Treatment of Perturbation in Energy Levels using Hypothetical Perturbers: A Case Study of Mg X

Abstract

Abstract: Rydberg atoms exhibit hydrogen-like behavior in which the motion of a single electron is governed by the effective potential of the ionic core, consisting of the nucleus and the remaining electrons. The energies of hydrogenic atoms are commonly calculated using the Rydberg-Ritz formula, which can also be adapted for lithium-like systems by introducing a non-integer principal quantum number. The deviation from the integer quantum number is referred to as the quantum defect. This approach successfully describes the energy levels of most Rydberg atoms and ions. However, when perturbations occur between nearby energy levels, the standard Rydberg-Ritz formula becomes inadequate and must be replaced by the Extended Martin formula.

Accurate determination of perturbed energy levels generally requires detailed knowledge of the interacting perturber states, which are often difficult to identify experimentally. This study presents an alternate and effective method for treating perturbed Rydberg levels using hypothetical perturbers. The proposed approach was applied to four perturbed series of Mg X, and the energies of all four series were successfully determined using a new technique based on hypothetical levels to account for perturbations arising from foreign configuration interaction.

The calculated Rydberg energies were further validated through the computation of transition probabilities, oscillator strengths, and line strengths. In total, 68 Rydberg energy levels and 935 spectroscopic parameters were calculated. Among these, 29 Rydberg levels and 751 transition probabilities, oscillator strengths, and line strengths are not currently available in the National Institute of Standards and Technology (NIST) database.

Keywords: Rydberg levels, Transition probabilities, Oscillator strength, Perturbation theory, Mg X.