Modern Quantum Look at the Periodic Table of Elements

Ostrovsky, V N

doi:10.1007/978-94-010-0113-7_49

Cited by 3 publications

(6 citation statements)

References 111 publications

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“…The reduction of the basic representation F + ss of the Rumer-Fet group on the subgroups is realized in accordance with the chain (9). Therefore, multiplets of a subgroup SO(3) ⊗ SU(2) are represented by vertical rectangles in Figure 1, and their elements compose well-known s, p, d and f -families (in particular, lanthanides and actinides are selected as multiplets of the subgroup SO(3) ⊗ SU(2)).…”

Section: Rumer-fet Groupmentioning

confidence: 99%

“…With this aim in view, we use mass formula (10). Formula (10) corresponds to the chain of groups (9), according to which we have a reduction of the basic representation F + ss on the subgroups of this chain; that is, a partition of the basic multiplets into the lesser multiplets. As noted above, Formula (10) is analogous to the "first perturbation" in SU(3) and SU(6)-theories, which allows us to calculate an average mass of the elements belonging to a given multiplet (therefore, in SU(3)-theory we have a Gell-Mann-Okubo mass formula…”

Section: Seaborg Tablementioning

confidence: 99%

“…With the aim of obtaining an analog of the "second perturbation", which leads to a mass splitting inside the multiplets of group G 2 = SO(3) ⊗ SU(2), it needs to find a subsequent lengthening of the group chain G ⊃ G 1 ⊃ G 2 (9). Therefore, we need to find another subgroup G 3 .…”

Section: Seaborg Tablementioning

confidence: 99%

“…The new basis is defined as follows. Since ν, s , λ are related to the groups G, G 1 , G 2 , they remain quantum numbers of chain (9), and instead, µ, s have new quantum numbers related to G 3 . First, quantum number ι λ relates with the Casimir operator of the subgroup G 3 , which is equal to…”

Section: Seaborg Tablementioning

confidence: 99%

“…Already from the first works in this direction, two different approaches are clearly manifested. The Navaro method (atomic physics approach), further developed in the works of Ostrovsky and Demkov [8][9][10], by analogy with atomic physics, relies on the search of a Hamiltonian model. On the other hand, the Rumer-Fet-Barut method (elementary particle approach) relies on the analogy with groups of dynamic (internal) symmetries of elementary particle physics, such as SU(2) (isotopic spin), SU (3) and SU (6).…”

Section: Introductionmentioning

confidence: 99%

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Group Theoretical Description of the Periodic System

2022

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The group theoretical description of the periodic system of elements in the framework of the Rumer–Fet model is considered. We introduce the concept of a single quantum system, the generating core of which is an abstract C*-algebra. It is shown that various concrete implementations of the operator algebra depend on the structure of the generators of the fundamental symmetry group attached to the energy operator. In the case of the generators of the complex shell of a group algebra of a conformal group, the spectrum of states of a single quantum system is given in the framework of the basic representation of the Rumer–Fet group, which leads to a group-theoretic interpretation of the Mendeleev’s periodic system of elements. A mass formula is introduced that allows giving the termwise mass splitting for the main multiplet of the Rumer–Fet group. The masses of elements of the Seaborg table (eight-periodic extension of the Mendeleev table) are calculated starting from the atomic number Z=3 and going to Z=220. The continuation of the Seaborg homology between lanthanides and actinides is established with the group of superactinides. A 10-periodic extension of the periodic table is introduced in the framework of the group-theoretic approach. The multiplet structure of the extended table’s periods is considered in detail. It is shown that the period lengths of the system of elements are determined by the structure of the basic representation of the Rumer–Fet group. The theoretical masses of the elements of 10th and 11th periods are calculated starting from Z=221 and going to to Z=364. The concept of hypertwistor is introduced.

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Section: Rumer-fet Groupmentioning

confidence: 99%

Section: Seaborg Tablementioning

confidence: 99%

Section: Seaborg Tablementioning

confidence: 99%

Section: Seaborg Tablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Group Theoretical Description of the Periodic System

2022

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Nuclear Lattice Model and the Electronic Configuration of the Chemical Elements

Garai¹

2018

Mendeleev to Oganesson

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In the earliest days of science researchers were arguing philosophically what might be the reasonable explanation for an observed phenomenon. The majority of the contemporary scientific community claims that these arguments are useless because they do not add anything to our understanding of nature. The current consensus on the aim of science is that science collects facts (data) and discerns the order that exists between and among the various facts (e.g., Feynman 1985). According to this approach the mission of science is over when the phenomenon under investigation has been described. It is left to the philosophers to answer the question what is the governing physical process behind the observed physical phenomenon. Quantum mechanics is a good example of this approach, “It works, so we just have to accept it.” The consequence is that nearly 90 years after the development of quantum theory, there is still no consensus in the scientific community regarding the interpretation of the theory’s foundational building blocks (Schlosshauer et al. 2013). I believe that identifying the physical process governing a natural phenomenon is the responsibility of science. Dutailly (2013) expressed this quite well: A “black box” in the “cloud” which answers our questions correctly is not a scientific theory, if we have no knowledge of the basis upon which it has been designed. A scientific theory should provide a set of concepts and a formalism which can be easily and indisputably understood and used by the workers in the field. In this study the main unifying principle in chemistry, the periodic system of the chemical elements (PSCE) is investigated. The aim of the study is not only the description of the periodicity but also the understanding of the underlying physics resulting in the PSCE. By 1860 about 60 elements had been identified, and this initiated a quest to find their systematic arrangement. Based on similarities, Dobereiner (1829) in Germany suggested grouping the elements into triads.

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Physical Explanation of the Periodic Table

Ostrovsky

2003

Annals of the New York Academy of Sciences

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The Periodic Table of the elements, the most important generalization in chemistry, is often considered as a representative special case in the study of the relation between chemistry and physics. Its quantum interpretation was initiated, but not completed, by Niels Bohr. In this paper, post-Bohr conceptual developments are discussed from historical and epistemological points of view. The difference between high-precision numerical calculations for individual atoms and the theory of the periodic system as a whole is emphasized. Periodic laws met in Nature are not restricted to the chemical Periodic Table. A comparative study of these laws makes it possible to single out essential features that define the particular pattern of periodicity. It is shown that the periodic system of neutral ground state atoms now has a firm nonempirical quantum-theoretical basis. Alternative approaches, based on group theory and other mathematical schemes, are briefly discussed. It is argued that, while quantum theory is capable of fully accurate calculations for relatively simple atoms or molecular objects, the complexity of polyatomic molecules and chemical reactions guarantees the flourishing of chemistry as a separate scientific discipline.

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Modern Quantum Look at the Periodic Table of Elements

Cited by 3 publications

References 111 publications

Group Theoretical Description of the Periodic System

Group Theoretical Description of the Periodic System

Nuclear Lattice Model and the Electronic Configuration of the Chemical Elements

Physical Explanation of the Periodic Table

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