Polarization

Polarization vector (Px, Py, Pz). Defines the polarization vector of the incoming neutron beam. Default (0,0,1)

Number_Of_q_Points

Number of sampled q values in Fourier space. Default value 1000

Number_Of_theta_Points

Number of angular sampling points in Fourier space. Default value 1000

Number_Of_r_Points

Number of sampled q values in real space (correlation). Default value 1000

Number_Of_alpha_Points

Number of angular sampling points in real space (correlation). Default value 1000

q_max

Maximum scattering vector in Fourier space in units of \(\mathrm{nm}^{-1}\) Default value 3.0

r_max

Maximum real-space correlation distance in units of \(\mathrm{nm}\). Default value ``15.0 ``

Micromagnetic Parameters

Parameters describing the magnetic properties of discretized simulation cells.

Cell_Nuclear_SLD

Description: Nuclear scattering length density of the cell Default 8e14

Cell_Magnetization

Description: Magnetization inside the discretized cell Default 486e3

Cuboid_Cell_Size

Description: Dimensions of the discretization cell (x,y,z) Default (2,2,2)

Output Options

2D SANS cross sections

In NuMagSANS, the incoming neutron beam is defined to propagate along the \(x\)-axis, such that the corresponding wave vector satisfies \(\mathbf{k}_0 \parallel \mathbf{e}_x\). The two-dimensional detector plane is oriented perpendicular to the incident beam direction. The scattering vector \(\mathbf{q}\) on the detector can therefore be written as

\[\begin{split}\mathbf{q} = \begin{bmatrix} q_x \\ q_y \\ q_z \end{bmatrix} = \begin{bmatrix} 0 \\ q \sin\theta \\ q \cos\theta \end{bmatrix}.\end{split}\]

In NuMagSANS the 2D SANS cross sections are exported in units of \(\mathrm{cm}^{-1}\).

Nuclear_2D

Nuclear SANS cross section on the 2D detector.

\[\frac{d\Sigma_{\mathrm{N}}}{d\Omega}(q,\theta) = \frac{8\pi^3}{V}\, |\widetilde{N}|^2\]

Unpolarized_2D

Unpolarized magnetic SANS cross section on the 2D detector.

\[\frac{d\Sigma_{\mathrm{M}}}{d\Omega}(q,\theta) = \frac{8\pi^3}{V}\, b_{\mathrm{H}}^2 |\widetilde{\mathbf{Q}}|^2\]

Polarized_2D

Auxiliary polarized magnetic SANS cross section on the 2D detector.

\[\frac{d\Sigma_{\mathrm{P}}}{d\Omega}(q,\theta) = \frac{8\pi^3}{V}\, b_{\mathrm{H}}^2 \left|\hat{\mathbf{P}}\cdot\widetilde{\mathbf{Q}}\right|^2\]

NuclearMagnetic_2D

Nuclear–magnetic SANS cross section on the 2D detector.

\[\frac{d\Sigma_{\mathrm{NM}}}{d\Omega}(q,\theta) = \frac{8\pi^3}{V}\, b_{\mathrm{H}} \hat{\mathbf{P}}\cdot\left[\widetilde{N}\widetilde{\mathbf{Q}}^{\ast}+\widetilde{N}^{\ast}\widetilde{\mathbf{Q}}\right]\]

Chiral_2D

Chiral SANS cross section on the 2D detector.

\[\frac{d\Sigma_{\chi}}{d\Omega}(q,\theta) = -i\frac{8\pi^3}{V}\, b_{\mathrm{H}}^2 \hat{\mathbf{P}}\cdot \left(\widetilde{\mathbf{Q}}\times\widetilde{\mathbf{Q}}^{\ast}\right)\]

SpinFlip_2D

Spin-flip SANS cross section on the 2D detector.

\[\frac{d\Sigma_{\mathrm{sf}}}{d\Omega}(q,\theta) = \frac{d\Sigma_{\mathrm{M}}}{d\Omega}(q,\theta) - \frac{d\Sigma_{\mathrm{P}}}{d\Omega}(q,\theta)\]

PM_SpinFlip_2D

Spin-flip SANS cross section on the 2D detector.

\[\frac{d\Sigma^{+-}}{d\Omega}(q,\theta) = \frac{d\Sigma_{\mathrm{sf}}}{d\Omega}(q,\theta) + \frac{d\Sigma_{\chi}}{d\Omega}(q,\theta)\]

MP_SpinFlip_2D

Spin-flip SANS cross section on the 2D detector.

\[\frac{d\Sigma^{+-}}{d\Omega}(q,\theta) = \frac{d\Sigma_{\mathrm{sf}}}{d\Omega}(q,\theta) - \frac{d\Sigma_{\chi}}{d\Omega}(q,\theta)\]

PP_NonSpinFlip_2D

Non-spin-flip SANS cross section on the 2D detector.

\[\frac{d\Sigma^{++}}{d\Omega}(q,\theta) = \frac{d\Sigma_{\mathrm{N}}}{d\Omega}(q,\theta) + \frac{d\Sigma_{\mathrm{NM}}}{d\Omega}(q,\theta) + \frac{d\Sigma_{\mathrm{P}}}{d\Omega}(q,\theta)\]

MM_NonSpinFlip_2D

Non-spin-flip SANS cross section on the 2D detector.

\[\frac{d\Sigma^{--}}{d\Omega}(q,\theta) = \frac{d\Sigma_{\mathrm{N}}}{d\Omega}(q,\theta) - \frac{d\Sigma_{\mathrm{NM}}}{d\Omega}(q,\theta) + \frac{d\Sigma_{\mathrm{P}}}{d\Omega}(q,\theta)\]

P_SANSPOL_2D

Non-Spin-flip SANS cross section on the 2D detector.

\[\frac{d\Sigma^{+}}{d\Omega}(q,\theta) = \frac{d\Sigma^{++}}{d\Omega}(q,\theta) + \frac{d\Sigma^{+-}}{d\Omega}(q,\theta)\]

M_SANSPOL_2D

Non-Spin-flip SANS cross section on the 2D detector.

\[\frac{d\Sigma^{-}}{d\Omega}(q,\theta) = \frac{d\Sigma^{--}}{d\Omega}(q,\theta) + \frac{d\Sigma^{-+}}{d\Omega}(q,\theta)\]

2D correlation functions

NuMagSANS can compute two-dimensional real-space correlation functions from the detector-plane SANS cross sections. The real-space vector in the detector plane is parameterized as

\[\begin{split}\mathbf r = \begin{bmatrix} 0 \\ r\sin\alpha \\ r\cos\alpha \end{bmatrix},\end{split}\]

while the scattering vector in reciprocal space is written as

\[\begin{split}\mathbf q = \begin{bmatrix} 0 \\ q\sin\theta \\ q\cos\theta \end{bmatrix}.\end{split}\]

Using these parametrizations the scalar product becomes

\[\mathbf q\cdot\mathbf r = qr\cos(\theta-\alpha).\]

The two-dimensional correlation functions are obtained from the SANS cross sections via the cosine transform

\[C(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta .\]

The following two-dimensional correlation functions can be calculated.

Nuclear_Corr_2D

2D correlation function of the nuclear SANS cross section.

\[C_{\mathrm N}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma_{\mathrm N}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

Unpolarized_Corr_2D

2D correlation function of the unpolarized magnetic SANS cross section.

\[C_{\mathrm M}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma_{\mathrm M}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

Polarized_Corr_2D

2D correlation function of the polarized magnetic SANS cross section.

\[C_{\mathrm P}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma_{\mathrm P}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

NuclearMagnetic_Corr_2D

2D correlation function of the nuclear–magnetic interference SANS cross section.

\[C_{\mathrm{NM}}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma_{\mathrm{NM}}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

SpinFlip_Corr_2D

2D correlation function of the spin-flip SANS cross section.

\[C_{\mathrm{sf}}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma_{\mathrm{sf}}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

Chiral_Corr_2D

2D correlation function of the chiral SANS cross section.

\[C_{\chi}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma_{\chi}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

PM_SpinFlip_Corr_2D

2D correlation function of the \((+,-)\) spin-flip channel.

\[C^{+-}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma^{+-}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

MP_SpinFlip_Corr_2D

2D correlation function of the \((-,+)\) spin-flip channel.

\[C^{-+}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma^{-+}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

PP_NonSpinFlip_Corr_2D

2D correlation function of the \((+,+)\) non-spin-flip channel.

\[C^{++}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma^{++}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

MM_NonSpinFlip_Corr_2D

2D correlation function of the \((-,-)\) non-spin-flip channel.

\[C^{--}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma^{--}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

P_SANSPOL_Corr_2D

2D correlation function of the SANSPOL \((+ )\) channel.

\[C^{+}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma^{+}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

M_SANSPOL_Corr_2D

2D correlation function of the SANSPOL \((- )\) channel.

\[C^{-}(r,\alpha) = \int_{0}^{\infty}\int_{0}^{2\pi} \frac{d\Sigma^{-}}{d\Omega}(q,\theta) \cos\left(qr\cos(\theta-\alpha)\right) q\,dq\,d\theta\]

1D Azimuthally averaged SANS cross sections

In NuMagSANS the 1D SANS cross sections are exported in units of \(\mathrm{cm}^{-1}\).

Nuclear_1D

Azimuthally averaged nuclear SANS cross section.

\[I_{\mathrm{N}}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma_{\mathrm{N}}}{d\Omega}(q,\theta) \, d\theta\]

Unpolarized_1D

Azimuthally averaged unpolarized magnetic SANS cross section.

\[I_{\mathrm{M}}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma_{\mathrm{M}}}{d\Omega}(q,\theta) \, d\theta\]

Polarized_1D

Azimuthally averaged polarized magnetic SANS cross section.

\[I_{\mathrm{P}}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma_{\mathrm{P}}}{d\Omega}(q,\theta) \, d\theta\]

NuclearMagnetic_1D

Azimuthally averaged nuclear–magnetic interference cross section.

\[I_{\mathrm{NM}}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma_{\mathrm{NM}}}{d\Omega}(q,\theta) \, d\theta\]

Chiral_1D

Azimuthally averaged chiral SANS cross section.

\[I_{\chi}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma_{\chi}}{d\Omega}(q,\theta) \, d\theta\]

SpinFlip_1D

Azimuthally averaged spin-flip SANS cross section.

\[I_{\mathrm{sf}}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma_{\mathrm{sf}}}{d\Omega}(q,\theta) \, d\theta\]

PM_SpinFlip_1D

Azimuthally averaged spin-flip SANS cross section for the \((+,-)\) polarization channel.

\[I^{+-}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma^{+-}}{d\Omega}(q,\theta) \, d\theta\]

MP_SpinFlip_1D

Azimuthally averaged spin-flip SANS cross section for the \((-,+)\) polarization channel.

\[I^{-+}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma^{-+}}{d\Omega}(q,\theta) \, d\theta\]

PP_NonSpinFlip_1D

Azimuthally averaged non-spin-flip SANS cross section for the \((+,+)\) polarization channel.

\[I^{++}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma^{++}}{d\Omega}(q,\theta) \, d\theta\]

MM_NonSpinFlip_1D

Azimuthally averaged non-spin-flip SANS cross section for the \((-,-)\) polarization channel.

\[I^{--}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma^{--}}{d\Omega}(q,\theta) \, d\theta\]

P_SANSPOL_1D

Azimuthally averaged SANSPOL cross section for positive neutron polarization.

\[I^{+}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma^{+}}{d\Omega}(q,\theta) \, d\theta\]

M_SANSPOL_1D

Azimuthally averaged SANSPOL cross section for negative neutron polarization.

\[I^{-}(q) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{d\Sigma^{-}}{d\Omega}(q,\theta) \, d\theta\]

1D Correlation functions

In addition to the azimuthally averaged SANS cross sections \(I(q)\), NuMagSANS can compute the corresponding real-space correlation functions \(c(r)\). These functions are obtained from the scattering intensity via a spherical Bessel transform

\[c(r) = \int_{0}^{\infty} I(q)\, j_0(qr)\, q^2 \, dq ,\]

where \(j_0(x)\) denotes the spherical Bessel function of order zero,

\[j_0(x) = \frac{\sin x}{x}.\]

In NuMagSANS the 1D correlation functions are exported in units of \(\mathrm{nm}^{-4}\). The following correlation functions can be calculated.

Nuclear_Corr_1D

Correlation function of the nuclear SANS cross section.

\[c_{\mathrm{N}}(r) = \int_{0}^{\infty} I_{\mathrm{N}}(q)\, j_0(qr)\, q^2 \, dq\]

Unpolarized_Corr_1D

Correlation function of the unpolarized magnetic SANS cross section.

\[c_{\mathrm{M}}(r) = \int_{0}^{\infty} I_{\mathrm{M}}(q)\, j_0(qr)\, q^2 \, dq\]

Polarized_Corr_1D

Correlation function of the polarized magnetic SANS cross section.

\[c_{\mathrm{P}}(r) = \int_{0}^{\infty} I_{\mathrm{P}}(q)\, j_0(qr)\, q^2 \, dq\]

NuclearMagnetic_Corr_1D

Correlation function of the nuclear–magnetic interference SANS cross section.

\[c_{\mathrm{NM}}(r) = \int_{0}^{\infty} I_{\mathrm{NM}}(q)\, j_0(qr)\, q^2 \, dq\]

Chiral_Corr_1D

Correlation function of the chiral SANS cross section.

\[c_{\chi}(r) = \int_{0}^{\infty} I_{\chi}(q)\, j_0(qr)\, q^2 \, dq\]

SpinFlip_Corr_1D

Correlation function of the spin-flip SANS cross section.

\[c_{\mathrm{sf}}(r) = \int_{0}^{\infty} I_{\mathrm{sf}}(q)\, j_0(qr)\, q^2 \, dq\]

PM_SpinFlip_Corr_1D

Correlation function of the \((+,-)\) spin-flip channel.

\[c^{+-}(r) = \int_{0}^{\infty} I^{+-}(q)\, j_0(qr)\, q^2 \, dq\]

MP_SpinFlip_Corr_1D

Correlation function of the \((-,+)\) spin-flip channel.

\[c^{-+}(r) = \int_{0}^{\infty} I^{-+}(q)\, j_0(qr)\, q^2 \, dq\]

PP_NonSpinFlip_Corr_1D

Correlation function of the \((+,+)\) non-spin-flip channel.

\[c^{++}(r) = \int_{0}^{\infty} I^{++}(q)\, j_0(qr)\, q^2 \, dq\]

MM_NonSpinFlip_Corr_1D

Correlation function of the \((-,-)\) non-spin-flip channel.

\[c^{--}(r) = \int_{0}^{\infty} I^{--}(q)\, j_0(qr)\, q^2 \, dq\]

P_SANSPOL_Corr_1D

Correlation function of the SANSPOL \((+ )\) channel.

\[c^{+}(r) = \int_{0}^{\infty} I^{+}(q)\, j_0(qr)\, q^2 \, dq\]

M_SANSPOL_Corr_1D

Correlation function of the SANSPOL \((- )\) channel.

\[c^{-}(r) = \int_{0}^{\infty} I^{-}(q)\, j_0(qr)\, q^2 \, dq\]

1D Pair-distance distribution functions

In addition to the correlation functions \(c(r)\), NuMagSANS can compute the corresponding pair-distance distribution functions \(p(r)\). These functions are obtained from the correlation functions via

\[p(r) = r^2 c(r).\]

Using the definition of \(c(r)\), the pair-distance distribution function can also be written as

\[p(r) = r^2 \int_{0}^{\infty} I(q)\, j_0(qr)\, q^2 \, dq .\]

In NuMagSANS the 1D pair-distance distribution functions are exported in units of \(\mathrm{nm}^{-2}\). The following pair-distance distribution functions can be calculated.

Nuclear_PairDist_1D

Pair-distance distribution function of the nuclear SANS cross section.

\[p_{\mathrm{N}}(r) = r^2 \int_{0}^{\infty} I_{\mathrm{N}}(q)\, j_0(qr)\, q^2 \, dq\]

Unpolarized_PairDist_1D

Pair-distance distribution function of the unpolarized magnetic SANS cross section.

\[p_{\mathrm{M}}(r) = r^2 \int_{0}^{\infty} I_{\mathrm{M}}(q)\, j_0(qr)\, q^2 \, dq\]

Polarized_PairDist_1D

Pair-distance distribution function of the polarized magnetic SANS cross section.

\[p_{\mathrm{P}}(r) = r^2 \int_{0}^{\infty} I_{\mathrm{P}}(q)\, j_0(qr)\, q^2 \, dq\]

NuclearMagnetic_PairDist_1D

Pair-distance distribution function of the nuclear–magnetic interference SANS cross section.

\[p_{\mathrm{NM}}(r) = r^2 \int_{0}^{\infty} I_{\mathrm{NM}}(q)\, j_0(qr)\, q^2 \, dq\]

Chiral_PairDist_1D

Pair-distance distribution function of the chiral SANS cross section.

\[p_{\chi}(r) = r^2 \int_{0}^{\infty} I_{\chi}(q)\, j_0(qr)\, q^2 \, dq\]

SpinFlip_PairDist_1D

Pair-distance distribution function of the spin-flip SANS cross section.

\[p_{\mathrm{sf}}(r) = r^2 \int_{0}^{\infty} I_{\mathrm{sf}}(q)\, j_0(qr)\, q^2 \, dq\]

PM_SpinFlip_PairDist_1D

Pair-distance distribution function of the \((+,-)\) spin-flip channel.

\[p^{+-}(r) = r^2 \int_{0}^{\infty} I^{+-}(q)\, j_0(qr)\, q^2 \, dq\]

MP_SpinFlip_PairDist_1D

Pair-distance distribution function of the \((-,+)\) spin-flip channel.

\[p^{-+}(r) = r^2 \int_{0}^{\infty} I^{-+}(q)\, j_0(qr)\, q^2 \, dq\]

PP_NonSpinFlip_PairDist_1D

Pair-distance distribution function of the \((+,+)\) non-spin-flip channel.

\[p^{++}(r) = r^2 \int_{0}^{\infty} I^{++}(q)\, j_0(qr)\, q^2 \, dq\]

MM_NonSpinFlip_PairDist_1D

Pair-distance distribution function of the \((-,-)\) non-spin-flip channel.

\[p^{--}(r) = r^2 \int_{0}^{\infty} I^{--}(q)\, j_0(qr)\, q^2 \, dq\]

P_SANSPOL_PairDist_1D

Pair-distance distribution function of the SANSPOL \((+ )\) channel.

\[p^{+}(r) = r^2 \int_{0}^{\infty} I^{+}(q)\, j_0(qr)\, q^2 \, dq\]

M_SANSPOL_PairDist_1D

Pair-distance distribution function of the SANSPOL \((- )\) channel.

\[p^{-}(r) = r^2 \int_{0}^{\infty} I^{-}(q)\, j_0(qr)\, q^2 \, dq\]

Angular Spectrum

Settings for angular spectrum calculations.

k_max

Maximum angular wave number. Default value 10

Angular_Spec

Enable angular spectrum calculation. (binary selection) Default value 0