J. Mod. Phys., 2010, 1, 86-89
doi:10.4236/jmp.2010.11012 Published Online April 2010 (http://www.scirp.org/journal/jmp)
Copyright © 2010 SciRes. JMP
Bohr Correspondence Principle and Multiphoton
Nature Raleigh Light Scattering
Valeriy E. Ogluzdin
Prokhorovs General Physics Institute, Russian Academy of Sciencesul, Moscow, Russia
E-mail: ogluzdin@kapella.gpi.ru
Received January 20, 2010; revised April 6, 2010; accepted April 10, 2010
The correspondence principle and the condition of supplementation were introduced by N. Bohr for the sub-
mission of light phenomena, taking into account the wave nature of electromagnetic radiation on one hand,
and its quantum structures on the other. In this paper, correspondence principle combines two models of
matter, namely, the classical point of view of environment can be considered as an ensemble no
equally-frequencies oscillators, i.e. electrons in the surrounding various atoms (molecules) of the matter and
characterized by its own set of frequencies (but not hesitant in the absence of an energy source) and the
quantum - environment could be presented as a set (ensemble) two-level systems, a wide range of Bohr fre-
quencies. According to the correspondence principle Bohr jump-frequencies of atoms (molecules or nano
particles) and natural frequencies oscillations of electrons of the same environment - oscillators are equal to
each other. The dispersion characteristics of the environment in the every study range of optical frequencies
correspond to the model of the classical harmonic oscillator of Lorenz, capable oscillates with Bohr fre-
quency. Using the laws of classical mechanics to describe the environment and its dispersion properties, and
the simultaneous presentation of light radiation in the form of a beam interacting with the environment of
photons (quanta, corpuscles) helps explain peculiarities of the spectral composition Raleigh light scattered.
Keywords: Correspondence Principle, Complementarily Condition, Raleigh Light Scattering, Classical
Harmonic Oscillator of Lorenz, Bohr Jump-Frequencies
1. Experimental Research RLS in Organic
Liquids by Fabelinskiy I. L. (1957)
The purpose of this message—the description of mul-
tiphoton model of Raleigh light scattering (RLS), using
the correspondence principle of N. Bohr.
Before turning to interpret RLS through multiphoton
model, we should remember the results of early experi-
ments, performed by I. L. Fabelinskiy (1957) [1], in
which it was found, that the fine structure of the spec-
trum of monochromatic light, scattered in pure organic
liquids, as a rule, consists of three spectral components.
Recall that to observe RLS in these experiments as a
source of radiation is used commonly available for such
studies mercury low pressure spectral lamp (line λ =
4358 A°). Through prolonged exposure photo plates
could benefit from economies of accumulation, which
even in the case of a weak signal was guaranteed for
black photo recording. In the article was presented an
overview of theories of molecular scattering of light in
pure liquids as well as a list of experimental works on
this subject (before 1957).
Typically, the structure of the spectrum RLS of pure or-
ganic liquid contains three spectral components. The spec-
tral shifts Stocks and anti-Stocks components concerning of
the central, unbiased, the most glaring components usually
are not equal to one another. In toluene, benzene and CS2
shifts Stocks and anti-Stocks components of the triplet in
different series of experiments for each substance do not
coincide with each other. This asymmetry was noted by I. L.
Fabelinskiy, and also attention was drawn to the fact that
anti-Stocks line less intense than Stocks. According to I. L.
Fabelinskiy, is the real reason for asymmetry shifts Stokes
and anti-Stocks components remained unknown while
writing the work? Disagreement Stocks and anti-Stocks
components on the frequency of the incident radiation may
indicate that the emergence of the spread of radiation com-
ponents are not connected to each other and are independent
of each other.
This difference is due to excitation of independent os-
Copyright © 2010 SciRes. JMP
cillators in the environment, some oscillator’s environ-
ment is responsible for Stocks frequency components,
while others—for anti-Stocks; detection of natural fre-
quencies of these oscillators and their search—is our
The only simultaneous recognition dispersion charac-
teristics of refractive indexes in this spectral field of dif-
ferent numerous (equal and unequal frequencies) oscil-
lators [2,3], uniformly filling the entire volume of the
environment can provide an answer to the question of
different intensity Stocks, anti-Stocks components of the
fine structure of RLS.
2. Correspondence Principle of N. Bohr [4];
Bohr Jump-Frequencies [5,6].
In the article, in the future statement considerable atten-
tion will be given to the simple oscillators of the medium.
It is their presence in the environment can be attributed
to our attention to the correspondence principle and to
the complementarily condition N. Bohr. The correspon-
dence principle and the complementarily condition has
been proposed by N. Bohr (1932) in order to remain as
long as possible in terms of the concepts of classical
physics, and as long as possible to explain physical re-
gularities with simple graphic models. Recall that the
correspondence principle (principle of supplementary,
complementarily, subsidiary) has been used Bohr to ex-
plain the relationship between the electromagnetic field
and light quanta [4].
In such system we have in accordance with the princi-
ple of correspondence (supplementary, complementarily,
subsidiary) different oscillators of environment associ-
ated with the electrons among the various two-level for-
mations (with atomic skeletons, fragments of molecules,
nanoparticles), the distance between the levels which can
be uniquely represented through the Bohr jump-fre-
quency ν0i (see Fermi E. 1965) [5]:
ν0i = (Ei E0)/h (1).
here Ei, E0—energy of excited and ground levels of me-
dium; h—Planck constant.
Important is the fact that the electrons in atomic (mo-
lecular ) environment can be represented in the form of
classic oscillators, each depending on the position in the
atom (molecule, nanoparticle) situation characterized by
some intrinsic of frequency vibrations. The frequency ν 0
i can be determined from the relationship between mass
of the electron m and the coefficient of elasticity G j, de-
scribing stiffness connection of electrons with the skele-
ton atom or molecule (Garbuny M. 1965) [7].
These frequencies (indices i and j denotes multiple
frequencies and communications within the molecule or
nanoparticle: i = 1,2,3 ... ; j = 1,2,3 ... ) easy to detect
and identify if we have the absorption or radiation spec-
tra of the investigated substance [6]. The degree of ab-
sorption (no transparency) of weak radiation by envi-
ronment in different parts of the spectrum and there are
ultimately a set of characteristic frequencies ν0i for the
given medium.
Narrow-lines nature of atomic spectra and stripe-ines
of molecular evidence that in the case of atoms electron
interaction with atomic skeleton (for the hydrogen - ker-
nel) is more simple than in the case of molecules or dif-
ferent-sized nanoparticles consisting of the ensemble of
molecules or atoms connected to one another.
At the same time, note that in the absence of a source
of excitation (that is, spectral lamps, arc, solar radiation
or laser) of investigated environment, its own character-
istics (Bohr jump-frequencies) do not appear explicitly,
and their detection is difficult.
As our research on scattering almost resonance radia-
tion in atomic vapor metals [8,9] or photoluminescence
phenomenon of Si-powder in the ethanol [10,11] in these
cases, direct observation characteristic Bohr jump-fre-
quencies ν0i environment with help of one-frequency ν
laser is made difficult and it is necessary additional
measurements spectrum. Their location can be calculated
only on the basis of processing of spectrograms, using
the ratio, follows from the conservation energy law, that
takes into account the spectral characteristics of envi-
ronment and has a kind of:
ν0i = 2ν νт (2).
here ν is the frequency of the radiation, that affects the
medium (environment); ν0i-frequencies oscillators envi-
ronment, they are Bohr jump-frequencies; h - Planck
constant is omitted;
index m is replaced by s (stoks), if ν < ν0i ,
index m is replaced by as (anti-stokes), if ν > ν0i .
Indexes s and as suited to the observed in the experi-
ment Stocks and anti-Stocks components radiation, scat-
tered by atomic medium [8,9], and can be applied to
photoluminescence [10,11].
If environment has continuous spectrum of absorption,
then using harmonics Fourier decomposition, we can
give all set of lines, each being determined her proper
Bohr jump-frequency.
A few words about the relationship (2):
νт = 2ν ν0i (3).
According to the theory [12] the probability of such
processes is low. However, all may be significantly sim-
plified, if one recalls the principle of correspondence and
classic dispersion theory, which describes the behavior
of the refractive index medium n (ν) near natural fre-
quencies ν0i classic Lorenz harmonic oscillators. Since in
this case the refractive index medium or less than unit, if
ν > ν0i, or many more units, if ν < ν0i, the processes, de-
scribed by relationship (3), are playing a decisive role in
these areas spectra, and, consequently; in this time the
the lower-order processes are ineffective. It is from this
perspective, we try to understand the nature RLS and its
complex spectral correct structure [1].
Copyright © 2010 SciRes. JMP
3. Dispersion of the Refractive Index N (v) of
Environment, Consisting of a Classical
Harmonic Oscillators Lorenz [2,3];
Multiphoton Nature RLS.
The purpose of this work is to explain the nature RLS,
based on attracting mechanisms suited to the role of cha-
racteristic frequency oscillators ν0i environment, as well
as contribute to the scattering processes multiphoton in-
terraction. Note that these characteristic frequencies os-
cillators ν0i we can compare (or equate them) Bohr fre-
quencies and use the condition of complementarity of
Bohr. The correspondence principle and condition of
complementarity of Bohr in this case connect the conclu-
sions follow from the model of classical harmonic oscil-
lator of Lorenz, on the one hand, and, on the other hand,
allow considering a two-level environments model and
the consequences arising from this model. We are in this
regard, in particular, would be interested in the corre-
spondence between the states of the classical harmonic
oscillator Lorenz and the electronic levels of atoms (mo-
lecules) of a two-level environment (in quantum model).
It should be noted, that in the classical model oscilla-
tor can be hesitate - after receiving a portion of energy,
or be able to stop; and one quarter period vibration oscil-
lators corresponds to a single act of converting kinetic
energy into potential, or vice versa. Such a portion of
energy in the quantum model of a two-level atomic sys-
tem corresponds to the transition of electron from the
level to level. This portion energy can either be absorbed
or be emitted. Once again, we remind you that if power
to the system is not introduced, the identification of fre-
quencies ν 0i , characterizing environment, difficult.
But in this case, we must remember that all frequencies
ν 0i environment, their full “virtual” spectrum is the call-
ing card of this media. And all frequencies ν0i—unique
and independent performances of the environment.
Due to the introduction of classical oscillators natu-
rally becomes our approach to the classical theory of
dispersion of the refractive index n (ν) of environment,
consisting of an ensemble of classical harmonic oscilla-
tors Lorenz. According to the theory of dispersion Lo-
renz [2,3] for the frequency of the incident radiation is
less than the natural frequency oscillators ν0i, the refrac-
tive index of environment more unit and with the reduc-
tion of the difference between frequency of the incident
radiation ν and frequency oscillators ν0i the refractive
index n (ν) can grow indefinitely: n (ν) ›› 1 [2].
Experiments on slow light, performed most recently
perfectly illustrate this, and the effect of slowing light
can be used to explain the long persistence of photolu-
minescence radiation [10,11]. Let us mark, that in these
same areas of the spectrum it is possible to create the
conditions for the spread of photons with “above light”
speed and they form a cone of Vavilov-Tcherenkov ra-
diation [8,9].
If the frequency of the radiation ν higher than the nat-
ural frequency oscillators ν0i, we face a situation, where
the refractive index of the environment becomes less
than unit: n (ν) < 1. The difference in the refractive index
of the unit serves as a natural barrier to the spread of
photons of light radiation, affects on the environment.
That obstacle can be overcome, assuming, that only
part of photons incident on environment almost reso-
nance radiation (ν ν0i) will be utilize on dynamic com-
pensation dispersion of the refractive index depending on
the frequency for protect: n (ν) 1. Populations lower
and upper levels in the atoms of a two-level environment
through the process (3) will be equalized and then we
will be n (ν) 1, which corresponds to enlightenment
environment, while another portion of the photons of the
same beam will be distributed through the medium
without signs of slowing down, which tends to be hap-
pening in physical experiments.
Multiphoton mechanism of dynamic compensation of
dispersion is well examplified by V. E. Ogluzdin [9] for
the near-resonant propagation of light through atomic
vapours potassium, as well as in the case application by
V. E. Ogluzdin [10,11] of this model to explain the phe-
nomenon of photoluminescence.
Before turning directly to the interpretation RLS based
on multiphoton model, we once again remind, that the
spectral structure RLS radiation is usually three spectral
component, and shifts Stockes and anti-Stockes compo-
nents relative to the central, unbiased frequency compo-
nent ν01 is not equal to each other. Typically, the inten-
sity Stockes components RLS, according I. L. Fa-
belinskiy, exceeds intensity anti-Stockes components and
in the spectrum of scattered radiation can abundant a
continuum that extends to 100-150 cm-1 in both sides of
the frequency of line of exciting radiation.
If the proposed model (see Equations (2) and (3)) is
true, then this scenario suggests, that the emergence of
Stokes and anti-Stockes components of RLS is associ-
ated with the excitement of independent sets of oscillator
environment and its opening on the frequency ν = ν01.
According to (3) Stokes and anti-Stockes components νs,
νas of RLS and their corresponding Bohr jump-frequencies
ν01, ν02ν0i are on different sides on the frequency of the
exciting radiation ν. Naturally, the emergence of Stokes
and anti-Stockes components can only appear in an area
occupied by light beam. Where excited radiation is lacking,
properties of environment do not change.
Under the experiment, this will not preclude the dis-
tribution of new frequency components νs, νas across im-
perturbable environment and registering them at photo-
plate. Generally speaking, this radiation is dispersed into
a 4 π steradian. Recall, that in the paper (I. L. Fabelinskiy
1957), the registration spectrum RLS realize in the
transverse direction concerning direction of the incident
The frequency ν of incident radiation may by accident
Copyright © 2010 SciRes. JMP
coincide with the frequency of the oscillator of environ-
ment (ν = ν0i). Since the refractive index [2] in this case
n (ν) = 1, the portion of the incident radiation at a fre-
quency ν can easily pass through medium. But we must
remember about of oscillators environment, Bohr jump-
frequencies of which are shifted to the frequency of the
incident radiation ν in the blue and red regions of the
spectrum. Ultimately, their presence, the dispersion
characteristics of the refraction indexes therefore: n (ν) >
1 or n (ν) < 1 determine process RLS, according to the
ratio of (3).
It is commonly supposed that RLS process is due mi-
crofluctuations density of the environment and the ori-
entation of its species. But the self influence of the radia-
tion to alter the optical properties and, in particular, the
emergence of these fluctuations is not considered.
However, microfluctuations of the refractive index of
the environment may arise from the fact, that the same
radiation is acted on by the environment, could be a
source of such microfluctuations and thus cause devia-
tions (or diffraction), as the radiation and its of Stokes
and anti-Stockes components, which is generally ob-
served in such experiments.
Incidentally, it is understandable situation, which oc-
curs in the case of the Stimulated (Mandelshtam-) Bril-
louin scattering (SBS), when the Stokes components of
radiation can be traced in the opposite direction; they are
reflected [13]. Really, in the moment of the generation of
the inversion of oscillators of medium for frequencies ν
< ν 0i at the front pulse of light can creat conditions, pro-
tecting to a change in the refractive index of the envi-
ronment: n (ν) < 1.
The inversion of a two-level environment produce in
the region Stocks of frequencies (νs < ν0i ) reduction in
the refractive index n (ν) of medium [14]. If will be real-
ized condition n (νs) < 1, then for SBS component take
place high reflectivity and this condition determine the
opposite direction of its spread.
4. Conclusions
A agreement between own frequencies different oscilla-
tors of environment and Bohr jump-frequencies of this
environment has brought to the interpretation of the fine
structure RLS mechanism, on the one hand, based on the
classical theory of dispersion, and on the other, based on
the concept of quantum, the corpuscular nature of light.
The possibility of observing RLS a wide body angle
(4π steradian) testifies to the absence of significant bar-
riers to its spread.
The intensity of anti-Stokes components observed in the
discussed experiment is smaller, than Stokes items and de-
pend from the refractive index of oscillators of environment,
whose frequencies correspond to a frequency of the incident
radiation. Reverse direction of the reflected Stokes SBS due
to a modified dispersion dependence of oscillators of envi-
ronment brought pumping radiation.
5. References
[1] I. L. Fabelinski, “Molecular scattering of light,” Uspekhi
Fizicheskikh Nauk, Russian Academy of Sciences, Mos-
cow, in Russian, Vol. 63, 1957, p. 355.
[2] M. Born and E. Wolf, “Principles of Optics,” Pergamon
Press, Oxford, London, Edinburg, New York, Paris,
Frankfurt, 1970.
[3] C. F. Bohren and D. R. Huffman, “Absorption and Scat-
tering of Light by Small Particles,” Willey, New York,
[4] N. Bohr, “Atomic Theory and the Description of Nature,”
Cambridge University Press, Cambridge, 1934.
[5] E. Fermi, “Notes on Quantum Mechanics: A Course
Given by Enrico Fermi at the University of Chicago,”
University of Chicago Press, Chicago, 1965
[6] V. E. Ogluzdin, “The Role of Bohr Freguencies in the
scattering, Luminescence, and Generation of Radiation in
Different Media,” Physics-Uspekhi, in English, Vol. 49,
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[7] M. Garbuny, “Optical Physics,” Academic Press, New
York and London, 1965.
[8] V. E. Ogluzdin, “Photons Traveling at the Speed of Light in
Two-Level Atomic Medium as a Sourse of Cherenkov Ra-
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p. 829; Uspekhi Fizicheskikh Nauk, Russian Academy of
Sciences, Moscow, in Russian, Vol. 174, 2004, p. 895.
[9] V. E. Ogluzdin, “Vavilov-Cherenkov Effect under Con-
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