\(\renewcommand\AA{\unicode{x212B}}\)

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:

import numpy as np
import matplotlib.pyplot as plt
fICC = IkedaCarpenterConvoluted()
fICC['scale'] = 1.0
fICC['A'] = 0.1
fICC['B'] = 1.e-2
fICC['R'] = 0.3
fICC['T0'] = 27000.
fICC['hatWidth'] = 0.5
fICC['k_conv'] = 120.

x = np.linspace(26000, 28000,100)
y = fICC(x)
plt.plot(x,y)

Categories: FitFunctions | General

Source¶

Python: ICConvoluted.py (last modified: 2020-03-27)