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# IkedaCarpenterConvoluted¶

## Description¶

This function is an Ikeda-Carpenter function convolved with a tophat function and a Gaussian function. The Ikeda-Carpenter function is given by:

$V = Scale \times \Big\{ (1-R)(\alpha t')^2 e^{-\alpha t'} + 2R\frac{\alpha^2 \beta}{(\alpha-\beta)^3} \times \big[ e^{-\beta t'} - e^{-\alpha t'} (1 + (\alpha - \beta)t' + \frac{1}{2}(\alpha-\beta)^2t'^2) \big] \Big\}$

This is convolved with a tophat function (of width hatWidth) and a Gaussian function $$exp(-k_{conv} t^2)$$.

There are no attributes for this function.

## Properties (fitting parameters)¶

Name

Default

Description

A

0.0

B

0.0

R

0.0

T0

0.0

Scale

0.0

HatWidth

0.0

KConv

0.0

See Ikeda, S. & Carpenter, J.M. (1985). Nuclear Instruments and Methods in Physics Research Section A 239, 536-544 for additional details on parameters

### Usage¶

Here is an example of generating an Ikeda-Carpenter function:

 1import numpy as np
2import matplotlib.pyplot as plt
3fICC = IkedaCarpenterConvoluted()
4fICC['scale'] = 1.0
5fICC['A'] = 0.1
6fICC['B'] = 1.e-2
7fICC['R'] = 0.3
8fICC['T0'] = 27000.
9fICC['hatWidth'] = 0.5
10fICC['k_conv'] = 120.
11
12x = np.linspace(26000, 28000,100)
13y = fICC(x)
14plt.plot(x,y)


Categories: FitFunctions | General

## Source¶

Python: ICConvoluted.py