Rydberg energies and transition probabilities of Li I for np–ms (m ≤ 5) transitions

Abstract

Background Mathematical modeling provides grounds for understanding scientific systems theoretically. It serves as a guide for experimentalists in determining directions of investigation. Recently, the Covid-19 pandemic has caused disturbances in almost every walk of life. Scientists have played their role and have continued research on the effects of the pandemic. Various mathematical models have been used in different branches of science (Djilali et al. in Phys Scr 96 12 124016, 2021; Math Biosci Eng 18(6):8245–8256, 2021; Zeb et al. in Alex Eng J 61(7):5649–5665). Well-established mathematical models give results close to those obtained by experiments. The Weakest Bound Electron Potential Model is one such model, which explains hydrogen-like atoms and ions. This model has been used extensively for hydrogen-like atoms and ions to calculate energies of Rydberg levels and ionization energies. This model has been used extensively for hydrogen-like atoms and ions to calculate energies of Rydberg levels and ionization energies. Results This paper presents the energies of the Rydberg series, 2s2ns, and 2s2np of Li I, calculated using WBEPM. The energies are used to calculate transition probabilities from np to 2s, 3s, 4s, and 5s levels. The transition probabilities are compared with corresponding values in published data where available. The agreement with known values is good; most of the transition probabilities calculated in this work are new. A computer program was developed to find the value of the dipole matrix element. The calculations were further verified by calculating the lifetimes of some low-lying levels. Conclusions Four series of Li I have been studied, and energies of the Rydberg levels in the series were calculated. The energies then are used to calculate transition probabilities from np to ms transitions, where m = 2, 3, 4, & 5 and n = 1–15. The results are compared where available. An excellent agreement with previously published data shows the reliability of calculations. Most of the transition probabilities are new.

Mean Lifetimes of ns, np, nd, & nf Levels of N V

“…The cooper minimum was first observed for alkali atoms. It occurs due to overlapping the positive and negative amplitude of the wavefunctions of the levels taking part in the transition [16]. Due to this, the dipole matrix elements have zero or a minimum value for a particular set of principal quantum numbers of both levels.…”

“…The reason could be its closeness to the core, which may affect the effective charge compared to the other levels that lie relatively far from the core. It was observed in the calculations of transition probability and lifetimes of the same configuration in Li I [16], Be II [17], and C IV [18] that the calculated and experimental values are slightly different. For the configuration 1s 2 2p in Li-like atoms and ions, one should expect a slight difference in theoretical and experimental lifetimes.…”

Computation of Characteristics of C IV Transitions

“…Hence Schrodinger equation for hydrogen atoms can be used for such atoms and ions with the approximation that all other electrons in the inner shells together with the nucleus form the core, like the hydrogen atom, e.g., hydrogen-like atoms and ions are Li I, Be II, B III, C IV, N V, and O VI. The theory used in this work is the same as in [22]. The Schrodinger equation for hydrogen-like atoms and ions is given by,…”

Non-Relativistic Calculation of Excited-State Ionization Potentials for Li-Like Ions Using Weakest Bound Electron Potential Model Theory

“…The group also reported transition probability of Lithium atom and lithium like ions by using the same theory [14][15][16][17][18][19]. In 2022, R. Siddiq et al studied the four series of Li, by using WBEPMT they calculated energies and transition probabilities of the series [20]. Saeed et al evaluated transition probabilities and lifetimes of the lithium levels, and found new lifetimes using polynomial of each of the ns, np, nd and nf series [21].…”