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# MultivariateGaussianComptonProfile¶

## Description¶

The fitted function for y-Space converted values is as described by G. Romanelli. [1].

$J(y) = \frac{1}{\sqrt{2\pi} \sigma_{x} \sigma_{y} \sigma_{z}} \frac{2}{\pi} \int_{0}^{1} d(\cos \theta) \int_{0}^{\frac{\pi}{2}} d \phi S^{2}(\theta, \phi) \exp \left( -\frac{y^{2}} {2 S^{2}(\theta, \phi)} \right)$

Where $$S^{2}(\theta, \phi)$$ is given by:

$\frac{1}{S^{2}(\theta, \phi)} = \frac{\sin^{2}\theta \cos^{2}\phi}{\sigma_{x}^{2}} + \frac{\sin^{2}\theta \sin^{2}\phi}{\sigma_{y}^{2}} + \frac{\cos^{2}\theta}{\sigma_{z}^{2}}$

The $$A_{3}$$ Final State Effects (FSE) correction is applied as an additive correction expressed as:

$-A_{3}(q)\frac{d^{3}}{dy^{3}}J(y) = \frac{\sigma_{x}^{4} + \sigma_{x}^{4} + \sigma_{x}^{4}} {9 \sqrt{2 \pi} \sigma_{x} \sigma_{y} \sigma_{z} q} \int_{0}^{1} d(\cos \theta) \int_{0}^{\frac{\pi}{2}} d \phi \left[ \frac{y^{3}}{S^{2}(\theta, \phi)^{4}} -3 \frac{y}{S^{2}(\theta, \phi)^{2}} \right] S^{2}(\theta, \phi) \exp \left( -\frac{y^{2}} {2 S^{2}(\theta, \phi)} \right)$

## Attributes (non-fitting parameters)¶

Name

Type

Default

Description

IntegrationSteps

Integer

256

Length of each dimension of integration grid (must be even)

## Properties (fitting parameters)¶

Name

Default

Description

Mass

0.0

Atomic mass (amu)

Intensity

1.0

Gaussian intensity parameter

SigmaX

1.0

Sigma X parameter

SigmaY

1.0

Sigma Y parameter

SigmaZ

1.0

Sigma Z parameter

## References¶

Categories: FitFunctions | General