Orthogonal Operators: Applications, Origin and Outlook

Abstract

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

Extension of the Pt III Analysis

“…The even levels in [1] were interpreted in a model of the mixed 5d 8 + 5d 7 6s + 5d 6 6s 2 configurations by means of the Cowan code [11,12], with the 53 cm −1 standard deviation of the calculated level energies from the measured ones. Later, the orthogonal parameters technique [13][14][15][16] was applied to the calculations of the even energy levels [17]. Wyart et al [18] performed a systematic study of the (5d + 6s) 8 mixed group in the isoelectronic sequence Ir II-Bi VIII by means of a generalized leastsquares (GLS) fit.…”

“…The energy parameters, representing these effects, used in the fitting of the odd levels, are shown in Table 3. The meaning of these parameters can be found in [15,16] and in the references therein. Ab initio values of these parameters were obtained by fitting the energy levels calculated using the Parpia et al MCDF program [21].…”

Wavelengths and Energy Levels of Singly Ionized Nickel (Ni ii) Measured Using Fourier Transform Spectroscopy

“…As a result, the mean deviation of the fit is frequently reduced by an order of magnitude in a physically significant way. A detailed explanation of the orthogonal operator approach is found in Uylings & Raassen (2019) and Uylings (2021).…”