Experimental Effects Tab

The Experimental Effects tab is used to apply corrections for experimental effects such as beam energy loss in targets, beam energy resolution, detector geometry, and energy straggling.

Warning

The target integration and beam resolution convolution routines implemented in AZURE2 are basic and may not cover all experimental situations. The developers strongly recommend evaluating these routines on a case-by-case basis. Modifications to the source code may be necessary for specific experimental setups.

Warning

There are known issues when using both the target convolution and target integration routines simultaneously. Exercise extreme caution if combining these options.

Overview

The experimental effects are modeled as:

\[F(E_0) = \int_{E_0 - \Delta}^{E_0} \frac{\sigma(E')}{\epsilon(E')} \int_{-\infty}^{+\infty} g(E - E_0) \, dE' \, dE\]

where \(\sigma(E')\) is the true cross section, \(g(E' - E)\) is a spreading function representing the beam energy distribution, and \(\epsilon(E')\) is the stopping cross section.

The spreading function is a Gaussian:

\[g(E - E_0) = \frac{1}{\sqrt{2\pi}\,\sigma_b} \exp\left(-\frac{(E - E_0)^2}{2\sigma_b^2}\right)\]

Managing Experimental Effects

  • Click + to create a new experimental effects entry.

  • Select an entry and click - to delete it.

  • Double-click to edit.

Note

Experimental effects entries apply to both data segments and calculation segments simultaneously. Remember to enable or disable them appropriately depending on the calculation being performed.

Add Experimental Effect Dialog

Associated Segments

The Segments List field specifies which calculation segments (from the Segments tab) this experimental effect applies to. Enter segment numbers using:

  • Comma-separated values: 3,4,5,7,8,9

  • Ranges: 3-9

  • Combinations: 3,6,7-14

Integration Points

The number of points used for numerical integration when computing energy convolution or target integration. The required number depends on how rapidly the cross section changes with energy. Adjust using the spinner or enter a value directly.

Gaussian Energy Convolution

Check Include Gaussian Convolution to convolve the calculated cross section with a Gaussian beam energy distribution.

Sigma (MeV)

The full width at half maximum of the Gaussian convolution function. Although beam resolution is typically of order keV, the value must be entered in MeV (e.g., 0.001 for 1 keV).

Target Integration

Check Include Target Integration to account for beam energy loss in the target.

Active Density (atoms/cm2)

The areal density of the active target material (the nuclei producing the reactions of interest in a mixed-material target).

Stopping Cross Section

The effective stopping cross section must be entered as a continuous function of energy using a parameterized equation:

  • The variable y represents the stopping cross section.

  • The variable x represents the energy.

  • Parameters are labeled a0, a1, a2, etc.

Example – a second-order polynomial with 3 parameters:

y = a0 + a1*x + a2*x^2

Set the Number of Parameters to 3 and enter the values for a0, a1, and a2 in the table.

AZURE2 also provides tools to look up stopping powers by element or compound formula.

Straggling

Check Include Straggling to account for energy straggling of beam particles in the target. Enter the straggling coefficient in the provided field.

Attenuation Coefficients (Q-Coefficients)

Attenuation coefficients correct for the finite solid angle of detectors in close geometry, following the method of M. E. Rose, Physical Review 91, 610 (1953).

The angular distribution is corrected as:

\[W(\theta) = \sum_{i=0}^{\infty} a_i \, Q_i \, P_i(\cos\theta)\]

where \(Q_i\) are the attenuation coefficients.

Set the number of coefficients using the spinner and enter the \(Q_i\) values in the table (default value is 1.0 for each).