Weakest Bound Electron Potential Model Research Articles

The calculation of transition probabilities for atomic oxygen

The atomic transition probabilities for multiplet and individual lines and oscillator strengths for multiplet lines between some triplet and quintet levels have been calculated using weakest bound electron potential model theory (WBEPMT) in neutral oxygen. The results obtained in this work are in good agreement with the data obtained from different theoretical methods given in the literature and with critically evaluated values taken from NIST. Moreover, some new transition probabilities and oscillator strengths for highly excited levels in atomic oxygen have been obtained using this method.

Theoretical calculation of energy levels of Sr I

In this paper, results of theoretical calculation of energy levels for the [Kr] 4d3/2nd3/2 (J= 1), [Kr] 4d3/2ng7/2 (J= 2), [Kr] 4d5/2ng9/2 (J=2), [Kr] 4d5/2ng7/2 (J=2), [Kr] 4d5/2ns1/2 (J=2) and [Kr] 4d5/2nd5/2 (J=1) series of doubly excited atom Sr are presented using the weakest bound electron potential model (WBEPM) theory. The comparison of the results with the perturbations and those without the perturbations shows that the effect of proper foreign levels is important in the calculation of energy levels, so we think perturbations of foreign levels should be taken into account in the calculation of doubly excited states of Sr I. The accuracy of most of our results is better than 1 cm−1 with few of them being more than 1 cm−1. Therefore, we can say that the WBEPM theory is an efficient one for calculating energy levels of doubly excited Sr I.

Comparison of transition probabilities calculated using different parameters on WBEPM theory for some p‐d and d‐p transitions in excited atomic nitrogen

AbstractThe transition probabilities between individual and multiplet lines for some quartet terms of excited p‐d and d‐p transition arrays of nitrogen atom have been calculated using the weakest bound electron potential model (WBEPM) theory. For determination relevant parameters, we employed both numerical Coulomb approximation (NCA) method and numerical nonrelativistic Hartree–Fock (NRHF) wave functions for expectation values of radii. The necessary energy values have been taken from experimental energy data in the literature. The expectation values of radii obtained using the two different methods have been employed in the calculation of transition probabilities of all transition arrays. The results obtained have been compared with either each other or NIST data. Good agreement with accepted values taken from NIST has been observed for related excited transitions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

The calculation of transition probabilities between individual lines for atomic lithium

The atomic transition probabilities for individual and multiplet lines of lithium atom are obtained using weakest bound electron potential model theory (WBEPMT) and exact quantum defect theory. The results obtained using two different methods agree very well with the accepted values taken from NIST, MCHF results and Opacity Project values. These methods require substantially less computational time than well-known theoretical methods, thereby permitting the study of 108 transitions.

The theoretical calculation of transition probabilities for some excited p-d transitions in atomic nitrogen

The atomic transition probabilities are calculated for individual lines between some quartet terms of 3p↦4d and 3p↦5d transition arrays using weakest bound electron potential model theory (WBEPMT). In the determination of relevant parameters which are needed for calculation of transition probabilities, we employed numerical non-relativistic Hartree-Fock wave functions for expectation values of radius in both ground and excited states unlike to NCA method used on traditional WBEPMT procedure. We have obtained very good agreement between our results and the accepted values taken from NIST.

Variational treatment on the energy of the He‐sequence ground state with weakest bound electron potential model theory

AbstractThe concept of spin–orbital of the weakest bound electron is described used to construct the antisymmetric wave function of atomic or ionic systems within weakest bound electron potential model theory (WBEPM theory). The total energies of He‐sequence (Z = 2–9) in the ground states is calculated with a variational method. The effect of fixed orbital approximation is discussed quantitatively. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Theoretical Analysis on 3dnl J=1e–5e Autoionizing Levels in Ca

Previous studies on the even parity 3dnl J=1–5 autoionizing levels of calcium have been critically evaluated. These levels have been studied within the framework of the weakest bound electron potential model theory. 30 3dnl series are treated and the results are listed here. In these calculations, the jj coupling scheme is used. It is remarkable that the perturbation approach that has been emphasized in our calculations so as to adequately consider the correlation between the two excited electrons is more important than in the case of singly excited states. Compared with the experimental results and the values from other theoretical methods, the present results are in concurrence with the experimental data, and showed comparative accuracy with other methods. Some levels, which have not been reported previously, are predicted here.

Theoretical study of energy levels of atomic Ga

There are few documented values of the energy levels of the gallium atom. The values in some series remain blank and some series have no values in high Rydberg states. In this paper, based on the weakest bound electron potential model theory we treat the many-valence electron system of the excited gallium atom as a single-electron system of the weakest bound electron and use Martin's expression to determine the parameters. Most of the results are satisfying with deviations less than 1 cm–1 compared with the documented values in the National Institute of Standards and Technology. In addition, we fill many blanks in some high Rydberg energy levels of the gallium atom. PACS Nos.: 31.15.Ct, 32.10.Fn

Weakest bound electron potential model theory

AbstractDiffering from the self‐consistent field (SCF) method, in which an N‐electron atom problem is treated as a one‐electron problem with the use of a basic assumption of average potential, we develop a unified weakest bound electron potential model (WBEPM) theory. The relativistic form of the theory is given for the first time and is combined with the nonrelativistic form introduced in previous work to arrive at the unified WBEPM theory. The theory has two main ideas. First, from consideration of viewpoints of the dynamic successive ionization and the choice of zero of energy in quantum mechanics, an N‐electron atom system can be subdivided into N subsystems only containing a weakest bound electron (WBE) in each of subsystems. For each subsystem by separation of WBE and non‐weakest bound electrons (NWBE), WBE is believed to move in an approximate potential field provided by a “core” consisting of NWBEs and the nucleus. Thus, a complicated N‐electron problem is reduced to a simple analytical one‐electron problem of WBE. Second, the properties of an atom, such as total wave function, total energy, atomic energy levels, and transition between energy levels, can be investigated through the behaviors of a WBE or several WBEs, or up to all WBEs. Several excellent illustrative results show that the theory is capable of attaining very good computational accuracy. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Calculation of excited‐state ionization potential for boron‐like sequence

AbstractExcited‐state ionization potentials for boron‐like sequence with Z = 5–19 are studied systematically, using the weakest bound electron potential model theory (WBEPM theory) and iso‐spectrum‐level series conception. Nonrelativistic ionization energy is derived from the theory. Relativistic effects are included in the Breit–Pauli approximation. Comparison of the calculated excited‐state ionization potential with available experimental data is carried out for 1s22s22p 2P, 1s22s23s 2S1/2, 1 s22s23p 2P, 1s22s23d 2D5/2, 1s22s24d 2D5/2, 1s22s25d 2D5/2, and 1s22s26d 2D5/2 series. The present results depart from experimental results by no more than 0.133 eV for all 81 results for which experimental data are available. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Calculation of the Energy Levels to High States in Atomic Oxygen

Energy levels of configuration 2s2 2p3 (4So, 2Do, 2Po) nl in atomic oxygen are reported within the weakest bound electron potential model theory (WBEPM theory). In the calculations interactions between different series are explicitly accounted for by introducing a combined quantum defect formula. The present results show a reasonably good agreement with the critically evaluated NIST data. Furthermore, predictions of energy levels are extended to high Rydberg states.

Theoretical Study of Energy Levels and Transition Probabilities of Singly Ionized Aluminum (Al II)

Within the Weakest Bound Electron Potential Model (WBEPM) theory, calculations for energy levels and transition probabilities of singly ionized aluminum (Al II) are performed, and good agreement with experimental or accepted values is obtained. To treat properly the perturbed states, foreign perturbers are taken into account in studying the energy levels, meanwhile, a set of coupled equations is employed to determine the parameters effective nuclear charge Z ', effective principal quantum number n ', and effective angular quantum number l ' needed for the calculation of transition probabilities.

Study on energy levels of atom neon

In this article, energy levels of atom neon are studied systematically using the weakest bound electron potential model theory. Under the concept of spectrum-level-like series, energy levels are expressed as a function of principal quantum number. In the calculation, the perturbations among different series are included. The results of 1s 22s 22p 5( 2P 3/2 o )ns, 1s 22s 22p 5( 2P 3/2 o )np and 1s 22s 22p 5( 2P 3/2 o )nd series are given and compared with experimental values. Deviations between the present results and experimental values are generally less than 1 cm −1.

Systematical study on the ionization potential of excited states in carbon-like sequence

Ionization potential of excited states have been calculated for the 1s 22s 22p 2 3P 2, 1s 22s 22p3s 3P 0 2, 1s 22s 22p3d 3D 0 3, 1s 22s 22p3d 1F 0 3, and 1s 22s 22p4d 3D 0 3 series of carbon-like sequence from Z=6 to Z=23 on the basis of the weakest bound electron potential model theory and the concept of iso-spectrum-level series. In the calculation, the non-relativistic weakest bound electron potential model theory is used to calculate the non-relativistic energies and a fourth-order polynomial in nuclear charge Z is employed to evaluate the relativistic correction. Calculated values are compared with the experimental compiled results. Agreement with the experimental compiled results is generally within 0.1%.

Transition probabilities for Ne II

The Weakest Bound Electron Potential Model (WBEPM) theory is employed to calculate transition probabilities for Ne II in this paper. The parameters Z *, n * and l * are determined through fitting the experimental value of energy level and the expectation value of radial distance. Compared with most experimental results presently available and the values of critical compilation, the present results are accurate and in good agreement with them. Simple calculation procedure and accurate results can be both obtained from the present method.

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

AbstractWith the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p 3P, [He]2s3s 1S0, [He]2s3p 1P, [He]2s3d 1D2, and [He]2s4d 1D2 series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003

Theoretical calculation of transition probabilities in neutral fluorine

The weakest bound electron potential model (WBEPM) theory is used to calculate transition probabilities for individual lines in neutral fluorine, for which transition probability data are scarce. A coupled equation concerning energy ε and the radial expectation value 〈 r〉 of the weakest bound electron is proposed to determine the parameters used in the calculation of transition probability. The accuracy of present results has been tested from comparisons with the most theoretical or experimental results presently available.

Calculation of High Rydberg Levels of Atom Zn with the WBEPM Theory

Within the weakest bound electron potential model theory, we treat the many-valance electron system of atom Zn as single electron system and use the extended martin's expression to determine parameters. The results are satisfying with deviations no more than 1 cm -1 compared with the experimental values.

Radiative Lifetimes and Atomic Transition Probabilities for Atomic Carbon and Oxygen

In this paper, the weakest bound electron potential model (WBEPM) theory is employed to calculate radiative lifetimes, transition probabilities, and oscillator strengths for atomic carbon and oxygen. Results for the lifetimes, transition probabilities, and oscillator strengths of individual lines are reported and compared with theoretical and experimental results currently available. In order to test the accuracy of our results further, oscillator strengths for multiplets are also calculated, and results are compared with other theoretical or experimental results. The good agreement obtained in comparison shows that present method with a simple approach is reliable.

Theoretical resonance transition probabilities and lifetimes for atomic nitrogen

In this paper, resonance transition probabilities and radiative lifetimes of atomic nitrogen are calculated employing the weakest bound electron potential model (WBEPM) theory. In the calculation, a coupled equation concerning the 〈 r〉 and the energy of the weakest bound electron is used to determine parameters Z ∗,n ∗ , and l ∗ . With these parameters, matrix element can be evaluated. And then, lifetimes and transition probabilities can be further obtained. The accuracy of present results has been tested from comparisons with the most accurate theoretical or experimental results presently available.