On electric polarization of helium atoms by acceleration
Possibility of explanation of high electric activity in superfluid helium [1–3] by polarization of helium atoms caused by acceleration is researched. It is shown that this effect is insufficient to explain the phenomenon. Исследована возможность объяснения наблюдаемой повышенной электрической активн...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
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| Цитувати: | On electric polarization of helium atoms by acceleration / Yu.M. Poluektov, V.N. Savchenko // Вопросы атомной науки и техники. — 2012. — № 1. — С. 299-301. — Бібліогр.: 6 назв. — англ. |
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Poluektov, Yu.M. Savchenko, V.N. 2016-10-14T10:40:31Z 2016-10-14T10:40:31Z 2012 On electric polarization of helium atoms by acceleration / Yu.M. Poluektov, V.N. Savchenko // Вопросы атомной науки и техники. — 2012. — № 1. — С. 299-301. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 67.40.Pm https://nasplib.isofts.kiev.ua/handle/123456789/107162 Possibility of explanation of high electric activity in superfluid helium [1–3] by polarization of helium atoms caused by acceleration is researched. It is shown that this effect is insufficient to explain the phenomenon. Исследована возможность объяснения наблюдаемой повышенной электрической активности сверхтекучего гелия [1–3] эффектом поляризации атома гелия при его ускорении. Показано, что этой причины не достаточно для объяснения величины эффекта. Досліджена можливість пояснення спостереженої підвищеної електричної активності надплинного гелію [1–3] ефектом поляризації атома гелію при його прискоренні. Показано, що цієї причини недостатньо для пояснення величини ефекту. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Section E. Phase Transitions and Diffusion Processes in Condensed Matter and Gases On electric polarization of helium atoms by acceleration Об электрической поляризации атомов гелия при ускорении Об електричній поляризації атомів гелію при прискоренні Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
On electric polarization of helium atoms by acceleration |
| spellingShingle |
On electric polarization of helium atoms by acceleration Poluektov, Yu.M. Savchenko, V.N. Section E. Phase Transitions and Diffusion Processes in Condensed Matter and Gases |
| title_short |
On electric polarization of helium atoms by acceleration |
| title_full |
On electric polarization of helium atoms by acceleration |
| title_fullStr |
On electric polarization of helium atoms by acceleration |
| title_full_unstemmed |
On electric polarization of helium atoms by acceleration |
| title_sort |
on electric polarization of helium atoms by acceleration |
| author |
Poluektov, Yu.M. Savchenko, V.N. |
| author_facet |
Poluektov, Yu.M. Savchenko, V.N. |
| topic |
Section E. Phase Transitions and Diffusion Processes in Condensed Matter and Gases |
| topic_facet |
Section E. Phase Transitions and Diffusion Processes in Condensed Matter and Gases |
| publishDate |
2012 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Об электрической поляризации атомов гелия при ускорении Об електричній поляризації атомів гелію при прискоренні |
| description |
Possibility of explanation of high electric activity in superfluid helium [1–3] by polarization of helium atoms caused by acceleration is researched. It is shown that this effect is insufficient to explain the phenomenon.
Исследована возможность объяснения наблюдаемой повышенной электрической активности сверхтекучего гелия [1–3] эффектом поляризации атома гелия при его ускорении. Показано, что этой причины не достаточно для объяснения величины эффекта.
Досліджена можливість пояснення спостереженої підвищеної електричної активності надплинного гелію [1–3] ефектом поляризації атома гелію при його прискоренні. Показано, що цієї причини недостатньо для пояснення величини ефекту.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/107162 |
| citation_txt |
On electric polarization of helium atoms by acceleration / Yu.M. Poluektov, V.N. Savchenko // Вопросы атомной науки и техники. — 2012. — № 1. — С. 299-301. — Бібліогр.: 6 назв. — англ. |
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2025-11-26T00:08:21Z |
| last_indexed |
2025-11-26T00:08:21Z |
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| fulltext |
ON ELECTRIC POLARIZATION OF HELIUM ATOMS BY
ACCELERATION
Yu.M. Poluektov 1∗and V.N. Savchenko 2
1National Science Center “Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
2V.N. Karazin Kharkov National University, 61077, Kharkov, Ukraine
(Received October 31, 2011)
Possibility of explanation of high electric activity in superfluid helium [1–3] by polarization of helium atoms
caused by acceleration is researched. It is shown that this effect is insufficient to explain the phenomenon.
PACS: 67.40.Pm
1. INTRODUCTION
In a number of experimental works [1–3] an unex-
pected high electric activity of superfluid helium was
observed, existing under different conditions. In work
[1] it was discovered that propagation of second sound
waves is followed by oscillations of electric field. In
subsequent experiments [2, 3] it was shown that the
polarization in helium can arise without temperature
oscillations if continuous fluxes are present. In order
to explain experiments [1–3], studying electric phe-
nomena in superfluid helium, in [4, 5] a mechanism
of polarization of helium atoms under the action of
gravitation and acceleration was proposed. It was
shown [4, 5], based on analogy with Stuart-Tolmen
effect and some phenomenological arguments, that
accelerated atom must gain dipole moment
�d = γ�̇v, (1)
where �̇v is the acceleration of atom, γ = Mκ0/2Z|e|
is the “gravitoelectric” susceptibility, κ0 is the polar-
izability of single atom, M,Z are the atomic mass
and nucleus charge, |e| is the elementary charge.
Gravitational and inertia forces are sensitive nei-
ther to magnitude, nor to the sign of the charge, thus
the nature of the predicted in [4,5] effect needs more
detailed analysis. In connection with this a quantum-
mechanical problem of helium atom in the ground
state under the action of external forces is considered
in this work. It is shown, that if these forces are of
gravitational and inertial nature, atom is not polar-
ized. Accelerated atom in gravitational field can be-
come polarized if there are also forces of other nature
acting upon it. The obtained value of polarization is
three orders of magnitude less than the estimated in
works [4, 5] and is of different sign.
2. CONSIDERATIONS
Consider hamiltonian of helium atom in ground state
with a constant force �F acting upon its nucleus and
�f acting upon its electrons:
H = − h̄2
2M0
��R − h̄2
2m
��r1 −
h̄2
2m
��r2−
−Ze2/|�R− �r1| − Ze2/|�R− �r2|+
+e2/|�r1 − �r2| − �F �R− �f�r1 − �f�r2,
(2)
where �R denotes coordinate of nucleus, �r1, �r2 are co-
ordinates of electrons, M0,m are masses of nucleus
and electron respectively. The next coordinate trans-
formation:
�x1 = �r1 − �R, �x2 = �r2 − �R,
�X = (M0
�R+m�r1 +m�r1)/(M0 + 2m),
(3)
reduces the problem to that of helium atom in effec-
tive electrical field with intensity of
�Eeff = (m�F −M0
�f)/(|e|M). (4)
Full wave function of helium atom can be presented
in the next form
Φ( �X, �x1, �x1) = ϕ( �X)Ψ(�x1, �x1), (5)
where ϕ( �X) is the wave function of whole atom
motion and is not responsible for its polariza-
tion. Variational approach is used for calculations.
For helium atom in ground state approximately
Ψ(�x1, �x1) = ψ(�x1)ψ(�x1), where probe function is
ψ(�r) = C(ψ0(�r) +Bψ1(�r)), (6)
∗Corresponding author E-mail address: yuripoluektov@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1.
Series: Nuclear Physics Investigations (57), p. 299-301.
299
C = (1 +B)1/2 is a normalization constant,
ψ0(�r) =
√
Z3∗
πa3
0
exp(−Z∗
r
a0
),
ψ1(�r) =
√
Z5∗
πa5
0
r cosϑ exp(−Z∗
r
a0
),
(7)
a0 = h̄2/me2 denotes Bohr radius, ϑ is the angle be-
tween the electric field and radius-vector of electron.
Wave function contains two variational parameters
Z∗ and B. Accuracy of calculation with this wave
function is about 10%.
In the first order of magnitude by small ratio of
external field to field, created by elementary charge
at distance of Bohr radius, the equation for dipole
moment is
�d = κ�Eeff , (8)
where in used estimation κ = 8a3
0/AZ
3
1 , A = 31/16,
Z1 = 27/16.
Consider helium atom in gravity field �g and
uniform electric field �E. In addition, consider a
force of another nature �Fe acting upon atomic nu-
cleus and a force �fe acting upon electrons. We
do not specify the nature of these forces yet.
Then the resultant force acting upon nucleus is
�F = M0�g + Z|e| �E + �Fe, and resultant force acting
upon electrons is �f = M0�g − |e| �E + �fe. Taking (4)
into account, effective intensity becomes
�Eeff = �E + (m�Fe −M0
�fe)/(|e|M). (9)
There is no term containing gravity in this equation.
Thus, in absence of electric field and forces of an-
other nature, �Eeff = 0, the atom can not be polar-
ized. For forces resulting in polarization the next
condition must be satisfied
m�Fe −M0
�fe �= 0. (10)
For gravitational forces this condition is not satis-
fied, so gravity itself can not lead to polarization. It
is natural, because under the action of gravity nu-
cleus and electrons move with the same acceleration
and no charge separation occurs. Inertial force −M�̇v
is also proportional to the mass, and therefore, as in
the case of gravity, can not itself result in polarization
of atom. Resultant force acting upon atom
�Fa = M�g + �Fe + Z �fe, (11)
is the sum of gravitational force and forces of other
nature. Under act of this force atom in non-
relativistic approximation moves with acceleration
�̇v = �Fa/M . Consider separately two cases. The first,
when the force of another nature acting upon electron
is zero: �fe = 0. Also assume the absence of electric
field �E = 0. Taking into account (8) and (9) the di-
pole moment of a single atom is
�d =
κm
|e| (�̇v − �g). (12)
If the force �Fe is so that atom is not accelerated �̇v = 0,
then from (12) can be concluded that direction of di-
pole moment of atom is opposite to the direction of
gravitational field. It is simple, because the position
of nucleus is fixed by the force of another nature, �Fe,
and electrons, that are assumed not to experience an-
other nature force, shift in the direction of gravity. If
there is no gravity, atom moves with acceleration �̇v
under the action of force �Fe, and dipole moment has
the same direction as acceleration. Electron, that ex-
periences coulomb force of the nucleus, lags from ac-
celerated nucleus. Then the force �Fe must be under-
stood as force acting upon nucleus from accelerated
lattice.
Now consider �Fe = 0 and force �fe acting upon
electrons. It is not clear how the case, when there is a
force that fixes the position of electron cloud and does
not affect the nucleus, can be implemented. Most
likely, this is just a hypothetical possibility. In this
case the mass of nucleus, instead of electron mass,
enters the numerator of the equation for dipole mo-
ment, and its sign changes to the opposite:
�d = −κM0
Z|e| (�̇v − �g). (13)
Note that in this form (1) the dipole moment, in-
duced by polarization and acceleration, is presented
in works [4, 5].
Consider polarization of solid dielectric, that con-
tains n atoms in unit volume and is accelerated under
the action of external force �Fe = M�̇v. The coulomb
force, that acts on electron from its nucleus, was
taken into account in the derivation of formula for
effective intensity (9). Atoms in the accelerated di-
electric are polarized under the action of effective
field. It means, that electric field �E appears acting
upon electrons of every atom. For displacement vec-
tor �D = �E + 4π �P in absence of external charges and
currents the equations div �D = 0 and ∂ �D/∂t = 0 are
true. Thus, in assumption of no spontaneous symme-
try breakdown, �E = −4π �P , where polarization den-
sity �P = n�d. Consider forces of another nature acting
upon electron �fe = 0. Taking into account the last
equations and (8), one finds
�P =
κnm
ε|e| �̇v = γ�̇v, (14)
where ε = 1 + 4πκn is the dielectric permittivity and
γ = κnm/ε|e| is the gravitoelectric susceptibility. In
our case this coefficient significantly differs from (1)
presented in [4, 5] because there is the electron mass
in the numerator instead of the atom mass. It means,
that the effect is three orders of magnitude less than
that given in works [4, 5]. Besides, equation (14)
differs in sign from the corresponding equation in
works [4, 5].
Estimated value of acceleration necessary for
gaining dipole moment of polar molecule, that is
about one debye, is �̇v = 0.5· 1024 cm/s2. Due to
some estimations (private communication from A.S.
300
Rybalko) atom in superfluid helium can have sta-
tic dipole moment about d ≈ 10−4D. Such value is
reached at acceleration �̇v = 1020 cm/s2. Amplitude
of acceleration in first sound wave is a = ωu(Δρ/ρ0),
where u denotes sound velocity, ω is the frequency,
Δρ/ρ0 is the ratio of density oscillation amplitude
to equilibrium density. At sound velocity u ≈
2.8· 104 cm/s and wavelength λ ≈ 10−1 cm the
frequency is ω ≈ 1.8· 106 s−1. For typical value
Δρ/ρ0 = 10−5 the amplitude of acceleration in sound
wave is a = 5· 105 cm/s2. This value is three or-
ders of magnitude less than necessary for obtaining
needed dipole moment. At such acceleration and
atomic density n ≈ 10−22 cm−3 an electric field
E = 4πnd ≈ 10−13 CGSE units arises in dielectric.
At wavelength λ ≈ 10−1 cm the appropriate poten-
tial difference is U ≈ 10−12 V, that is three orders of
magnitude less, than observed in work [1].
3. CONCLUSIONS
The research made in the present work allows to con-
clude the following:
• Neither gravitational nor inertial forces can lead
to the polarization of atom, since they are not
sensitive to the sign and magnitude of charge,
and the acceleration under the action of these
forces do not depend on the particle mass. Ac-
tion of forces of another nature is necessary to
respond for the polarization of atom.
• Estimation of polarization of an accelerated
solid dielectric, obtained in this work, is three
orders of magnitude less than given in works
[4,5].
• Considered effect in normal fluids must be even
less than in solid dielectrics because of absence
of long-range correlations.
• There is a specific long-range order in superflu-
ids, connected with the phase symmetry break-
down, but apparently it cannot significantly in-
crease the considered effect. Thus, estimations
and considerations given in this paper allow us
to conclude that observed electric activity of
superfluid cannot be explained by the effect of
polarization of helium due to acceleration.
References
1. A.S. Rybalko. Observation of electrical induction
in a wave of the second sound in He II // Fiz.
Nizk. Temp. 2004, v. 30, p. 1321-1325.
2. A.S. Rybalko and S.P. Rubets. Observation of
the mechanoelectric effect in He II // Fiz. Nizk.
Temp. 2005, v. 31, p. 820-825.
3. A.S. Rybalko, S.P. Rubets, E.Ya. Rudavskii,
V.A. Tikhiy, S.I. Tarapov, R.V. Golovashchen-
ko, and V.N. Derkach. Microwave experiments in
He II. New features of undamped superfluid flows
// Fiz. Nizk. Temp. 2008, v. 34, p. 631-639.
4. L.A. Melnikovsky. Polarization of Dielectrics
by Acceleration // arXiv :cond-mat/0505102v3
[cond-mat.soft], 2 Feb. 2008.
5. L.A. Melnikovsky. Polarization of Dielectrics by
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p. 559-564.
6. L.D. Landau, E.M. Lifshitz. Electrodynamics of
Continuous Media. Moscow: “Nauka”, 1982 (in
Russian).
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