Nanoscience, Vol. 2, Issue 1, Dec  2019, Pages 1-7; DOI: 10.31058/j.nano.2019.11001 10.31058/j.nano.2019.11001

New Research of Atomic Terms in the Nanoscience

, Vol. 2, Issue 1, Dec  2019, Pages 1-7.

DOI: 10.31058/j.nano.2019.11001

Nikolay V. Serov 1*

1 Rozhdestvenskiy Optical Society, Birzhevaya Linia, St. Petersburg, Russia

Received: 23 July 2019; Accepted: 25 July 2019; Published: 9 September 2019


This report is about creation of information models of light quantization and absorption by an atom and/or a molecule in a language alternative to the one-electron approach. For this purpose the analysis of trigonometrical functions has been done which has revealed quantum numbers which have been applied to differentiating interpretation of the concepts quantum/photon and getting earlier unknown dependences for the terms of neutral atoms. It has enabled to enter actual multielectronic classification of atoms.


Information Models of Radiation/Absorption, Alternative to the one-Electron Approach, Nuclear Terms

1. Introduction

Quite often researchers [1] are surprised by the fact that the quantum theory developed for systems of nuclear sizes works well also for scales much smaller and considerably bigger. There is a feeling that all properties of matter are quantum-mechanical, – scientists conclude and ask the question: What can we learn about the quantum optics, using the concept of information? In particular, this paper is devoted to this question too.

At the same time, other scientists remind that the quantum mechanics for its history has faced larger number of crises, contradictions, interpretations and recessions of interest than any other science. Albert Einstein could not reconcile with its consequences [2] till the end of his life. So, for example, it is considered that quantized energy of optical radiation in the form of “photon” has no reliable justification in the theoretical physics [3]. Probably therefore today, appeals sound even more often: Time to begin anew, to throw out the existing axioms of quantum mechanics and to return to the fundamental physical principles has come. And where to find them? – In the quantum theory of information – Christopher Fuchs, a quantum physicist from the Bell Laboratories claims (quote of [4]).

Information appears only about data. But data in quantum mechanics are ambiguous (the principle of uncertainty) and are inconsistent (one-electron approach for multielectronic systems) quite often that can be proved only by mathematical methods, for example, during quantization of the field [3]. Therefore it is necessary to look for other ways of information search. The essence of information modeling is identification of characteristic parameters and attributes of difficult phenomena with elimination of insignificant ones to create basic prerequisites for development of a relevant theory. So, for example, study of spectral characteristics of stationary conditions of nuclear and/or molecular systems and characteristics of transitions between energy levels is reduced to the Ritz principle for the main series (the Lyman system in absorption) where only transitions from the main level to higher are considered so that the energy difference between states is determined by size of the spectral term proportional to transition frequency ν.


where h is the Planck constant, c is the light velocity, λ is wavelength. Due to this model, the ratios determining the arrangement of spectral lines in various series can be obtained from the combinational principle of Ritz according to the Grotrian diagrams, which theorists apparently consider excessively unambiguous and consistent [5].

The current state of the theory of nuclear spectra allows rather strict consideration only in the case of one-electron atoms, i.e. for atom of hydrogen and hydrogen-like ions He+, Li2+, Be3+, etc. If physically electrons compose a uniform system in a polyatomic atom and/or molecule whether then it would be admissible to select separate electrons about which the concept in an atom/molecule was based on the one-electron approach? [6]. In this regard there is a question: whether there is an alternative to the one-electron description of multielectronic atoms and/or molecules?

Perhaps, it makes sense to analyze tangential functions for research of characteristics of a substance at absorption of radiation? The appeal to this type of the trigonometric functions (TF) has been caused by the fact that the system of harmonious octaves [7] correlates with the optics of radiation sources on characteristic features of their trigonometric functions [8].

Taking into account these problems, targets of this work are tangential sampling of a light continuum to define dependence of nuclear terms of the main series on the photon value of natural light and, in turn, determination of the electronic terms of molecules from terms forming a molecule of effective atoms. The ultimate purpose is the study of spectroscopic regularities in the information models (IM) of quantization (IMQ), absorption of light by atom (IM of atomic absorption – IMNA) and relative additivity of atomic terms (IMAT) during formation of molecules by them [9].

2. Theoretical Background

We use combination of the Cartesian coordinate system and the polar one with the required functions in radians for achievement of the purpose. Linear sampling of a light continuum can be done with the straight line equation in the Cartesian coordinates , where is the slope of straight line with angle φ from the Ox axis, b is the segment cut by a straight line on the Oy axis. At the sampling step determined by the slit delwidth Δλ, compliance is obtained between the wavelength λ and the relevant serial number in the continuum “spectrum”. For example, at the sampling step 1 nm, by starting the continuum from the wavelength 1 nm, we have


from which , that gives value with formal dimension of length [nm].

It follows from the ratio (2) that it is possible to establish dependence for arbitrarily set wavelength in the continuum at some “slit delwidth” Δλ with the meter to nanometer scale coefficient

where λ/Δλ is the resolving power at the difference of wavelengths Δλ, which are “separated by hardware function” yet. In turn, the interrelation of and has been obtained at coordination of sufficient resolving power with the relevant area of spectrum [3, p.31]


It follows from the formulas (1) and (3) that


On the other hand, if the continuum of natural light is presented through change of energy (1) as a function of wavelength variation Δλ and the relation of tangent square of this energy to this variation , then we get the tangential functions of discrete decomposition of light to characteristic components


where q is the integer slope of transformation of energy of a photon to the energy of an electron at equilibrium interaction of light with substance. This dependence has already demanded sampling of light stream in polar coordinates with radians (the length of an arch l is equal to the radius-vector r(p) with the polar angle φ).

Transition to the Cartesian coordinates has been done for correlation with the linear sampling

which presupposes division of the steps of sampling by ¼π in each octave (volume 2π) per relevant serial numbers of under the condition:

It follows from the ratio (5) that the value for a discrete spectrum , at the same resolution λ/Δλ as for is equal to


If the dimension of is electron-volt per radian [eV/rad], unlike the dimension of length [nm] then it is possible to connect their λ by a uniform algorithm of sampling with serial numbers и in a linear continuum and/or a discrete spectrum.

The discrete signal of both ones can be considered as a result of multiplication of functions (4) and (6):


that yields an alternative result depending on size of : in the continuum of the light stream, according to which whereas the value nm·eV/rad in the discrete spectrum of at that is shown in Figure 1 with vertical lines with the numbers on top of the relevant and for the 1 octave.

Figure 1. Sampling of the light continuum in the IMQ. The abscissa is the wavelength in nm; the ordinate nm, eV/rad and nm·eV/rad.

Figure 2. Regressions of the atomic terms of hydrogen and helium depending on sampling of the light field. The abscissa is Z, the ordinate is , nm·eV.

The ratio between and while matching of the scales of and on the abscissa is presented in Figure 1 from where it follows that linearly grows with wavelength increase according to equation (4) whereas decreases according to (6). has appeared identical for the relevant and equal to 1578.63 nm·eV/rad that corresponds to the value .

At the same time in the area of the hard x-ray and gamma radiations (λ < 40 nm, from ), the quantization gains another character, which is not connected with IMQ sampling on . Perhaps it is caused by reduction of the resolving power in this area [7] with the given “slit delwidth” of 1 nm.

3. Division of a Photon and a Quantum

Experience of creation of information models has shown that information as a product and/or result, turns into data immediately. What' s the matter? How it is possible and whether it is possible to divide data and information, and, in particular, a quantum and a photon?

The natural light presented through change of energy according to (1) as a function of change of wavelength , the relation of squared tangent of this value of energy to these changes give directly the tangential functions (TF) of decomposition to the characteristic components presented in Figure 1.

It is indicative that all points of this octave (,, etc) within 5 and above digits coincide with the known scale of energy in electron-volt (, , etc). From here according to the formula (1), wavelengths and the numbers and corresponding to serial numbers of indexes of and have been obtained.

Verification of the obtained octave: the charge and/or a term of an atom/molecule has to be multiple to an elementary charge and/or a term. And it has already indicated possible ratio of the TF parameters with ratio of angles of radiation impact on substance as it was presented in [9] .

Adequacy of the values of the first octave obtained in such way has also confirmed by compliance of the energy in the point of intersection of curves and i.e. the characteristic value at . And it, in its turn, has confirmed the famous provision on minimization of quantum effects upon transition of radiation from the visible range to IR under normal conditions of experiment (in particular, for weak fields).

At the assumption that a photon is a source radiation with energy and the unit eV, and a quantum is its “angle” of incidence on the projection/atom in radians, the equation (5) has naturally included both quantity and quality of photons relevant to the corresponding parameters of electrons as self-coordinated codes of information processing. Since in the Ist octave and it equals to relevant values per (5) in the subsequent ones then from positions of the theory of dimensions, the elementary principles of radiation quantization with relevant creation of IMQ as functions IMQ(TF) and IMAA(TF) have been obtained.

Strictly speaking from the informatics positions, a photon and a quantum have been separated in the physical sense not only quantitatively but qualitatively too. Because if we consider in the formula as a proportionality factor between continuums of energy and frequency only, then what is the physical sense of their quantization? Whether it is in sampling only or there could be some natural ways of identification of the discreteness in the continuums of energy and frequency? Since energy values of a photon are expressed by the ratio between then at the “initial” energy of IMQ corresponding to the angle from the formula (5), the following ratio has been obtained

Taking into account that for the first member of an octave q=φ_i/φ_1 =1,

From here it follows that, on the one hand, the value Z is an expression of energy per radian and, on the other one, is an original quantum number, which consistently increases by unit at the quantization step ¼π.

In other words, if earlier the quantization was done with the step 2π

Then in IMQ, the quantization value

ν = ⅛Z          (8)

Firstly, gives the integer values Z of photons number by the equality (6), which are absent in (1), secondly, is the dependence on quantum numbers mediated by (2)-(9). And what is the most essential, Z follows naturally from the light nature because both the first and all other nodal points of TF are connected with each other by the uniform information denotation.

In its turn, the value q by the formula (5) shows qualitative differences of photons in each octave, according to the angle φ

Formulas (6) and (8) where the angle value has been replaced with frequency ν and quantum energy (number of photons per radian Z) have attracted attention that at their substitution to the Planck formula have given direct confirmation of the previous conclusion on equality (6)

From these positions, the dimensional compliances of energy and radiation


incidence angle (1 eV = 1 rad) have appeared explainable since not absolute values of energy but relative, i.e. their changes relative to changes of angle/projection and/or wavelength have been used in all formulas of TF. Because earlier we have presented experimental data [9], according to which the criterion of manifestation of radiation maxima/minima in octaves is change of energy of radiation ΔE in IMQ and/or its absorption by atom in IMAA with values, which, on the one hand, are multiple of Δπ, and, on the other, of Δλ.

4. Conclusion

It can be assumed that continued studies of the IMQ and IMAA will create powerful tools and means for other optical correlations and/or information models that can produce new optical theories. Together with our results, this can be a definite contribution to prospective developments in the information-based interpretation of the concept of a photon in terms of quantum optics and in the nanoscience.

Conflicts of Interest

The author declares that there is no conflict of interest regarding the publication of this article.


© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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