Fourth-order relativistic corrections to electrical first-order properties using direct perturbation theory

2011 ◽  
Vol 134 (20) ◽  
pp. 204106 ◽  
Author(s):  
Stella Stopkowicz ◽  
Jürgen Gauss
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
First Order ◽  
Relativistic Corrections ◽  
Direct Perturbation

scholarly journals High-precision calculation of relativistic corrections for hydrogen-like atoms with screened Coulomb potentials

2021 ◽  
Author(s):  
Hui Xie ◽  
Li Guang Jiao ◽  
Ai Liu ◽  
Y.K. Ho
Keyword(s):  
Perturbation Theory ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
First Order ◽  
Relativistic Corrections ◽  
Relativistic Mass ◽  
Mass Correction ◽  
Direct Perturbation ◽  
Good Agreement

The first-order relativistic corrections to the non-relativistic energies of hydrogen-like atom embedded in plasma screening environments are calculated in the framework of direct perturbation theory by using the generalized pseudospectral method. The standard Debye-Hückel potential, exponential cosine screened Coulomb potential, and Hulthén potential are employed to model different screening conditions and their effects on the eigenenergies of hydrogen-like atoms are investigated. The relativistic corrections which include the relativistic mass correction, Darwin term, and the spin-orbit coupling term for both the ground and excited states are reported as functions of screening parameters. Comparison with previous theoretical predictions shows that both the relativistic mass correction and spin-orbit coupling obtained in this work are in good agreement with previous estimations, while significant discrepancy and even opposite trend is found for the Darwin term. The overall relativistic-corrected system energies predicted in this work, however, are in good agreement with the fully relativistic calculations available in the literature. We finally present the scaling law of the first-order relativistic corrections and discuss the validity of the direct perturbation theory with respect to both the nuclear charge and the screening parameter.

FIRST- AND SECOND-ORDER CROSSOVERS OF SPIN TUNNELING IN Mn12-ACETATE MOLECULAR MAGNET WITH FOURTH-ORDER ANISOTROPY

2002 ◽  
Vol 16 (15n16) ◽  
pp. 555-567
Author(s):  
CHANG-SOO PARK
Keyword(s):  
Perturbation Theory ◽  
External Field ◽  
Fourth Order ◽  
Easy Axis ◽  
Second Order ◽  
Molecular Magnet ◽  
Crossover Temperature ◽  
Transverse Anisotropy ◽  
First Order ◽  
Spin Tunneling

We have studied the escape rate of spin tunneling in a molecular magnet with a fourfold easy axis, such as Mn 12-acetate, in the presence of an external field applied perpendicular to the easy axis. Both perturbation theory and numerical diagonalization have been used to investigate the type of quantum-classical crossover and the crossover temperature T c . We have observed that T c ~ 1.2 K which agrees with experimental results,9 and the first-order region increases due to the fourth-order transverse anisotropy. More interestingly, when the field is applied along the hard axis, first- and second-order regions alternate as the field increases.

scholarly journals Energy, fine structure, hyperfine structure, and transitions for the high-lying multi-excited 4Pe,o states of B-like ions

2016 ◽  
Vol 94 (5) ◽  
pp. 448-457
Author(s):  
Chun Mei Zhang ◽  
Yan Sun ◽  
Chao Chen ◽  
Feng Wang ◽  
Bin Shao ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Fine Structure ◽  
Hyperfine Structure ◽  
Excited States ◽  
Quantum Electrodynamic ◽  
Higher Order ◽  
Variation Method ◽  
First Order ◽  
Relativistic Corrections ◽  
First Order Perturbation

The energies of the high-lying multi-excited states 1s22s2pnl and 1s22p2nl 4Pe,o (n ≥ 2) for B-like C+, N2+, F4+, and Mg7+ ions are calculated using Rayleigh–Ritz variation method with multiconfiguration interaction, and the inclusion of mass polarization and relativistic corrections. The fine structure and hyperfine structure for these systems are investigated using first-order perturbation theory. The configuration structure of the high-lying multi-excited series is identified not only by energy, but also by its contribution to normalization of the angular spin components, and it is further tested by the addition of relativistic corrections and fine structure splittings. Transition wavelengths including the quantum electrodynamic effects and higher-order relativistic corrections are determined.

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

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