Calculate Tab

The Calculate tab controls the execution of AZURE2 calculations. Select a calculation type from the drop-down menu and click Save and Run to execute.

Calculation Types

Calculate With Data

Performs a single R-matrix calculation using the current parameters, comparing against the experimental data defined in the Segments tab. No fitting is performed.

This mode is useful for:

  • Checking the quality of initial parameter values before fitting.

  • Manually adjusting parameters (especially interference signs) until a reasonable starting point is reached.

Fit With Data

Performs an automated least-squares (\(\chi^2\)) fit to the experimental data using the MINUIT2 minimization package. The fit adjusts all unfixed parameters to minimize the chi-squared.

During the fit:

  • The \(\chi^2\) values are updated every 1000 iterations.

  • Output files are written periodically so progress can be monitored in the Plot tab.

  • The final \(\chi^2\) is printed to the output area and to chiSquared.out.

Important

Each fit overwrites all standard output files. If you are testing different fitting options, rename or move the output files before starting a new fit.

Extrapolate Without Data

Performs a single calculation (no minimization) using the segments defined in the Segments Without Data section. No experimental data is considered.

Common uses:

  • Interpolate a cross section with finer energy spacing for plotting.

  • Extrapolate to astrophysically relevant energies.

  • Calculate the total cross section from a differential fit.

  • Compute the cross section for the inverse reaction.

  • Calculate a previously unobserved cross section using only level parameters.

Perform MINOS Error Analysis

Runs the MINOS uncertainty estimation routine from MINUIT2 to calculate asymmetric parameter uncertainties. Results are written to param.errors and covariance_matrix.out.

Tip

Running MINOS is also a useful test of fit robustness. If MINOS crashes, it often indicates that one or more parameters are unconstrained by the data. Try fixing different parameters to identify the problematic one(s).

Calculate Reaction Rate

Calculates the thermonuclear reaction rate by numerically integrating the cross section over a Maxwell-Boltzmann energy distribution:

\[N_A \langle \sigma v \rangle = \left(\frac{8}{\pi\mu}\right)^{1/2} \frac{N_A}{(kT)^{3/2}} \int_0^\infty \sigma(E) \, E \, e^{-E/kT} \, dE\]

Additional fields appear for this mode:

Entrance / Exit Pair Keys

Specify the particle pair keys for the reaction.

Temperature Source

Choose between:

  • Grid – specify minimum, maximum, and step temperatures (in GK).

  • File – provide a file listing specific temperatures (single column, in GK).

Results are written to reactionrates.dat.

Warning

Numerical integration is limited to broad resonance structures. If resonances are narrower than approximately 1 keV, the integration may fail. For narrow resonances, calculate the contribution separately using the narrow-resonance approximation.

Minimizer Selection

Minuit2 (default)

The standard MINUIT2 minimizer from CERN.

NLopt (if available)

Alternative minimizer with several algorithms: SBPLX, COBYLA, BOBYQA, NEWUOA, PRAXIS, Nelder-Mead.

The minimizer selection is only available for fitting modes.

Chi-squared Variance

The target variance for the chi-squared minimization (default: 1.0). Only applies to fitting modes.

Parameter and Integral Files

Parameters File

  • Create New Parameters File (default) – use the parameters currently entered in the GUI.

  • Use – load parameters from a previously saved file (e.g., param.sav from a completed fit).

External Capture Integrals File

  • Create New Integrals File (default) – compute the external capture integrals from scratch.

  • Use – load a previously computed integrals file (intEC.dat) to speed up calculations.

Note

The integrals file can be reused as long as the calculation segments, channel radii, and \(J^\pi\) values have not changed. Level energies, widths, and ANCs can be changed freely.

Execution Controls

Save and Run

Saves the project and starts the selected calculation. Output is displayed in real time in the text area at the bottom.

Stop AZURE2

Gracefully stops a running calculation. There may be a brief delay before the calculation concludes. Output files from the last completed iteration are preserved.