scholarly journals Atomic Structure Calculations of Helium with Correlated Exponential Functions

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1246
Author(s):  
Vladimir A. Yerokhin ◽  
Vojtěch Patkóš ◽  
Krzysztof Pachucki
Keyword(s):  
Wave Function ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
Perturbation Expansion ◽  
Structure Constant ◽  
Basis Functions ◽  
Fine Structure Constant ◽  
Compact Representation ◽  
Electron Mass ◽  
Qed Effects

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1, r2 and r=|r→1−r→2|. The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order α5m (where m is the electron mass) are complemented with the systematic treatment of higher-order α6m and α7m QED effects.

scholarly journals Theory of the Anomalous Magnetic Moment of the Electron

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 28 ◽  
Author(s):  
Tatsumi Aoyama ◽  
Toichiro Kinoshita ◽  
Makiko Nio
Keyword(s):  
Fine Structure ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Penning Trap ◽  
Weak Interactions ◽  
Perturbation Expansion ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Best Value

The anomalous magnetic moment of the electron a e measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α , with an effective parameter α / π . Both numerical and analytic evaluations of a e up to ( α / π ) 4 are firmly established. The coefficient of ( α / π ) 5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to a e ( theory ) = 1 159 652 181.606 ( 11 ) ( 12 ) ( 229 ) × 10 − 12 , where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: α − 1 ( Cs ) = 137.035 999 046 ( 27 ) . The discrepancy between a e ( theory ) and a e ( ( experiment ) ) is 2.4 σ . Assuming that the standard model is valid so that a e (theory) = a e (experiment) holds, we obtain α − 1 ( a e ) = 137.035 999 1496 ( 13 ) ( 14 ) ( 330 ) , which is nearly as accurate as α − 1 ( Cs ) . The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of a e , in this order.

scholarly journals Rejection of Rutherford's Planetary Model of the Atom, Bohr's Postulates and the Tunnel Effect

2021 ◽  
pp. 1-4
Author(s):  
Leo G Sapogin ◽  
◽  
Stanislav Konstantinov ◽  
Keyword(s):  
Fine Structure ◽  
Quantum Electrodynamics ◽  
Chemical Elements ◽  
Hadron Collider ◽  
Energy Levels ◽  
Structure Constant ◽  
Electron Shell ◽  
Fine Structure Constant ◽  
Tunnel Effect ◽  
Integer Number

The article raises the question of the strange behavior of electrons in an atom, when the electronic orbitals of the P- and d-states of the atom have the form of eights with nodal points in the nucleus of the atom, as well as the discovery of the mysterious K-capture of an electron when the nuclei of atoms of some isotopes of chemical elements someh they sometimes capture an electron from the inner (K- or L-) electron shell of the atom. It has not been possible to explain these phenomena within the framework of the atomic model existing in quantum electrodynamics. In the new model of the atom, proposed by Professor Lev Sapogin in Unitary Quantum Theory, the electron makes quantum leaps within the orbital not randomly, as physicists thought, but through the nucleus of the atom, each time tunneling through it. In this case, the quantization of the energy levels (orbitals) of electrons in an atom is explained by the distribution of nodes and antinodes in a standing wave of an electron, and an integer number of de Broglie wavelengths should be located in the diameter of the electron orbital. The article shows the dependence of the magnitude of the interaction constants in the hydrogen nucleus and, in particular, the fine structure constant, discovered by the CMS cooperation in experiments at the Large Hadron Collider in 2019, during reactions in pp collisions with energies from 1 TeV to 13 TeV and an intranuclear pressure of 10³⁵ Pascal. The value of the fine structure in the near-Earth medium and in a neutron star is given

scholarly journals Measurement of Wavelengths and Abundances from Solar Flare X-Ray Spectra

1984 ◽  
Vol 86 ◽  
pp. 151-153
Author(s):  
J.F. Seely ◽  
U. Feldman ◽  
G.A. Doschek
Keyword(s):  
Fine Structure ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Transition Energies ◽  
X Ray ◽  
Hydrogenic Ions ◽  
Charged Ions ◽  
Important Test

The measurement of transition energies in highly charged ions represents an important test of quantum electrodynamics (QED) in strong fields. The OED contributions to the hydrogenic transition energies increase as (αZ)4, where α is the fine structure constant and Z is the atomic number. Transitions in hydrogenic ions of sulfur, chlorine, argon, and iron have previously been measured to a precision of 100 ppm or better. These measurements are in satisfactory agreement with accurate calculations of the energy levels, and this confirms the calculation of the QED contributions to the energy levels of one-electron ions.

scholarly journals Calculations of QED Effects with the Dirac Green Function

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 800 ◽  
Author(s):  
Vladimir A. Yerokhin ◽  
Anna V. Maiorova
Keyword(s):  
Green Function ◽  
Quantum Electrodynamics ◽  
Nuclear Charge ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Strength Parameter ◽  
Theoretical Treatment ◽  
Binding Strength ◽  
Qed Effects ◽  
Nuclear Charge Number

Modern spectroscopic experiments in few-electron atoms reached the level of precision at which an accurate description of quantum electrodynamics (QED) effects is mandatory. In many cases, theoretical treatment of QED effects need to be performed without any expansion in the nuclear binding strength parameter Z α (where Z is the nuclear charge number and α is the fine-structure constant). Such calculations involve multiple summations over the whole spectrum of the Dirac equation in the presence of the binding nuclear field, which can be evaluated in terms of the Dirac Green function. In this paper we describe the technique of numerical calculations of QED corrections with the Dirac Green function, developed in numerous investigations during the last two decades.

scholarly journals New Limit on Space-Time Variations in the Proton-to-Electron Mass Ratio from Analysis of Quasar J110325-264515 Spectra

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 344
Author(s):  
T. D. Le
Keyword(s):  
Fine Structure ◽  
Structure Constant ◽  
Space Time ◽  
Fine Structure Constant ◽  
Electron Mass ◽  
Mass Ratio ◽  
Quasar Spectra ◽  
Time Variations ◽  
Using Data ◽  
The Universe

Astrophysical tests of current values for dimensionless constants known on Earth, such as the fine-structure constant, α , and proton-to-electron mass ratio, μ = m p / m e , are communicated using data from high-resolution quasar spectra in different regions or epochs of the universe. The symmetry wavelengths of [Fe II] lines from redshifted quasar spectra of J110325-264515 and their corresponding values in the laboratory were combined to find a new limit on space-time variations in the proton-to-electron mass ratio, ∆ μ / μ = ( 0.096 ± 0.182 ) × 10 − 7 . The results show how the indicated astrophysical observations can further improve the accuracy and space-time variations of physics constants.

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

scholarly journals Fundamental physics and the fine-structure constant

2017 ◽  
Vol 5 (2) ◽  
pp. 46 ◽  
Author(s):  
Michael Sherbon
Keyword(s):  
Fine Structure ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Electron Mass ◽  
Fundamental Constants ◽  
Mass Ratio ◽  
Fundamental Physics ◽  
Weak Force ◽  
Strong Force ◽  
Symmetry Principles

From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.

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