Segments Tab

The Segments tab defines the energies and angles at which cross sections are calculated. It is divided into two halves:

Segments From Data (upper) – for calculations that reference experimental data files.
Segments Without Data (lower) – for pure calculations and extrapolations.

Each segment is automatically assigned a numerical key that is referenced in the Experimental Effects tab.

Segments From Data

These segments are used with the Calculate Segments From Data and Fit Segments From Data calculation modes. Cross sections are computed only at the energies and angles present in the experimental data file.

Creating a Data Segment

Click the + button in the lower-left corner of the upper frame. A dialog appears with the following fields:

Entrance and Exit Pair Keys

Select the entrance and exit particle pairs by their numerical keys (as assigned in the Particle Pairs tab). Values can be entered directly or set using the spinner controls.

Energy Range

The Low Energy and High Energy fields select a range of data from the data file. To include all data, set the range to cover the entire file. Energies are in the laboratory frame, in MeV.

Angle Range

For differential cross sections, specify the Low Angle and High Angle (in degrees, laboratory frame) to select a subset of the data. For angle-integrated or phase-shift data types, these fields are disabled.

Data Type

Select from the drop-down menu:

Angle Integrated	Angle-integrated cross section data.
Differential	Differential cross section data at specific angles.
Phase Shift	Phase shift data. Requires specifying the total angular momentum (J) and orbital angular momentum (l). The convention is \(-90° < \theta_\text{lab} < 90°\).
Total Capture	Angle-integrated total capture cross section, summed over all gamma-ray transitions. Each significant gamma-ray cascade transition must be defined as a separate particle pair.
C.M. Differential	Differential cross section data given in the center-of-mass frame.
Analyzing Power	Vector analyzing power \(A_y\) for a spin-1/2 projectile, in the Madison convention. Angles are centre-of-mass, as for C.M. Differential, and the data file carries `E_lab theta_cm A_y dA_y`. Because \(A_y\) is a ratio, Vary Norm? is disabled for it – a normalization factor has no meaning for a quantity that is already normalized. See Polarization Observables in R-Matrix Theory.

Data Normalization

A normalization factor applied to the data yield. Default is 1.0.

Normalization Error (%)

The relative systematic uncertainty of the data set, entered as a percentage. This is included in the chi-squared calculation using the D’Agostini method.

Vary Norm?

Check this box to allow the normalization factor to be varied as a free parameter during fitting.

Energy Shift

An energy calibration shift applied to the data (in MeV).

Vary Energy Shift?

Check this box to allow the energy shift to be varied during fitting.

Data File

Path to the experimental data file. Use the Choose… button to browse, or enter the path directly. Paths can be absolute or relative to the Input file directory.

Advanced Mode

When checked, enables advanced operations for combining multiple reaction channels:

Sum – sum cross sections from multiple entrance/exit pair combinations.
Ratio – compute the ratio of cross sections from different channels.

Editing and Managing Data Segments

Double-click a segment to edit it.
Select a segment and click - to delete it.
Use the arrow buttons on the right to reorder segments.
Use Check All / Uncheck All to quickly enable or disable all segments.
Use the entrance and exit pair filter dropdowns to show only segments for specific particle pairs.

Tip

Data from different experiments should be placed in separate files. Multiple segments can reference the same data file with different energy or angle ranges to create separate excitation curves or angular distributions.

Important

When including systematic uncertainties, carefully consider the segmentation scheme to avoid double-counting uncertainties across segments that share the same data.

Segments Without Data

These segments define energy and angle ranges for pure calculations (no experimental data), and are used with the Calculate Segments Without Data mode. Typical uses include:

Interpolating a cross section with finer energy steps than the data provides.
Extrapolating to astrophysically relevant energies.
Calculating a total cross section from a differential fit, or vice versa.
Computing the cross section for the inverse reaction.
Extracting angular distribution coefficients.

Creating a Test Segment

Click the + button in the lower half. The dialog is similar to the data segment dialog but includes:

Energy Range with Step Size

Specify Low Energy, High Energy, and Energy Step (all in MeV). For a single energy point, set low and high to the same value and step to zero.

Angle Range with Step Size

Same as energy: specify Low Angle, High Angle, and Angle Step (in degrees).

Data Types

In addition to the standard types, this mode supports:

Angular Distribution Coefficient – output Legendre polynomial coefficients. Requires specifying the polynomial order.
Analyzing Power – the vector analyzing power on the chosen energy and angle grid, in the centre-of-mass frame.

Warning

Errors may occur if you specify an energy or angular range that is not kinematically allowed, or if the energy is too low and the penetrability becomes vanishingly small.

Note

An analyzing power measured on a thin target should be given a segment with no target integration. \(A_y\) averaged over a thick target is weighted by the cross section, and since Rutherford scattering diverges at low energy where \(A_y\) is essentially zero, a thick target drives the average towards zero. This is physical, and it is explained in Computing the Analyzing Power in AZURE2.

When an analyzing-power segment is plotted, the Plot tab switches the y-axis to a linear scale and to Cross Section automatically: a logarithmic axis cannot display a quantity that goes negative, and an S-factor conversion is meaningless for a ratio.