scholarly journals Quantum-Mechanical Substantiation of the Periodic System of Isotopes. Models of Nuclear Orbitals

2021 ◽  
pp. 1-26
Author(s):  
AS Magula ◽  
Keyword(s):  
Periodic System ◽  
Degrees Of Freedom ◽  
Nucleon Nucleon ◽  
Quantum Mechanical ◽  
Spherical Coordinate ◽  
Crystal Forms ◽  
Electromagnetic Interactions ◽  
Quantum Numbers ◽  
The Family ◽  
Fundamental Cause

The topic of this article lies in the field of problems: substantiating the periodic system of isotopes and the principle of multilevel periodicity using quantum mechanical calculations, combining strong and electromagnetic interactions, and searching for the fundamental cause of periodicity in general. This article is a theoretical section and a continuation of the article: "Periodic system of isotopes", in which the system was checked against 10 types of experimental data, the periodic change of properties at the level of nuclei and the vertical symmetry of subgroups of isotopes were found. Periodic system of isotopes was constructed with the help of a special algorithm, the principle of multilevel periodicity of the atom, from the electrons to the nucleus. As a description of the multilevel periodicity, this paper presents a unified system of quantum numbers, which is used to describe both electron and nucleon shells (binomial probabilistic interpretation). With the binomial interpretation the problem of a particle in a one-dimensional potential well has been solved; quantummechanical calculations for the probability functions of the orbitals and periods of both electrons and nucleons have been performed - characteristic equations have been obtained, the projections of electronic orbitals have been reproduced and the binomial interpretation has been shown to correspond to the family of spherical harmonics. For the electron orbitals the calculation and analysis of solutions of the Schrödinger equation for the binomial interpretation of quantum numbers have been performed. The spatial nature of quantum numbers, for this interpretation, in the form of degrees of freedom is shown. Based on the principle of multilevel periodicity, expressions are derived and planar projections of nucleon nucleon orbitals are constructed, and similarity of the forms with electron orbitals is analyzed and revealed. A critical analysis of the modern spherical coordinate system was made, possible errors in the construction of electron orbitals were shown and, taking into account the drawbacks, two alternative spherical coordinate systems were proposed, for which Lame coefficients were calculated and Laplace equations were derived. As a search for the fundamental cause of multilevel periodicity, a spatial model with changing degrees of freedom 0-n is presented, its manifestation in nature (crystal forms) is found; a number of experiments are proposed; the predictions about the applicability of the multilevel periodicity principle in quark theory are made

scholarly journals Relations between Clifford Algebra and Dirac Matrices in the Presence of Families

Particles ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 518-531
Author(s):  
Dragan Lukman ◽  
Mickael Komendyak ◽  
Norma Susana Mankoč Borštnik
Keyword(s):  
Clifford Algebra ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Family Members ◽  
Matrix Representations ◽  
Quantum Numbers ◽  
The Family ◽  
Family Theory ◽  
The Matrix ◽  
Basis Vectors

The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of γ a ’s. Arranged into irreducible representations of “eigenvectors” of the Cartan subalgebra of the Lorentz algebra S a b ( = i 2 γ a γ b | a ≠ b ) these objects form 2 d 2 − 1 families with 2 d 2 − 1 family members each. Family members of each family offer the description of all the observed quarks and leptons and antiquarks and antileptons, appearing in families. Families are reachable by S ˜ a b = 1 2 γ ˜ a γ ˜ b | a ≠ b . Creation operators, carrying the family member and family quantum numbers form the basis vectors. The action of the operators γ a ’s, S a b , γ ˜ a ’s and S ˜ a b , applying on the basis vectors, manifests as matrices. In this paper the basis vectors in d = ( 3 + 1 ) Clifford space are discussed, chosen in a way that the matrix representations of γ a and of S a b coincide for each family quantum number, determined by S ˜ a b , with the Dirac matrices. The appearance of charges in Clifford space is discussed by embedding d = ( 3 + 1 ) space into d = ( 5 + 1 ) -dimensional space. The achievements and predictions of the spin-charge-family theory is also shortly presented.

scholarly journals Über der Kopplung von Schwingungsfreiheitsgraden an die Koordinate intramolekularer Umlagerungen / Coupling of Vibrational Degrees of Freedom lo the Coordinate of Intramolecular Rearrangements

1973 ◽  
Vol 28 (11) ◽  
pp. 1759-1781 ◽  
Author(s):  
J. Brickmann
Keyword(s):  
Degrees Of Freedom ◽  
Energy Surface ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Damping Term ◽  
Intramolecular Rearrangements ◽  
Quantum Numbers ◽  
The Matrix ◽  
Localized Quantum States ◽  
Internal Degrees Of Freedom

Intramolecular rearrangements A ⇌ B are investigated, which can be described in terms of the motion of an effective quantum mechanical ‘‘particle’’ on an energy surface with at least two minima. We regard the energy surface as a function of a limited number of relevant internal degrees of freedom. The rate of isomerization is calculated from the matrix elements of a transition operator W with respect to the localized quantum states of the two isomers, and the coupling to the inter- and intramolecular degrees of freedom, not explizitely considered in the energy surface. It is shown that the matrixelements of W be reduced to integrals over functions of the adiabatic reaction coordinate of the isomerization, and selection rules for the vibrational quantum numbers for the motion perpendicular to this coordinate. The degrees of freedom not relevant for the reaction are summarily taken into account by introducing a heath bath in thermodynamic equilibrium and a simple damping term. Applications are discussed.

Crystal Forms of Semisynthetic Ergot Alkaloid Terguride

2002 ◽  
Vol 67 (4) ◽  
pp. 479-489 ◽  
Author(s):  
Michal Hušák ◽  
Bohumil Kratochvíl ◽  
Ivana Císařová ◽  
Ladislav Cvak ◽  
Alexandr Jegorov ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Ergot Alkaloid ◽  
Simplified Model ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
X Ray Diffraction ◽  
Torsion Angles ◽  
Crystal Forms ◽  
X Ray ◽  
Independent Molecules

Two new structures of semisynthetic ergot alkaloid terguride created by unusual number of symmetry-independent molecules were determined by X-ray diffraction methods at 150 K. Form A (monoclinic, P212121, Z = 12) contains three symmetry-independent terguride molecules and two molecules of water in the asymmetric part of the unit cell. The form CA (monoclinic, P21, Z = 8) is an anhydrate remarkable by the presence of four symmetry-independent molecules in the crystal structure. Conformations of twelve symmetry-independent molecules that were found in four already described terguride structures are compared with torsion angles obtained by ab initio quantum-mechanical calculations for the simplified model of N-cyclohexyl-N'-diethylurea.

scholarly journals ON SUPERLUMINAL FERMIONS WITHIN THE SECOND DERIVATIVE EQUATION

2012 ◽  
Vol 27 (14) ◽  
pp. 1250081 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Energy Momentum Tensor ◽  
Canonical Quantization ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Order Equation ◽  
Quantum Mechanical ◽  
Projection Operators ◽  
The Novel ◽  
First Order ◽  
Electromagnetic Interactions

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy–momentum tensor are found. The minimal and nonminimal electromagnetic interactions of fermions are considered and Schrödinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.

An Efficient Weighted Residual Time Integration Family

2021 ◽  
pp. 2150106
Author(s):  
Mohammad Rezaiee-Pajand ◽  
S. A. H. Esfehani ◽  
H. Ehsanmanesh
Keyword(s):  
Degrees Of Freedom ◽  
Time Integration ◽  
Nonlinear Damping ◽  
Implicit Methods ◽  
New Family ◽  
Error Analyses ◽  
Damping Behavior ◽  
The Family ◽  
New Strategy ◽  
Time Integration Methods

A new family of time integration methods is formulated. The recommended technique is useful and robust for the loads with large variations and the systems with nonlinear damping behavior. It is also applicable for the structures with lots of degrees of freedom, and can handle general nonlinear dynamic systems. By comparing the presented scheme with the fourth-order Runge–Kutta and the Newmark algorithms, it is concluded that the new strategy is more stable. The authors’ formulations have good results on amplitude decay and dispersion error analyses. Moreover, the family orders of accuracy are [Formula: see text] and [Formula: see text] for even and odd values of [Formula: see text], respectively. Findings demonstrate the superiority of the new family compared to explicit and implicit methods and dissipative and non-dissipative algorithms.

scholarly journals Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains

Science ◽  
2020 ◽  
Vol 367 (6474) ◽  
pp. 186-189 ◽  
Author(s):  
Jayadev Vijayan ◽  
Pimonpan Sompet ◽  
Guillaume Salomon ◽  
Joannis Koepsell ◽  
Sarah Hirthe ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Spatial Separation ◽  
Real Space ◽  
Quantum Gas ◽  
Interacting Particles ◽  
Time Resolved ◽  
One Dimensional ◽  
Quantum Numbers ◽  
Charge Correlations ◽  
The Individual

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

scholarly journals η meson physics with WASA-at-COSY

2019 ◽  
Vol 199 ◽  
pp. 01006
Author(s):  
Nils Hüsken ◽  
Kay Demmich ◽  
Alfons Khoukaz
Keyword(s):  
Beyond Standard Model ◽  
Standard Model ◽  
Bound States ◽  
Focal Point ◽  
Nucleon Nucleon ◽  
Large Datasets ◽  
Research Center ◽  
Decay Modes ◽  
Electromagnetic Interactions ◽  
Physics Programme

In recent years, the η meson has been a focal point of research for the WASA experiment at the Cooler Synchrotron COSY of the Research Center Jülich. Production experiments using nucleon-nucleon and nucleon-nucleus collisions have been performed, studying the η − N interaction in various configurations. A better understanding of this interaction is a key aspect in the ongoing search for η-nuclear bound states. In addition, the η meson itself represents an ideal laboratory for precision studies of the strong and electromagnetic interactions as well as for searches for beyond Standard Model physics. Large datasets were assembled using the WASA experiment to enable studies on rare and forbidden decay modes. An overview over recent highlights of the WASA η meson physics programme was given.

scholarly journals INFINITE STATISTICS, SYMMETRY BREAKING AND COMBINATORIAL HIERARCHY

2009 ◽  
Vol 24 (18) ◽  
pp. 1425-1435 ◽  
Author(s):  
VLADIMIR SHEVCHENKO
Keyword(s):  
Symmetry Breaking ◽  
Mechanical Model ◽  
Degrees Of Freedom ◽  
High Energy ◽  
Low Energy ◽  
Effective Theory ◽  
Quantum Mechanical ◽  
Hierarchy Problem ◽  
Induced Gravity ◽  
Large Numbers

The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments, it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarchy problem without necessity to introduce any artificially large numbers. Quantum mechanical model illustrating this scenario is presented.

scholarly journals The Ground-State Calculations for Some Nuclei by Mesonic Potential of Nucleon-Nucleon Interaction

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
K. M. Hanna ◽  
S. H. M. Sewailem ◽  
R. Hussien ◽  
L. I. Abou-Salem ◽  
Asmaa G. Shalaby
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Theoretical Models ◽  
Nucleon Nucleon ◽  
Particle Energy ◽  
Exchange Potential ◽  
Hartree Fock ◽  
Scalar And Vector Fields ◽  
Nucleon Nucleon Interaction

The interaction of nucleon-nucleon (NN) has certain physical characteristics, indicated by nucleon, and meson degrees of freedom. The main purpose of this work is calculating the ground-state energies of  12H and  24He through the two-body system with the exchange of mesons (π, σ, and ω) that mediated between two nucleons. This paper investigates the NN interaction based on the quasirelativistic decoupled Dirac equation and self-consistent Hartree-Fock formulation. We construct a one-boson exchange potential (OBEP) model, where each nucleon is treated as a Dirac particle and acts as a source of pseudoscalar, scalar, and vector fields. The potential in the present work is analytically derived with two static functions of meson, the single-particle energy-dependent (SPED) and generalized Yukawa (GY) functions; the parameters used in meson functions are just published ones (mass, coupling constant, and cutoff parameters). The theoretical results are compared to other theoretical models and their corresponding experimental data; one can see that the SPED function gives more satisfied agreement than the GY function in the case of the considered nuclei.

Spin-orbital exclusion principle and the periodic system

2020 ◽  
Vol 92 (3) ◽  
pp. 515-525
Author(s):  
Viktor Vyatkin
Keyword(s):  
Atomic Nucleus ◽  
Quantum Number ◽  
Atomic Number ◽  
Periodic System ◽  
Value Distribution ◽  
Exclusion Principle ◽  
Real Sequence ◽  
Spin Orbital ◽  
Quantum Numbers ◽  
Madelung Rule

AbstractGroups of electrons, radial with respect to the atomic nucleus and with the same value of the orbital quantum number and the same number on the subshell, are considered. A spin-orbital exclusion principle is established, regulating the spin value distribution on the subshells with the same value of the orbital number. According to this principle, all subshells are divided into positive and negative ones, depending on the direction of the spin of their first electron. It is found that, in the real sequence of the appearance of new subshells, a spin-orbital periodicity takes place, which develops in cycles consisting of two periods that are mirror-symmetric to each other in the direction of the spin of their electrons. Moreover, atomic number of any period is equal to the sum of the principal and orbital quantum numbers of its subshells, and this can serve as an explanation for the Madelung rule. It is demonstrated that Mendeleev’s chemical periodicity lags behind the spin-orbital periodicity by two elements and repeats its structure. From these positions, the absence of a pair in the first period of Mendeleev’s table and the pairing of all its other periods are explained. Based on the obtained results, an eight-period table of elements, the prototype of which being Janet’s left-step table, is compiled and briefly described.

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