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

This paper suggests a method of evaluation of uncertainties in calculated transition probabilities by randomly varying parameters of an atomic code and comparing the results. A control code has been written to randomly vary the input parameters with a normal statistical distribution around initial values with a certain standard deviation. For this particular implementation, Cowan’s suite of atomic codes (R.D. Cowan, The Theory of Atomic Structure and Spectra, Berkeley, CA: University of California Press, 1981) was used to calculate radiative rates of magnetic-dipole and electric-quadrupole transitions within the ground configuration of titanium-like iron, Fe V. The Slater parameters used in the calculations were adjusted to fit experimental energy levels with Cowan’s least-squares fitting program, RCE. The standard deviations of the fitted parameters were used as input of the control code providing the distribution widths of random trials for these parameters. Propagation of errors through the matrix diagonalization and summation of basis state expansions leads to significant variations in the resulting transition rates. These variations vastly differ in their magnitude for different transitions, depending on their sensitivity to errors in parameters. With this method, the rate uncertainty can be individually assessed for each calculated transition.