Vol.3, No.8, 733-737 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.38097
Radioactivity of nuclei in a centrifugal force field
Oleg Khavroshkin*, Vladislaw Tsyplakov
Schmidt Institute of the Earth Physics, RAS Moscow, Russia; *Corresponding Author:
Received 23 May 2011; revised 2 June 2011; accepted 8 June 2011.
ABSTRACT
Radioactivity of nuclei in a centrifugal force field
of an ultracentrifuge is considered for heavy
radioactive nuclei, i.e., for the same nuclei, but
with a significant virtual mass thousands of
times larger than the actual mass and is char-
acterized by an angular momentum. As the nu-
cleus leaves the centrifugal force field, the vir-
tual mass disappears, but the spin number ap-
pears and/or changes. The role of centrifugal
and gravitational forces in radioactive decay of
nuclei is studied. According to the terminology
of western researchers, such a virtual mass
state is called the dynamic gravitation which is
more adequate. The oscillator and possible
changes in the nucleus state are considered
under conditions of dynamic gravitation and
taking into account features of atomic nucleus
physics. To a first approximation, the drop
model of the nucleus was used, in which shape
fluctuations have much in common with geo-
physical and astrophysical analogues. Shape
fluctuations of analogues strongly depend on
the gravitational force g defined by their mass
(or nucleus mass). Experiments were performed
by radiometric measurements of transbaikalian
uranium ore (1.5 g) with known composition in a
centrifuge at various rotation rates or gravita-
tional forces g. The existence of characteristic
times or the effect of rotation frequencies (i.e., g)
on atomic nuclei, which, along with the nucleus
type itself, controls the nucleus response to
perturbation (stability increase or decay), is
found statistically significant.
Keywords: Radioactivity; Nuclei; Ultracentrifuge;
Increase of Virtual Mass; Stability Increase of
Nucleis
1. INTRODUCTION
It is known that the state of the electron shell of heavy
radioactive nuclei has an effect on the half-life. For ex-
ample, more than several decades ago, French research-
ers showed a minor change in the half-life of a radioac-
tive element, depending on the type of chemical bonds
of elements forming a substance with a complex chemi-
cal composition. B.A. Mamyrin, Corresponding Member
of the Russian Academy of Sciences (St. Petersburg)
experimentally showed that the tritium ion is character-
ized by a shorter half-life which is decreased by 20% -
25% at total ionization. Theorists of the Kurchatov In-
stitute (Filippov et al.) studied the role of strong mag-
netic fields on the electron shell: the half-life of some
radioactive elements decreased by a factor of 10–7 in this
case. Of particular interest are long-term studies of the ά
decay by S.E. Shnol. Therefore, the heavy nucleus ra-
dioactivity in the centrifugal force field was considered.
That is the features of the same nucleus, but with a sig-
nificant virtual mass exceeding the actual mass by a fac-
tor of thousands and characterized by an angular mo-
mentum. This means that the virtual nucleus mass dis-
appears without centrifugal forces, but the spin appears
and/or changes. Centrifugal forces or dynamic gravita-
tion were widely used in studying the Möossbauer effect
and in experiments on testing the general relativity the-
ory (GRT) and equivalence principle [1-5]. According to
the equivalence principle, the motion in the gravitational
field is indistinguishable from the motion in an acceler-
ated system, e.g., in the centrifugal force field of a cen-
trifuge.
2. CENTRIFUGAL FORCE FIELD AND
RADIOACTIVE PROCESSES [1-3]
The energy of -ray photons of 57Fe nuclei was shifted
in the accelerated system [1-3] in the simplest centrifuge
[3]. In this case, the use of various statistical estimates
makes it possible, e.g., at the beginning of an increase in
the number of revolutions, to obtain an intensity de-
crease (0 - 100 revolutions per second (rps)) or a zero
increase plateau (200 - 300 rps). It is also of interest to
estimate the temperature thermal shift of the resonance
line in the Mössbauer effect [2], which would allow si-
multaneous consideration of the role of centrifugal

O. Khavroshkin et al. / Natural Science 3 (2011) 733-737 734
forces or dynamic gravitation [1,2].
The thermal acceleration aT as a factor affecting the
nucleus was estimated. At the lattice vibration frequency
  1013 Hz and harmonic vibrations, we have aT  1016
g which is insignificant for objects of nuclear scale [2].
The last statement for heavy radioactive and/or unstable
deformed nuclei does not seem convincing; however,
observations confirm this statement. Therefore, the exis-
tence of unexpected physical mechanisms “preserving”
the nucleus can be assumed. For example, the electron
shell is similar to a damping system at external accelera-
tions of the atom and internal accelerations of the nu-
cleus with respect to the electron shell. At times of
~10–12 s, the force constant at a relative displacement of
neutron and proton components in the 57Fe nucleus is
3·1023 dyn/cm; at an acceleration of 1016 g, the maxi-
mum displacement in the nucleus is ~10–13 of the nu-
cleus radius [4]. Even shorter times correspond to the
elastic interaction of particles with nucleus. Therefore,
the consideration of the nucleus as a purely mechanical
system (shell model) determines its mechanical charac-
teristics as a superstrength nuclear matter. In all experi-
ments when a -ray source was under conditions of dy-
namic gravitation, some radiation anomalies were ob-
served, which, unfortunately, were unnoticed by the au-
thors of [1-5].
2.1. Dynamic Gravitation and Features of
Atomic Nucleus Physics
2.1.1. Oscillator under Conditions of Dynamic
Gravitation [6,7]
Let us mainly consider only frequency properties. For
the classical oscillator, the oscillation frequency is
km  , where k and m are the oscillator stiffness
and mass. For the quantum-mechanical oscillator, the
features follow from the solution to the Schrödinger
equation, i.e., there exists a discrete set of energy eigen-
values En = ħ(12),km n n = 0, 1, 2,; ħ = h/2,
h is Planck’s constant; energy levels are arranged at
equal distances, the selection rule allows transitions only
between adjacent levels, the quantum oscillator emits
only at one frequency coinciding with the classical one
km  . The zero-point energy ħ  /2(  = 2/T, Т is
the oscillation period) exists for the quantum oscillator.
The zero-point oscillation amplitude is lm

, i.e.,
under conditions of dynamic gravitation, the quantum
oscillator emission frequency and the zero-point oscilla-
tion amplitude decrease. The harmonic oscillator Ham-
iltonian is expressed in terms of creation ˆ
A
 and anni-
hilation ˆ
A
operators,

ˆˆ ˆ12HhA A


.
All modern models of the quantum field theory are
determined on the multivariate generalization of this
expression, i.e., dynamic gravitation can have many ef-
fects, including those on the quantum oscillator transi-
tions from one energy level (n) to others (m) under an
external force. This is also true for oscillations of ele-
mentary particles and selection rules between energy
levels of quantum systems (elementary particle, atomic
nucleus, atom, molecule, crystal). Let us consider in
more detail the behavior of the atomic nucleus.
2.1.2. Atomic Nucleus under Conditions of
Dynamic Gravitation [8]
The atomic nucleus 10–12 - 10–13 cm in size has a posi-
tive electric charge multiple of the electron charge e
magnitude, Q = Ze, Z is the integer number, i.e., the
atomic number of the element in the periodic system.
The atomic nucleus consists of nucleons. The total
number of nucleons is the mass number A, the nucleus
charge Z is the number of protons, the number of neu-
trons characterizes the isotope; isotopes with different Z,
but equal N are isotones; isotopes with equal A, but dif-
ferent Z and N are isobars. Nucleons consist of quarks
and gluons; the nucleus is a complex system of quarks
and interacting gluon and meson fields. (The meson is a
complex system constructed of a pair of particles with
spin 1/2, i.e., quark and antiquark (qq
) and a small frac-
tion of gluons; the gluon is a neutral particle with spin 1
and zero mass; it is a carrier of the strong interaction
between quarks). However, the nuclear state cannot be
described within quantum chromodynamics because of
significant complexity. At not too high excitation ener-
gies or under normal conditions, deviations from the
nucleus steady state are minor and manifest themselves
as follows. During the interaction, nucleons can transit to
excited states (resonances) or nucleon isobars (1% in
time). In the nucleus, a quark-gluon matter bunch can
arise for a short time due to nonabsolute blocking of
quarks in nucleons. Nucleon properties in the nucleus
can differ from properties in the free state. In nuclei,
(virtual) mesons periodically (10–23 - 10–24) appear. The
study of non-nucleon degrees of freedom of the nucleus
is the problem of relativistic nuclear physics; however,
proceeding from the general nature of resonances and
instabilities, these processes will be suppressed under
conditions of dynamic gravitation.
Nucleons as hadrons exhibit the strong interaction
(nuclear forces) which confines them in the nucleus (the
result of the interaction between quarks and gluons; the
theory is not completed). The interaction via meson ex-
change is characterized by the interaction radius, i.e., the
Compton wavelength

с = h/µc, µ is the meson mass.
During the µ-meson exchange,

с = 1.41 ФМ (1 ФМ =
10–13 cm). In the case of heavier mesons (
 ,  , and oth-
ers), the interaction of nucleons is affected at shorter

O. Khavroshkin et al. / Natural Science 3 (2011) 733-737
735735
distances, repulsion between them occurs at ≤0.4 ФМ.
Under conditions of dynamic gravitation, the interaction
radius increases due to an increase in

с; however, re-
pulsion of nucleons can strengthen due to the dynamic
meson mass. It is important to note that the structure of
rotational spectra of nuclei changes during centrifugal
effects (an increase in the nucleus moment of inertia as
the angular momentum increases, Coriolis forces, and
others) [9,10]. In particular, this is true for deformed
nuclei where the gravitation effect can also manifest
itself. These effects are simpler explained by the drop
and superfluid models of the nucleus. In general, the
nucleus model choice is associated with the general
quantum formalism of the nucleus state description, and
the strict criterion does not exist up to now.
It seems that a simpler criterion can be used, i.e.,
characteristic frequencies of perturbations; the cutoff
frequencies for the shell model (≤10–12), below which
the drop model is preferable, are known. An analogy
from megascale effects can be presented. For the Earth,
in the case of perturbations with characteristic times of
105 - 106 s, the matter characteristics are close to those of
steel; at times 108 - 1010 s, seismotectonic flows are ob-
served. That is, the atomic nucleus at characteristic times
of 10–12 under quasi-static perturbations can exhibit
properties of liquid. In this case, perturbations of the
heavy deformed nucleus surface have the form of stand-
ing surface waves, and its oscillation description in-
cludes g in the first power. As the simplest estimates
show, the acceleration on the nucleus surface does not
exceed ~10–6 g. Therefore, we will consider nucleus os-
cillations under conditions of dynamic gravitation.
2.2. Vibrational Excitations of Nuclei [11,12]
In the case of dynamic gravitation, to a first approxi-
mation, it is easy to consider excitations within the drop
model; nucleus shape fluctuations are much in common
with geophysical and astrophysical analogues (Figures
1(а) and 1(b)), where the role of g is significant. For the
quantum description, for each vibrational mode (L, M),
vibrational quanta, i.e., photons, are introduced.
In deformed nuclei, the equilibrium shape has axial
symmetry. The photon energies depend on |K|; therefore,
the modes longitudinal and transverse to the symmetry
axis have different frequencies (Figure 1(b)).
Under strong deformations, oscillations are unstable
and the nucleus split. The strongest deformations are
observed for quadrupole and octupole modes of nucleus
oscillations (Figure 1(a)). At the same time, an increase
in the nucleus mass due to dynamic gravitation even by a
factor of 103 first of all suppresses these vibrational
modes, and reduces them to the monopole mode with
much smaller amplitude. Therefore, the nucleus stability
(a)
(b)
Figure 1. (a) Monopole (L = 0), dipole (L = 1), quadrupole (L
= 2), and octupole (L = 3) vibrational modes of the spherical
nucleus with the angular momentum L projection onto the
motion axis М = 0. The dipole mode is “false” (displacement
without changing the shape). The monopole mode (L = 0) cor-
responds to density fluctuations while retaining the spherical
symmetry. The dipole mode (L = 1) corresponds to the nucleus
centroid displacement and is not realized as the shape fluctua-
tion. In the quadrupole (L = 2) and octupole (L = 3) modes, the
oscillating nucleus is spheroid- and pear-shaped, respectively;
(b) The simplest nucleus shape fluctuations with axially sym-
metric quadrupole deformation (nucleus shape projections in
the directions perpendicular and parallel to the symmetry axis
are shown);
 R (  ,  , t) is the surface radius variation in the (  ,
 ) direction with time. The mode with K = ±1 is “false” (rota-
tion without changing the shape). Key: колебание --> oscilla-
tion; вращение --> rotation.
can increase, the decay process will be suppressed, and
the nucleus will get the property of the quasi-static one.
In the case of dynamic gravitation, the transition to the
monopole vibrational mode stabilizes the excited nu-
cleus state, but simultaneously lowers its frequency.
However, if we assume that the introduction of dynamic
gravitation is analogous to an increase in the number of
neutrons, we will obtain a decrease in the nucleus stabil-
ity. It is difficult to represent the complexity and ambi-
guity of radioactivity processes under conditions of dy-
namic gravitation without experimental study.
3. RADIOMETRIC STUDIES OF
RADIOACTIVITY UNDER
CONDITIONS OF DYNAMIC
GRAVITATION
Radiometric measurements of transbaikalian uranium

O. Khavroshkin et al. / Natural Science 3 (2011) 733-737 736
ore (1.5 g) with known composition (see Figures 2(а)
and 2(b)) were performed in a centrifuge with various
rotation rates.
The sample was fixed at an aluminum rod at a dis-
tance of 25 cm from the rotation center.
Preliminarily, radiometric measurements of the back-
ground were performed using a SOSNA ANRI-01-02
radiometer in
 and  modes (see the table, the first
column); then radiation of rapid rotation (4000 - 5000
rpm) was measured. The distance from the source to the
radiometer is 0.05 m at the nearest point during rotation.
Accelerations (g-forces) during rotation were determined
by the formula: а = (2N)2R, where N is the number of
revolutions per minute and R is the distance from the
rotation center. At 50 rpm, accelerations were on the
order of unity; at 4000 rpm, accelerations were 4400 g,
(g = 9.8 m/s2 is the gravitational acceleration on the
Earth). The measurement unit was microroentgen. The
results are listed in the table. The second column con-
tains background values, the third and fourth columns
correspond to rates of ~50 rpm and ~4000 - 5000 rpm,
respectively.
The difference between the background average and
the average for slow rotation exceeds four standard de-
viations and is 8.072; the difference between averages
for slow and rapid rotation is 6.858 which exceeds the
standard deviation by a factor of 3.46. Thus, the prob-
ability of the random effect is very low (P < 0.99). That
is, for rapid rotation, we observe a decrease in
 -radia-
tion below the background level.
(a)
(b)
Figure 2. (a) Non-calibrated source by the authors; (b) Calibrated source by the Institute of Geochemistry and Analytical Chemistry,
Russian Academy of Sciences, containing the following radioactive elements: 40K (78th channel, 1420 keV), 137Cs (37th channel, 662
keV), 60Со (64-72th channels, 1.17 and 1.33 MeV); 510 channel = 9.5 MeV.

O. Khavroshkin et al. / Natural Science 3 (2011) 733-737
737737
Table 1. Comparison of radioactivity of nuclei under condi-
tions of dynamic gravitation with background level.
No. μR (backgr.) μR (50 rpm) μR (4000 rpm)
1 7 22 10
2 10 17 11
3 11 19 11
4 8 18 12
5 12 16 15
6 8 18 13
7 14 15 11
8 10 16 11
9 13 19 11
10 12 18 15
11 10 17 10
12 11 18 11
13 10 20 8
14 5 21 9
Averages 10.071 18.142 11.285
Standard
deviations 2.432 1.955 1.97
4. DISCUSSION AND CONCLUSIONS
As follows from the above consideration, there are
characteristic times or frequencies of the influence on
atomic nuclei, which, along with the nucleus type itself,
define the nucleus response to a perturbation (stability
increase or decay). The elastic and inelastic interaction
processes and the efficiency of the nucleus shell model
point to times of ~10–10 s. Longer times or threshold
perturbations can be expected, depending on the nucleus
state and type, from 10–8 s and larger. Centrifuge experi-
ments point to effective perturbations at ~10–2 s. Proc-
esses with a pulsed increase in inertial forces (an impact
of a depleted uranium rod on an armored plate) cause
nucleus radioactivity at times of ~10–4 s. As the experi-
ments showed, at a g-force duration (~5000.0 g) of 10–4
s, nuclei can be only stabilized; for 238U, this means that
strongly deformed nuclei will take a spherical shape due
to dynamic gravitation. A g-force of 50000 g disap-
pears in ~10–7 s and is controlled by the uranium rod end
configuration. A pulse 10–7 s long is not short for the
nucleus; however, as the dynamic gravitation is relieved,
quadrupole and octupole nucleus oscillations can be ex-
cited for this time interval. Under such conditions, exci-
tation of nucleus oscillations results in instability and the
appearance of radioactivity.
We also note that the formalism of dynamic quantum
chaos is most appropriate to describe the above proc-
esses [13]. Thus, there exist still approximately deter-
mined time parameters for acceleration (perturbation)
durations for atomic nuclei, when (radioactive) proc-
esses occur in nuclei at a certain acceleration. These
phenomena can be most easily studied under conditions
of dynamic gravitation
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