Weakest Bound Electron Potential Model Theory Research Articles

Spectroscopic properties of lithium like ions: Prospective elements for quantum computation

Rydberg physics is the most exquisite playground for the exploration of quantum technologies. Therefore, in this spectral investigation based on weakest bound electron potential model theory (WBEPMT). The quantum defects and Rydberg energies of low-lying and high-lying spectral Rydberg energy sequence in the following configurations: 1s2ns2Se1/2 and 1s2np2Po1/2 in Lithium-like ions (Z=4-6) Beryllium (Be II), Boron (B III) and Carbon (C IV) are computed with their radial expected values. Total 43 low-lying energies and quantum defects are computed and compared with 25 low lying radial expected values. The results are in good agreement with the previously published experimental / theoretical results. Based on the good agreement of low-lying data, total 257 new values of high-lying Rydberg energies and quantum defects are computed with 575 radial expected values currently not listed at NIST. The deviation in both sets of data doesn’t exceed 1 cm-1 .

Rydberg energy levels and quantum defects of B II, Ge II, Si II of subgroups III and IV

Theoretical computations of Rydberg energy levels series and atomic lifetimes for singly ionized boron (B II), silicon (Si II), and germanium (Ge II) have been performed. In the theoretical computation weakest bound electron potential model theory (WBEPMT) is employed. Regularities of changes in quantum defects for the following Rydberg states series: 2sns (1S0), 2snp ([Formula: see text]), 2snf ([Formula: see text], [Formula: see text], [Formula: see text]), 2snf ([Formula: see text]) of B II; 3s2ns (2S1/2), 3s2nd (2D3/2,5/2), 3s2nf ([Formula: see text]), 3s2ng (2G7/2,9/2) of Si II; and 4s2nf ([Formula: see text]), 4s2nf ([Formula: see text]), 4s2ng (2G7/2,9/2) of Ge II, up to n = 50 are presented. The atomic lifetimes of the following series: 1s22sns (1S0), 1s22snp ([Formula: see text]), 1s22snd (1D2) of B II; 3s2ns (2S1/2), 3s2nf ([Formula: see text]) of Si II; and 4s2ns (2S1/2) of Ge II are predicted with good accuracy. Some high-lying Rydberg energy levels and atomic lifetimes have been presented for the first time. The series for which Rydberg energy levels are computed in this work are unperturbed series.

Precise Computation of Energy Levels and Radiative Lifetimes in the s, p, d, and f Sequence of Hydrogen Isotope, with Natural Line Widths

Energy levels and Radiative lifetimes in Deuterium for the following: ns 2 S 1/2 (n≥2), np 2 P o (1/2,3/2) (n≥2), nd 2 D (3/2,5/2) (n≥3), and nf 2 F o (5/2,7/2) (n≥4) sequence have been evaluated with uncertainties in energies caused due to uncertainty principal. Theoretical calculations performed utilizing the Weakest Bound Electron Potential Model Theory (WBEPMT). Both sets of data show quite an excellent agreement with the experimental data listed at NIST. This theoretical computation is also a continuation of the work by Raza. S. et al. in Neutral Hydrogen. The high ‘n’ (principal quantum number) values for both sets of data are presented very first time by utilizing WBEPMT. Keywords: Energy levels, Radiative lifetimes, Quantum defects, Weakest bound electron, Natural line width. DOI : 10.7176/JNSR/9-10-07 Publication date :May 31 st 2019

Oscillator strengths and transition probabilities for singly ionized terbium

Electric dipole transition probabilities and oscillator strengths for singly ionized terbium (Tb II) have been calculated with the weakest bound electron potential model (WBEPM) theory using experimental energy levels and theoretical expectation values of orbital radii corresponding to those energy levels under the assumption of the Jj coupling scheme. The transition probabilities and the oscillator strengths calculated have been compared with available data in the literature. A good agreement has been obtained. In this work, the WBEPM theory has been applied to heavy atoms, such as Tb II, for the first time.

Electric quadrupole transition probabilities for atomic lithium

Electric quadrupole transition probabilities for atomic lithium have been calculated using the weakest bound electron potential model theory (WBEPMT). We have employed numerical non-relativistic Hartree–Fock wavefunctions for expectation values of radii and the necessary energy values have been taken from the compilation at NIST. The results obtained with the present method agree very well with the Coulomb approximation results given by Caves (1975). Moreover, electric quadrupole transition probability values not existing in the literature for some highly excited levels have been obtained using the WBEPMT.

Transition probabilities, oscillator strengths and radiative lifetimes for Zn II

The electric dipole transition probabilities, the oscillator strengths and the lifetimes of excited levels have been calculated using the weakest bound electron potential model theory (WBEPMT) and the quantum defect orbital theory (QDOT) for singly ionized Zinc. In the calculations, the many of transition arrays including both multiplet and fine-structure transitions are considered. We have employed numerical Coulomb approximation (NCA) wave functions and numerical non-relativistic Hartree–Fock (NRHF) wave functions for expectation values of radii in determination of parameters. The present results are consistent with the available theoretical and experimental results. Some of these results are reported for the first time.

Lifetimes of excited levels for atomic silicon

The lifetimes of some excited levels for atomic silicon are calculated using the weakest bound electron potential model theory (WBEPMT) and the quantum defect orbital theory. In the WBEPMT framework, we have employed both numerical Coulomb Approximation wave functions and numerical non-relativistic Hartree–Fock wave functions for expectation values of radii. The obtained lifetime results have been compared with theoretical and experimental data in the literature.

Electric quadrupole transition probabilities for singly ionized magnesium

Electric quadrupole transition probabilities for Mg II have been calculated within the weakest bound electron potential model (WBEPM) theory using experimental energy levels and theoretical expectation values of orbital radii corresponding to those energy levels under the assumption of the LS coupling scheme. In this work, the WBEPM theory has been applied to forbidden transitions for the first time. The present results are consistent with earlier theoretical calculations. Some of these results are reported for the first time.

Transition probabilities and radiative lifetimes of levels in F I

The electric dipole transition probabilities and the lifetimes of excited levels have been calculated using the weakest bound electron potential model theory (WBEPMT) and the quantum defect orbital theory (QDOT) in atomic fluorine. In the calculations, many of transition arrays included both multiplet and fine-structure transitions are considered. We employed Numerical Coulomb Approximation (NCA) wave functions and numerical non-relativistic Hartree–Fock (NRHF) wave functions for expectation values of radii in determination of parameters. The necessary energy values have been taken from experimental energy data in the literature. The calculated transition probabilities and lifetimes have been compared with available theoretical and experimental results. A good agreement with results in literature has been obtained. Moreover, some transition probability and the lifetime values not existing in the literature for some highly excited levels have been obtained using these methods.

Transition probabilities, oscillator strengths and lifetimes for singly ionized magnesium

The electric dipole transition probabilities, oscillator strengths and lifetimes have been calculated using the weakest bound electron potential model theory (WBEPMT) for singly ionized magnesium. In the calculations both multiplet and fine structure transitions are studied. We have employed both the numerical Coulomb approximation (NCA) method and numerical non-relativistic Hartree–Fock (NRHF) wave functions for expectation values of radii. The calculated oscillator strengths and lifetimes have been compared with MCHF results given by Fischer et al. (2006). A good agreement has been obtained with the MCHF results. Moreover, some new transition probabilities, oscillator strengths and lifetime values, not existing in the data bases for highly excited levels in singly ionized magnesium, have been obtained using this method.

Oscillator strengths for singly ionized oxygen

The electric dipole oscillator strengths for multiplet and individual lines between some doublet and quartet levels have been calculated using the weakest bound electron potential model theory (WBEPMT) in singly ionized oxygen. We employed both numerical Coulomb approximation (NCA) wave functions and numerical non-relativistic Hartree-Fock (NRHF) wave functions for expectation values of radii in determination of parameters. The calculated oscillator strengths have been compared with available theoretical and experimental results. A good agreement with results in literature has been obtained. Moreover, oscillator strengths not existing in the literature for some highly excited levels have been obtained using this method.

Calculation of He Atom Ground-State Energy Using Double Generalized Laguerre Polynomial in the Weakest Bound Electron Potential Model Theory

We calculated the He atom ground-state energy using a double generalized Laguerre polynomial in the weakest bound electron potential model(WBEPM) theory. An expression for the expectation value of the He atom ground-state energy was derived. We obtained minimum values for the He atom ground-state energy(Emin) . A comparison was made to the results from the Hartree-Fock(HF) method using a double zeta function. Our result was slightly better than the result obtained using a double zeta function in the HF method. We thus show that the linear combination technique can easily be used in WBEPM theory.

Investigation of the effects of expectation values for radii on the determination of transition probabilities using WBEPM theory

Transition probabilities for some excited s-p and p-s transition arrays of neutral nitrogen have been calculated using the weakest bound electron potential model theory (WBEPMT) for the investigation of effects of expectation values of radii.We have used both numerical non-relativistic Hartree-Fock (NRHF) wave functions and numerical Coulomb approximation (NCA) wave functions to calculate expectation values of radii. The transition probability results obtained using the parameters determined with two different wave functions agree well with each other and accepted values taken from NIST for low values of transition probability. However, the NRHF wave functions present better results for p-s transitions, while NCA wave functions are better in s-p transitions for large values of transition probability.

Theoretical calculations of transition probabilities for individual and multiplet lines between some excited levels of atomic potassium

The transition probabilities for individual and multiplet lines between some excited levels of atomic potassium are calculated using weakest bound electron potential model theory (WBEPMT). The numerical nonrelativistic Hartree–Fock wave functions for the expectation values of radii in all excited states, unlike the Numerical Coulomb Approximation method traditionally used for WBEPMT and experimental ionization energies, have been employed to determine the parameters. The results obtained during this work agree very well with the accepted values taken from National Institute Standards and Technology. Moreover, some transition probabilities not existing on the data bases for highly excited levels in atomic potassium have been obtained using this method. PACS No.: 32.70.Cs

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.

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