User`s guide

3 Fitting Data
3-46
Example: Fitting with Custom Equations
You can define your own equations with the Create Custom Equation GUI. You
open this GUI one of two ways:
• From the Curve Fitting Tool, select
Tools->Custom Equation.
• From the Fitting GUI, select
Custom Equations from the Type of fit list,
then click the
New Equation button.
The Create Custom Equation GUI contains two panes: one for creating linear
custom equations and one for creating general (nonlinear) custom equations.
These panes are described in the following examples.
Linear Equation: Legendre Polynomial Fit
This example fits data using several custom linear equations. The data is
generated, and is based on the nuclear reaction
12
C(e,e’α)
8
Be. The equations
use sums of Legendre polynomial terms.
Consider an experiment in which 124 MeV electrons are scattered from
12
C
nuclei. In the subsequent reaction, alpha particles are emitted and produce the
residual nuclei
8
Be. By analyzing the number of alpha particles emitted as a
function of angle, you can deduce certain information regarding the nuclear
dynamics of
12
C. The reaction kinematics are shown below.
The data is collected by placing solid state detectors at values of θ
α
ranging
from 10
o
to 240
o
in 10
o
increments.
θ
e’
θ
α
12
C
α
e’
e
e is the incident electron.
12
C is the carbon target.
q is the momentum transferred to
8
Be.
e’ is the scattered electron.
α is the emitted alpha particle.
θ
e’
is the electron scattering angle.
θ
α
is the alpha scattering angle.
q