KAMLAND-EXPERIMENT AND SOLITON-LIKE NUCLEAR GEOREACTOR
1 1 2 1 3
V.D. Rusov , D.A. Litvinov , S.Cht. Mavrodiev , E.P. Linnik , V.N. Vaschenko , T.N. 
1 1 1 1 1 1
Zelentsova , M.E. Beglaryan , V.A. Tarasov , I.V. Sharph , S.A. Chernegenko , V.P. Smolyar , 
1 1 1
P.A. Molchinikolov , K.K. Merkotan , S.A. Babiy   
1
 Odessa National Polytechnic University, 65044 Odessa, Ukraine, Shevchenko av., 1, 
siiis@te.net.ua
2
  The Institute for Nuclear Research and Nuclear Energy, BAS, 1784 Sofia, Bulgaria,
Tsarigradsko chaussee Blvd., 72, mavrodi@inrne.bas.bg
3
   State Ecological Academy for Second University-level Education and Management, 
03035 Kyiv, Ukraine, Urytskogo str., 35, daniilko@mail.ru
Abstract. We give an alternative description of the new data produced in the KamLAND experiment, 
assuming the existence of a natural nuclear reactor on the boundary of the liquid and solid phases of 
the Earth's core. Analyzing the uncertainty of antineutrino spectrum of georeactor origin, we show that 
the theoretical (which takes into account the soliton-like nuclear georeactor with power about 20 TW) 
reactor antineutrino spectrum describes with good accuracy the new experimental KamLAND-data. 
2 -5 2 2
At the same time the parameters of mixing ( m =2.5х10  eV , tan Θ =0.437) calculated within the 
21 12
framework of georeactor hypothesis are substantially closer to the data of solar flux SNO-experiment 
then the parameters of mixing obtained in KamLAND-experiment.
Key words: KamLAND-experiment; soliton-like nuclear georeactor; geoantineutrino spectrum 
Today it is obvious that the experiments of KamLAND-collobaration which are conducted 
during last five years (Eguchi et al., 2003; Araki et al., 2003, 2005; Abe et al., 2008) are extremely 
important not only for the observation of reactor antineutrino oscillations, but they make it possible to 
verify for the first time one of the most vivid and mysterious ideas in nuclear geophysics – the 
hypothesis of natural nuclear georeactor existence (Rusov et al., 2007). In spite of its singularity and 
long history, today this hypothesis is especially attractive because it enables clearly to explain in the 
view of physics many, on the face of it, unrelated geophysical anomalous effects, whose fundamental 
character is beyond any doubt.
3
First of all it concerns the problem of He isotope origin in the Earth interior, whose 
concentration, as is well known, “mystically” increases to the center of Earth. This is practically 
impossible to explain within the framework of classic geophysical notions, because, on the one hand, 
the existence of this isotope in nature is caused and predetermined exclusively by nuclear processes, 
3
and, on the other hand, the high mobility and chemical inertness of He atoms exclude their retention 
by any chemical or physical traps. For example, as is customary to consider within the framework of 
hypothesis of “solar” helium in the Earth's core, which was captured as far back as the period of 
accretion of the Earth and slowly seeped to the surface during a few milliards years. 
A potent argument in favour of nuclear georeactor existence are results of recent seismo-
tomography researches of abnormally high global core-mantle boundary heat flow (13±4 TW), which 
is several times higher than the value of radiogenic heat in lower mantle (D”-region) (Lay et al., 2006). 
To explain such an anomalous high heat flow the authors of this paper advanced the hypothesis of 
Δ
УКРАЇНСЬКИЙ АНТАРКТИЧНИЙ
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УАЖ № 9, 100-108 (2010)
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ЯДЕРНО-ФІЗИЧНІ ДОСЛІДЖЕННЯ
NUCLEAR-PHYSICAL RESEARCH
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young age (?) for the Earth's solid core, where the crystallization energy of the young solid core is the 
reason of anomalous temperature effect.
In full measure it concerns the known problem of the nature of power source maintaining the 
convection in the Earth's liquid core or, more precisely, the mechanism of magneto-hydrodynamic 
40
dynamo generating the Earth's magnetic field. Obviously, that the well-known K-mechanism of 
radiogenic heat production in the solid core of the Earth does not solve a problem in the whole, 
because it can not explain the heat flow energy balance on a core-mantle boundary. It should be noted 
also the so-called mechanism of the Earth's magnetic field inversions closely associated with the 
problem of convection in a liquid core. Surprisingly, both these fundamental mechanisms have simple 
and clear physical explanation within the framework of hypothesis of the existence of natural nuclear 
georeactor on the boundary of the liquid and solid phases of the Earth (Rusov et al., 2007, 2010) too.
If the georeactor hypothesis is true, the fluctuations of georeactor thermal power can influence 
on the Earth's global climate as anomalous temperature jumps due to following circumstances. Strong 
fluctuations of georeactor thermal power can lead to the partial blocking of convection in a liquid core 
(Rusov et al., 2010) and to the change of angular velocity of liquid geosphere rotation, and in that way 
by virtue of conservation law of Earth's angular moment to the change of angular velocity of mantle 
and the Earth's surface, respectively. This means that heat or, more precisely, dissipation energy 
caused by the friction of earthly surface and bottom layer can make a considerable contribution to 
atmosphere general energy balance and thereby substantially to influence on the Earth's global 
climate evolution (Rusov et al., 2010).
However, in spite of obvious efficiency and allurement of hypothesis of natural nuclear 
georeactor existence, the main difficulties of its perception are predetermined by non-trivial 
properties which georeactor must possess. At first, the natural, i.e. unenriched uranium or thorium 
must be used as a nuclear fuel. Secondly, the reactivity regulation system of reactor by traditional 
control rods is completely absents, but for all that a reactor must possess the property of so-called 
internal safety. It means that the critical state of reactor core must be continually maintained in any 
situation, i.e. the normal operation of the reactor is automatically maintained not as a result of operator 
activity, but by virtue of physical reasons-laws preventing the explosive development of chain 
reaction by the natural way. Figuratively speaking, the reactor with internal safety it is “nuclear 
installation which never explode” (Feoktistov, 1998).
Strangely enough, but reactors satisfying such an unusual requirements are possible in reality. 
For the first time the idea of such reactor was proposed by Feoktistov (1989) and independently by 
Teller, Ishikawa and Wood (1996).
The main idea of reactor with internal safety consists in the selection of fuel composition so that, 
at first, characteristic time  of the nuclear burning of fuel active (fissile) component is substantially 
greater than the characteristic time of delayed neutrons production and, secondly, the necessary self-
regulation conditions are meet during reactor operation (that always take place, when the equilibrium 
concentration of fuel active component is greater than critical concentration (Feoktistov, 1989)). 
These very important conditions can practically always to be attained, if among other reactions in a 
reactor the chain of nuclear transformations of Feoktistov uranium-plutonium cycle type (Feoktistov, 
1989)
or Teller-Ishikawa-Wood thorium-uranium cycle type (Teller et al., 1996)
will be enough appreciable 
239 233
In both cases the produced fissile isotopes of Pu or U are nuclear fuel active components. 
Characteristic time of such reaction, i.e. the time of proper β-decays, is approximately equal to  
(1)
(2)
V.D. Rusov. KAMLAND-EXPERIMENT AND SOLITON-LIKE NUCLEAR GEOREACTOR
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τ =2.3/ln2≈3.3 days and  39.5 days for reactions (1) and (2), respectively, that is several orders 
β
greater than the time of delayed neutrons production.
Self-regulation of the nuclear burning process (at indicated above ration between equilibrium 
and critical concentrations of fuel active components (Feoktistov, 1989)) is stipulated by the fact that 
such system left by itself can not pass from a critical condition to the reactor acceleration mode, 
because a critical concentration is bounded from above by finite value of plutonium equilibrium 
concentration, i.e. ñ >n . On phenomenal level the self-regulation of nuclear burning is manifested 
Pu crit
as follows. The neutron flux increase due to some reasons will result in the rapid burnup, for example, 
of plutonium, i.e. to decrease of its concentration as well as the neutron flux decrease, while the new 
239
nuclei of  Pu are produced with the same generation rate during about  = 3.3 days. And vice versa, 
if the neutron flux is sharply decreased due to external action, the burnup rate decrease too and 
plutonium accumulation rate will be increased as well as the number of neutron production in 
approximately same time. The analogical situation will be observed for thorium-uranium cycle (2), 
but in time  τ =39.5 days. 
β
Generation of the system of kinetic equations for components of nuclear fuel and neutrons (as 
the diffusion approximation) in such chains is sufficiently simple and was described in detail in our 
paper (Rusov et al., 2007). The solutions as concentration soliton-like waves of nuclear fuel 
components and neutrons which are typical for such problem (see Eqs. (3)-(9) in Ref. (Rusov et al., 
2007)) for uranium-plutonium cycle are presented in Fig.1. Within the framework of soliton-like fast 
reactor theory it is easily show that phase velocity u of soliton-like neutron wave of the nuclear 
burning is generally predetermined by following approximate equality: 
where ñ and n  are the equilibrium and critical concentrations of active (fissile) isotope, 
Pu crit
respectively; L is the average diffusion distance of neutron, τ  is delay time caused by active (fissile) 
β
isotope production, which amounts to the effective period of intermediate nuclei β-decay in uranium-
plutonium cycle (1) or in thorium-uranium cycle (2). 
τ ≈
β
τ
β
(3)
238 239 239
Fig. 1. Concentration kinetics of neutrons, U, U, Pu in the core of cylindrical reactor with radius 
of 125 cm and 1000 cm long at the time of 240 days. Here r is transverse spatial coordinate axis 
(cylinder radius), z is longitudinal spatial coordinate axis (cylinder length).
V.D. Rusov. KAMLAND-EXPERIMENT AND SOLITON-LIKE NUCLEAR GEOREACTOR
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Note that Eq. (3) automatically contains the self-regulation condition of nuclear burning because 
the wave existence is predetermined by inequality . In other words Eq.  (3) is the necessary 
physical requirement for the existence of the soliton-like neutron wave of nuclear burning. As it 
follows from Eq. (3), the upper bounds of the phase velocity of nuclear burning wave are 3.70 cm/day 
for uranium-plutonium cycle (1) and 0.31 cm/day for thorium-uranium cycle (2) at almost equal 
average diffusion distance (L~5 cm) of fast neutrons (1 MeV) both for uranium and thorium. 
Finally, we consider the some important details and properties of such soliton-like fast reactor, 
assuming the existence of which, we obtain the theoretical spectra of reactor and terrestrial 
antineutrino which are in good agreement with the experimental KamLAND data (Rusov et al., 2007) 
corresponding to first (Eguchi et al., 2003) and third (Araki et al., 2005) expositions. 
According to our notions (Rusov et al., 2007), a soliton-like fast reactor is located on the 
boundary of the liquid and solid phases of the Earth. The average thickness of such a shell-boundary, 
which has increased density and mosaic structure, is ~2.2 km (Kracnoshchekov et al., 2005). In our 
opinion, the most advanced mechanism for formation of such a shell below the mantle now are the 
experimental results of Anisichkin et al. (2005). According to these results, the chemically stable high-
density actinide compounds (particularly uranium carbides and uranium dioxides) lose most of their 
lithophilic properties at high pressure, sink together with melted iron and concentrate in the Earth's 
core consequent to the initial gravitational differentiation of the planet. On the other words, during 
early stages of the evolution of the Earth and other planets, U and Th oxides and carbides (as the most 
dense, refractory, and marginally soluble at high pressures) accumulated from a magma “ocean” on 
the solid inner core of the planet, thereby activating chain nuclear reactions, and, in particular, a 
progressing wave of Feoktisov and/or Teller-Ishikawa-Wood type. 
What is the thermal power of such a reactor? As a natural quantitative criterion of the georeactor 
3 4
thermal power we used the well-known (based on the geochemical measurements) He/ He radial 
distribution in the Earth's interior (Rusov et al., 2007). It turned out that the experimental average 
 3 4
values of He/ He for crust, the depleted upper mantle, the mantle (minus the depleted upper mantle) 
and the so called D”-region in the lower mantle are in good agreement with the theoretical data 
obtained by the model of Feoktistov's uranium-plutonium georeactor with thermal power of 30 TW. 
Fig. 2 shows the especial experimental investigation of geologically produced antineutrinos with 
KamLAND (Araki et al., 2005) and an alternative description of these data by georeactor model 
(Rusov et al., 2007).
Thereupon let us estimate the uncertainty of nuclear georeactor thermal power and then the 
uncertainty of the georeactor antineutrino spectrum. There is a need to notice here that, generally 
speaking, such uranium-plutonium georeactor can consist of a few hundreds or thousands reactors 
(with the total thermal power of 30 TW), which represents the individual burning “rivers' and 'lakes” 
of an inhomogeneous actinide shell located in the valleys of rough surface of the Earth's solid core 
239
(Rusov et al., 2007). In the general case, the fission rate of Pu for the uranium-plutonium cycle (1) it 
is possible to write down in the form
where Ф = υ∙n is the neutron-flux density;  is the neutron velocity; n is the neutron concentration;     
239  239
σ   is the fission cross-section of Pu; n   is Pu concentration; V is the volume of burning area.
f Pu
 ñ >n
fis crit 
υ
(4)
V.D. Rusov. KAMLAND-EXPERIMENT AND SOLITON-LIKE NUCLEAR GEOREACTOR
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It is easily seen, that due to the randomicity of the critical and equilibrium concentrations of 
plutonium in an actinoide shell and also stochastic geometry of the “rivers” and “lakes” of actinoide 
medium the relative variation of neutron flux density, plutonium concentration and size of burning 
areas can run up to 50% and more. In full measure it concerns the fission cross-section, whose 
variations are determined, first of all, by the non-trivial thermodynamics features (temperature and 
pressure) of actinoide shell. In this case for the relative variation of fission velocity following relation 
is right:
Let us show to what uncertainty of georeactor antineutrino oscillation spectrum the relative error 
of the fission rate of plutonium (5) leads. For this purpose we write down the theoretical form of 
measured total energy antineutrino oscillation spectrum dn/dE in the ith energetic bin:
Fig. 2. The      energy spectra in KamLAND (Rusov et al., 2007). Main panel, experimental points 
(solid black dots with error bars) together the total expectation obtained in KamLAND experiment 
(dotted black line) (Araki et al., 2005) and presented paper (thick solid blue line). Also shown are 
expected neutrino spectrum (solid green line) from Japan's reactor, the expected neutrino spectrum 
238 232
from georeactor 30 TW (red line), the expected signals from U (dashed red line) and Th 
13 16
(dashed green line) geoneutrinos, C( ,n) O reactions (dashed blue line) and accidentals (dashed 
black line). Inset, expected spectra obtained in KamLAND experiment (solid black line) (Araki et 
al., 2005) and our paper (Rusov et al., 2007) (solid green line) extended to higher energy. 
α
(5)
(6)
where
(7)
Here m  is the total number of fissions during exposure time Δ  determined by fission rate λ ; 
λ t Pu
υ (E) is the average number of detected antineutrino per fission in the ith energetic bin; ε is the 
i
detection efficiency of positrons of the inverse β-decay reaction; Np is the number of protons in the 
detector sensitive volume; Δ  is exposure time; p(E,L) is neutrino oscillation probability with the 
t
V.D. Rusov. KAMLAND-EXPERIMENT AND SOLITON-LIKE NUCLEAR GEOREACTOR
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104
2corresponding parameters of mixing and energy E at the distance L from reactor; (1/4πL ) is effective 
solid angle; σ  is the antineutrino-proton interaction cross-section of inverse β-decay reaction with the 
υp
corresponding radiation corrections (Rusov et al., 2007); Σαρ (E) is the energy antineutrino spectrum 
i i
of nuclear fuel in the ith energetic bin, MeV/fission; α  is the part of ith isotope.
i
Here we should note that, in general, it is rightfully to consider the energy antineutrino spectra at 
different reactor heat power as self-similar, that considerably lightens its further analysis. At the same 
time the self-similarity takes place only for equilibrium neutrino spectra (Aleksankin et al., 1989) 
typical for stationary processes in reactor core. And vice versa, the self-similarity conditions for 
equilibrium neutrino spectra are violated at nonstationary processes in the reactor core. This means, if, 
for example, the variations of energy neutron spectrum (and therefore the variations of mass yields 
239
induced by the fission of Pu) in the reactor core are considerable, corresponding neutrino spectra are 
not self-similar. Therefore calculated (“stationary”) spectra and experimental (“nonstationary”) 
spectra are differ up to 25% and higher (Aleksankin et al., 1989).
Obviously, due to the stochastic change of nuclear georeactor heat power caused by the 
variations of neutron flux, plutonium concentration, medium geometry (5) and georeactor neutrino 
geo
spectrum (7) the relative uncertainty of georeactor antineutrino oscillation spectrum n (E) in the ith 
i
energy bin (with allowance for Eqs. (5)-(7)) looks like:
where (Δ / )≥25% is the relative uncertainty of georeactor neutrino spectrum.
Therefore the lower estimation of the uncertainty of general antineutrino oscillation spectrum, 
which taking in account Eq. (8) and the contribution of uncertainty (4.14%) of antineutrino spectrum 
Jap
n (E)from the Japanese reactors (Abe et al., 2008), become
i
ρ ρ
i i
(8)
(9)
Note that just this uncertainty is shown as a violet band on the blue histogram in Fig.3.
Now we are ready to use the model of uranium-plutonium georeactor (Rusov et al., 2007) for the 
alternative description of the data produced in new KamLAND experiment (Abe et al., 2008). 
Obviously, that the standard methods of obtaining consistent estimates (e.g., the maximum-likelihood 
2 2
method) normally used for the determination of the oscillation parameters (Δm tg Θ ) (Eguchi et al., 
12, 12
2003; Araki et al., 2003, 2005; Abe et al., 2008) must take into account one more reactor, or, more 
specifically, account for the antineutrino spectrum of georeactor with the power ~30 TW which is 
6
located at a depth of  L ~ 5.2∙10  m. However following (Rusov et al., 2007), we apply here a simplified 
approach, the results of which application show that the hypothesis of the existence of a georeactor on 
the boundary of liquid and solid phases of the Earth's core does not conflict with the experimental data.
So, we proceed as in Ref. (Rusov et al., 2007): if CPT-invariance is assumed, the probabilities of 
the υ →υ  and               oscillations should be equal at the same values L/E. On the other hand, it is 
e e
2
known that the variations of Δm  are dominated over the more stable small variations of angle Θ in the 
spectral distortion (oscillations) of the “solar” neutrino spectrum. Therefore we can assume (basing on 
2
CPT-theorem) that the angle which is determined by the experimental "solar" equality tan Θ  = 0.447 
12
(Aharmim et al., 2008) may be used as the reference angle of mixing in KamLAND-experiment.
Finally, following the computational ideology of Ref. (Rusov et al., 2007) we give the results of 
2 -5 2 2
the verification of optimal oscillation parameters (Δm =2.5∙10  eV , tan Θ  =0.437) in the 
21 12
framework of the test problem of comparing the theoretical (which takes into account the georeactor 
operation) and the experimental spectrum of the reactor antineutrino on the base of new KamLAND 
V.D. Rusov. KAMLAND-EXPERIMENT AND SOLITON-LIKE NUCLEAR GEOREACTOR
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105
data (Abe et al., 2008) (Fig.3). We compare also the -profiles for KamLAND-hypothesis without 
georeactor and our georeactor hypothesis (Fig. 4). 
χ
2
Fig. 3. Prompt event energy spectrum of       candidate events. The shaded background and 
geo-neutrino histograms are cumulative. Statistical uncertainties are shown for the data; the 
violet band on the blue histogram indicates the event rate systematic uncertainty. The georeactor 
power is 19.5 TW 
2
Fig. 4. Dependences of /NDF on the mass squared difference          corresponding to KamLAND-
2
hypothesis without georeactor (blue line, tg =0.56 (Abe S. et al., 2008)) and our georeactor 
12
2
hypothesis (red line, tg =0.437).
12
χ
Θ
Θ
Not looking at the low statistics of neutrino events (≤150 events/bin), the theoretical (which 
takes into account the soliton-like nuclear georeactor with power 19.5 TW) reactor antineutrino 
spectrum describes with acceptable accuracy the new experimental KamLAND-data (Abe et al., 
2008) (Fig. 3). Here we pay attention to some important moments. Firstly, the average georeactor heat 
power is changed from 30 TW at the exposure time of 749.1±0.5 days in 2005 (Araki et al., 2005) (Fig. 
2) to ~20 TW at total exposure of 1890 days in 2008 (Abe et al., 2008) (Fig.3). This reflects the 
nonstationary nature of the georeactor. Secondly, we have positive in respect to CPT-theorem physical 
fact that the parameters of mixing obtained within the framework of georeactor hypothesis are 
V.D. Rusov. KAMLAND-EXPERIMENT AND SOLITON-LIKE NUCLEAR GEOREACTOR
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106
2 -5 2 2
substantially closer to the data of solar flux SNO-experiment (Δm = 4.57∙10  eV , tan Θ =0.447 
21 12
2 -5 2 2
(Aharmim et al., 2008)) then the parameters of mixing (Δm = 7.58∙10  eV , tan Θ =0.56 (Abe et al., 
21 12
2008)) obtained in KamLAND-experiment.
In conclusion, we should note that although the nuclear georeactor hypothesis which we used for 
the interpretation of KamLAND-experiment seems to be very effective, it can be considered only as a 
possible alternative variant for describing the KamLAND experimental data. In this sense, 
paradoxically as it may seem, only direct measurements of the geoantineutrino spectrum in the energy 
range >3.4 MeV in the future underground or submarine experiments will finally settle the problem of 
the existence of a natural georeactor and will make it possible to determine the "true" values of the 
reactor antineutrino oscillation parameters. At the same time just solution of the direct and the inverse 
problems of the remote neutrino tomography for the intra-terrestrial processes which is essential to 
obtain the pure geoantineutrino spectrum and to determine correctly the radial profile of the β-sources 
in the Earth's interior (Rusov et al., 2004, 2008) will undoubtedly solve the problem of the existence of 
a natural nuclear reactor on the boundary of the liquid and solid phases of the Earth's core as well as the 
determination of the true geoantineutrino spectrum.
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