Assessing Uncertainties of Theoretical Atomic Transition Probabilities with Monte Carlo Random Trials

Area of Science:

• Atomic Physics
• Computational Quantum Chemistry
• Spectroscopy

Background:

• Accurate calculation of transition probabilities is crucial for understanding atomic spectra and astrophysical phenomena.
• Quantifying uncertainties in these calculations is essential for reliable scientific interpretation.

Purpose of the Study:

• To develop and demonstrate a method for evaluating uncertainties in calculated atomic transition probabilities.
• To assess the impact of parameter variations on transition rates.

Main Methods:

• A control code was developed to randomly vary input parameters of an atomic code (Cowan's suite) using a normal statistical distribution.
• Slater parameters were fitted to experimental energy levels using Cowan's RCE program, and their standard deviations were used to define parameter distribution widths.
• The method was applied to calculate radiative rates of magnetic-dipole and electric-quadrupole transitions in Fe V.

Main Results:

• Propagation of errors through matrix diagonalization and basis state expansions led to significant variations in transition rates.
• The magnitude of these variations differed substantially among transitions, indicating varying sensitivity to parameter errors.
• The developed method allows for individual uncertainty assessment for each calculated transition rate.

Conclusions:

• The proposed method effectively quantifies uncertainties in calculated transition probabilities.
• This approach provides a more robust understanding of the reliability of atomic transition rate calculations.
• The findings are applicable to various atomic systems and transitions, enhancing the accuracy of spectroscopic data.