Potential Model Theory Research Articles

Theoretical calculations of transition probabilities and oscillator strengths for Ti III and Ti IV

AbstractDue to the complicated electronic configuration of atoms and ions of the transition metal elements, the studies for properties such as transition probabilities and oscillator strengths for these atoms and ions are not systematic. Because of the existence in a variety of stellar objects and wide use in the field of astrophysics, titanium has long been of interest for many researchers. In this article within the Weakest Bound Electron Potential Model (WBEPM) theory, comprehensive set of calculations for transition probabilities and oscillator strengths for Ti III and Ti IV are performed. Many of our results had no previous experimental or theoretical values, so these predictive results could be of some value to the workers in this field. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Calculations of Transition Probabilities for Some Excited Levels of Na I

Transition probabilities are calculated for individual and multiplet lines between some excited states in neutral sodium by using the weakest bound electron potential model theory. In the determination of parameters required for calculation of transition probabilities, we employed numerical non-relativistic Hartree–Fock wave functions for expectation values of radii in all levels. The necessary energy values were taken from experimental energy data in the literature. The obtained results were compared with accepted values taken from National Institute of Standards and Technology data and multi-configurational Hartree–Fock results given by Fischer. A good agreement was observed in related excited states.

New reaction rate forO16(p,γ)F17and its influence on the oxygen isotopic ratios in massive AGB stars

The O-16(p, gamma)F-17 reaction rate is revisited with special emphasis on the stellar temperature range of T=60-100 MK, important for hot bottom burning in asymptotic giant branch (AGB) stars. We evaluate existing cross-section data that were obtained since 1958 and, if appropriate, correct published data for systematic errors that were not noticed previously, including the effects of coincidence summing and updated effective stopping powers. The data are interpreted by using two different models of nuclear reactions, that is, a potential model and R-matrix theory. A new astrophysical S factor and recommended thermonuclear reaction rates are presented. As a result of our work, the O-16(p, gamma)F-17 reaction has now the most precisely known rate involving any target nucleus in the mass A >= 12 range, with reaction rate errors of about 7% over the entire temperature region of astrophysical interest (T=0.01-2.5 GK). The impact of the present improved reaction rate with its significantly reduced uncertainties on the hot bottom burning in AGB stars is discussed. In contrast to earlier results we find now that there is not clear evidence to date for any stellar grain origin from massive AGB stars.

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

铊原子能级与辐射寿命的理论计算

Considering the perturbation, the results of theoretical calculation of five Rydberg series energy levels 6s^2ns^2S_1/2(n=7-20),6s^2nd^2D_3/2(n=6-20),6s^2nd^2D_5/2(n=6-20),6s^2np^2P^(0)_(1/2)(n=7-20), and 6s^2np^2P^(0)_(3/2)(n=7-20) for Tl I are presented using the weakest bound electron potential model (WBEPM) theory. Furthermore, the radiative lifetimes of this five series are also calculated. The calculated values of energy levels and lifetimes are in good agreement with the experimental results.

Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case.

Determination of Excited-State Ionization Potentials for Lithium-Like Sequence Using Weakest Bound Electron Potential Model Theory

tentials for 1s 2 2p 2 P1=2, 1s 2 3s 2 S1=2, 1s 2 3d 2 D1=2, 1s 2 4s 2 S1=2, 1s 2 4p 2 P1=2, and 1s 2 4d 2 D1=2 iso-spectrum series of lithium-like elements were carried out using a weakest bound electron potential model theory for nuclear charges from Z = 3 to Z = 18. The Breit{Pauli approximation was used for relativistic contributions. The obtained values are compared with the experimental results from literature. The overall agreement between data obtained in this work and experimental data from literature can appear to be quite good being generally within 0.1% of experimental values.

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.

Improved Boussinesq-type equations for highly variable depth

Intermediate-depth, Boussinesq-type modelling is used to generalize previously known results for surface water waves propagating over arbitrarily shaped topographies. The improved reduced wave model is obtained after studying how small changes in the linear dispersion relation (over a flat bottom) can become dramatically important in the presence of a highly fluctuating topography. Numerical validation of the dispersive properties, regarding several possible truncations for the reduced models, are compared with the complete (non-truncated) linear potential theory model. Moreover, linear L 2 -estimates are extended from the analysis of KdV-type models to include the improved Boussinesq systems in contrast with potential theory. Discrepancies observed among the different possible reduced models become even more important in the wave-form inversion problem. The time reversal technique is used for recompressing a long fluctuating signal, representing a highly scattered wave that has propagated for very long distances. When properly back-propagated (through a numerical model), the scattered signal refocuses into a smooth profile representing the onset of the ocean's surface disturbance. Previous Boussinesq models underestimate the original disturbance's amplitude. The improved Boussinesq system agrees very well with the full potential theory predictions.

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

Oscillator strengths and transition probabilities for Mg-like ions

Oscillator strengths and transition probabilities for transitions among the fine-structure levels in Mg-like P IV, S V, Cl VI, and Ar VII are calculated within the weakest bound electronic potential model theory. Our results are discussed and compared with the calculations and experimental values. Oscillator strengths for 3 s 3 d 3 D J – 3 s 4 f 3 F J ′ 0 and 3 s 4 d 3 D J – 3 s 4 f 3 F J ′ 0 transitions, for which very few results exist, are also computed.

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.