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## Summary¶

Corrects the input data for the effects of attenuation & multiple scattering

## Properties¶

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

Input workspace with X units in TOF. The workspace must also have a sample with a cylindrical shape and an instrument with a defined source and sample position.

MultipleScattering

Input

boolean

False

If True then also correct for the effects of multiple scattering.Please note that the MS correction assumes the scattering is elastic.

MSEvents

Input

number

10000

Controls the number of second-scatter events generated. Only applicable where MultipleScattering=True.

MSRuns

Input

number

10

Controls the number of simulations, each containing MSEvents, performed. The final MS correction is computed as the average over the runs. Only applicablewhere MultipleScattering=True.

OutputWorkspace

Output

MatrixWorkspace

Mandatory

An output workspace.

## Description¶

Calculates and applies corrections due to the effects of absorption (plus optionally multiple scattering) on the signal and error values for a given workspace. The full background to the algorithm is described by Lindley et al. [1] and is briefly described here.

• the sample shape is a cylinder

• for multiple scattering:
• the scattering is assumed to be elastic and isotropic

• the ratio of successive orders of scattering are all equal to $$\beta(\theta, \phi, E)$$

The aim is to correct the number of neutrons at a given detector ($$N_d$$) to compute the number of neutrons ($$N_c$$) that would reach the detector if there was no absorption (or multiple scattering). Ignoring detector efficiency we can write:

$N_d = \frac{N_c}{A_s} \cdot \frac{1}{1-\beta}$

where $$A_s(\theta, \phi, E)$$ is the absorption and self-shielding factor and is computed by numerical integration over the sample cylinder.

The multiple scattering factor (if requested) is computed by simulating over a fixed number of second order scattering events and computing the ratio of second order and first order scattering. Since we have assumed the ratio is the same between successive orders, the $$\frac{1}{1-\beta}$$ factor simply comes from taking the sum of a geometric series.

The cylinder radius $$r$$ combined with the inverse attenuation length $$\mu = \mu(E)$$ (derived from the total scattering cross-section) gives a range of $$\mu r$$ against input time-of-flight (“energy”) for the cylinder. The $$\mu r$$ range is divided into a discrete number of points for each point.

A weighted least-squares fit is applied to both the set of attenuation and multiple scattering factors to allow interpolation of the correction factor from any time-of-flight value in the input range. For each time-of-flight value the factor is computed from the fit coefficients and the correction applied multiplicatively:

\begin{split}\begin{aligned} y_{out} &= y_{in} * corrfact \\ e_{out} &= y_{out} * e_{in} / y_{in} \end{aligned}\end{split}

The above procedure is repeated separately for each spectrum in the workspace.

## Usage¶

Example - Correct Vanadium For Both Absorption & Multiple Scattering

# Create a fake workspace with TOF data
sample_ws = CreateSampleWorkspace(Function='Powder Diffraction',
NumBanks=1,BankPixelWidth=1,XUnit='TOF',
XMin=1000,XMax=10000)
# Set meta data about shape and material
cyl_height_cm = 4.0
material = 'V'
num_density = 0.07261
SetSample(sample_ws,
Geometry={'Shape': 'Cylinder', 'Height': cyl_height_cm,
Material={'ChemicalFormula': material, 'SampleNumberDensity': num_density})

# Run corrections
MultipleScattering=True)

# Print a bin