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# ApplyDetailedBalance v1¶

## Summary¶

Transform scattering intensity to dynamic susceptibility.

## Properties¶

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

An input workspace.

Temperature

Input

string

SampleLog variable name that contains the temperature, or a number

OutputWorkspace

Output

MatrixWorkspace

Mandatory

An output workspace.

OutputUnits

Input

string

Energy

Susceptibility as a function of energy (meV) or frequency (GHz). Allowed values: [‘Energy’, ‘Frequency’]

## Description¶

The fluctuation dissipation theorem [1,2] relates the dynamic susceptibility to the scattering function

$$\left(1-e^{-\frac{E}{k_B T}}\right) S(\mathbf{q}, E) = \frac{1}{\pi} \chi'' (\mathbf{q}, E)$$

where $$E$$ is the energy transfer to the system. The algorithm assumes that the y axis of the input workspace contains the scattering function $$S$$. The y axis of the output workspace will contain the dynamic susceptibility. The temperature is either extracted as the average of the values stored in the appropriate entry of the log attached to the workspace (user supplies the name of the entry) or user can pass a number for the temperature.

[1] S. W. Lovesey - Theory of Neutron Scattering from Condensed Matter, vol 1

[2] I. A. Zaliznyak and S. H. Lee - Magnetic Neutron Scattering in “Modern techniques for characterizing magnetic materials”

## Usage¶

Example - Run Applied Detailed Balance

ws = CreateWorkspace(DataX='-5,-4,-3,-2,-1,0,1,2,3,4,5',DataY='2,2,2,2,2,2,2,2,2,2',DataE='1,1,1,1,1,1,1,1,1,1',UnitX='DeltaE')
ows = ApplyDetailedBalance(InputWorkspace='ws',OutputWorkspace='ows',Temperature='100', OutputUnits='Frequency')

print("The Y values in the Output Workspace are")


Output:

The Y values in the Output Workspace are
[-4.30861792 -3.14812682 -2.11478496 -1.19466121 -0.37535083]
[ 0.35419179  1.00380206  1.58223777  2.09729717  2.55592407]


Categories: AlgorithmIndex | Inelastic\Corrections