Negative ions in liquid helium
Structure of negative ions in liquid ⁴He is analyzed. The possibility of cluster or bubble formation around impurity ions of both signs is discussed. It is demonstrated that in superfluid helium, around negative alkalineearth metal ions, bubbles are formed and, around halogen ions, clusters are form...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1185692017-05-31T03:08:16Z Negative ions in liquid helium Khrapak, A.G. Schmidt, W.F. 8th International Conference on Cryocrystals and Quantum Crystals Structure of negative ions in liquid ⁴He is analyzed. The possibility of cluster or bubble formation around impurity ions of both signs is discussed. It is demonstrated that in superfluid helium, around negative alkalineearth metal ions, bubbles are formed and, around halogen ions, clusters are formed. The nature of “fast” and “exotic” negative ions is also discussed. It is assumed that the “fast” ions are negative ions of helium excimer molecules localized inside bubbles. The “exotic” ions are stable negative impurity ions, which are always present in small amounts in gas discharge plasma. Around such ions, bubbles or clusters are created with radius smaller the radius of electron bubbles. 2011 Article Negative ions in liquid helium / A.G. Khrapak, W.F. Schmidt // Физика низких температур. — 2011. — Т. 37, № 5. — С. 494–499. — Бібліогр.: 46 назв. — англ. 0132-6414 PACS: 67.25.D–, 47.55.D– http://dspace.nbuv.gov.ua/handle/123456789/118569 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals Khrapak, A.G. Schmidt, W.F. Negative ions in liquid helium Физика низких температур |
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Structure of negative ions in liquid ⁴He is analyzed. The possibility of cluster or bubble formation around impurity ions of both signs is discussed. It is demonstrated that in superfluid helium, around negative alkalineearth metal ions, bubbles are formed and, around halogen ions, clusters are formed. The nature of “fast” and “exotic” negative ions is also discussed. It is assumed that the “fast” ions are negative ions of helium excimer molecules localized inside bubbles. The “exotic” ions are stable negative impurity ions, which are always present in small amounts in gas discharge plasma. Around such ions, bubbles or clusters are created with radius smaller the radius of electron bubbles. |
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Khrapak, A.G. Schmidt, W.F. |
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Khrapak, A.G. Schmidt, W.F. |
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Khrapak, A.G. |
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Negative ions in liquid helium |
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Negative ions in liquid helium |
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Negative ions in liquid helium |
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Negative ions in liquid helium |
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Negative ions in liquid helium |
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negative ions in liquid helium |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2011 |
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8th International Conference on Cryocrystals and Quantum Crystals |
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| citation_txt |
Negative ions in liquid helium / A.G. Khrapak, W.F. Schmidt // Физика низких температур. — 2011. — Т. 37, № 5. — С. 494–499. — Бібліогр.: 46 назв. — англ. |
| series |
Физика низких температур |
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AT khrapakag negativeionsinliquidhelium AT schmidtwf negativeionsinliquidhelium |
| first_indexed |
2025-07-08T14:15:16Z |
| last_indexed |
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| _version_ |
1837088497796644864 |
| fulltext |
© A.G. Khrapak and W.F. Schmidt, 2011
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5, p. 494–499
Negative ions in liquid helium
A.G. Khrapak
Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow 125412, Russia
E-mail: khrapak@mail.ru
W.F. Schmidt
Free University, Berlin 14195, Germany
Received December 1, 2010
Structure of negative ions in liquid 4He is analyzed. The possibility of cluster or bubble formation around
impurity ions of both signs is discussed. It is demonstrated that in superfluid helium, around negative alkaline-
earth metal ions, bubbles are formed and, around halogen ions, clusters are formed. The nature of “fast” and
“exotic” negative ions is also discussed. It is assumed that the “fast” ions are negative ions of helium excimer
molecules localized inside bubbles. The “exotic” ions are stable negative impurity ions, which are always present
in small amounts in gas discharge plasma. Around such ions, bubbles or clusters are created with radius smaller
the radius of electron bubbles.
PACS: 67.25.D– Superfluid phase;
47.55.D– Drops and bubbles.
Keywords: liquid helium, negative ions, electron and ion bubbles.
1. Introduction
The positive helium ions and electrons in liquid helium
exhibit very low mobilities. This is due to the fact that a
spherical region of solid helium with a radius of about
0.7 nm is formed around the ion because of a polarization
interaction with the atoms of the liquid, whereas the elec-
tron is localized in a bubble, whose radius is close to 2 nm,
because of a strong exchange interaction (e.g., see [1–3]).
The mobility was also measured for a number of positive
impurity ions in superfluid 4He [4–6]. A qualitative differ-
ence between the mobilities of alkali and alkaline-earth
metal ions was found (see Table 1): the mobilities of alkali
metal ions were smaller than the He+ mobility and de-
creased with the atomic number, but the mobilities of the
alkaline-earth metal ions (other than Be+) were higher than
the He+ mobility and increased with the atomic number.
These differences cannot be interpreted in terms of the
simple electrostatic model proposed by Atkins [7], in
which the structure of a complex depends only on the ionic
charge. Cole and Bachman [8] gave a qualitative explana-
tion for the effects observed. In their considerations the
radius of the ionic complex strongly depends on the exten-
sion of the wave function of the lone valence electron,
which causes a repulsive interaction with the surrounding
helium. In the case of alkali metal ions the van der Waals
interaction of the ion core with helium atoms plays an ap-
preciable role. This interaction results in an increase in the
radius of a solid ion complex and in the dependence of this
radius on the atomic number. In the case of alkaline-earth
metal ions, the valence electrons have extended orbits and
the formation of empty voids around the ions is possible.
This effect is connected with the strong exchange interac-
tion of the valence electrons with the shell electrons of the
atoms of the surrounding liquid.
Table 1. Mobilities of positive impurity ions in liquid 4He at
= 1.3T K [5]
Ion He+ K+ Rb+ Cs+ Be+ Ca+ Sr+ Ba+
μ , cm2/(V·s) 0.88 0.85 0.78 0.78 0.81 0.98 1.01 1.12
The structure and transport properties of electrons and
positive ions in low temperature atomic liquids have been
well studied. Much less is known about the properties of
negative ions. Only in a few works the mobility of 2O− in
Ar, Kr [9], and Xe [9,10] was investigated. Berezhnov et
al. [11] discussed a possibility of the bubble creation
around H − ions in liquid hydrogen. Experimental data on
the mobility of electrons in liquid hydrogen and deuterium
at the saturation line [12,13] are in a good agreement with
the electron bubble model in the region of relatively high
temperatures from 22 to 32 K for liquid hydrogen and in
deuterium at all temperatures. However in liquid hydrogen,
in the low temperature region from 17 to 22 K, in the expe-
riment of Levchenko and Mezhov-Deglin [13] an anoma-
lous high mobility of negative charge carriers was ob-
served, which was 1.5 times higher than the mobility
Negative ions in liquid helium
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 495
observed earlier by Sakai, Bötcher, and Schmidt [12]. Lev-
chenko and Mezhov-Deglin interpret this distinction by the
peculiarity of the experimental conditions. In the work of
Sakai et al. [12] the excess electrons were injected in the
liquid as result of photoemission from the cathode. The
energy of such electrons is ∼ 1 eV, too small for the dis-
sociation of the molecular hydrogen. In the work of Lev-
chenko and Mezhov-Deglin [13] the excess electrons were
created by β -decay of tritium atoms. The energy of such
electrons is ∼ 10 keV, large enough not only for ionization
but also for multiple dissociation of molecular hydrogen.
Therefore, in the latter experiment a significant concentra-
tion of hydrogen atoms was generated near the track of the
β -particle in the liquid. These atoms are able to form sta-
ble negative ions in contrast to hydrogen molecules. The
anomalous mobility of the negative charges at low temper-
atures in β -irradiated liquid hydrogen corresponds to the
mobility of H − ions. Levchenko and Mezhov-Deglin as-
sumed that at low temperatures clusters are formed around
the negative ions of atomic hydrogen which move as a
single entity in the liquid. However, calculations per-
formed by Berezhnov et al. [11] have shown that the bub-
ble creation around the negative ion H − is energetically
more favored. The mobility of the negative ion bubble is
higher, as was observed in the experiment [13].
2. Negative impurity ions
The mobility of negative impurity ions in superfluid
4He was measured by Kasimov et al. [14]. The mobilities
of the negative ions of both halogens (Cl − , F − , and I − )
and alkaline-earth metals (Ba− and Ga − ) were found to be
lower than the mobilities not only of He + ions but also of
electron bubbles (see Tables 1 and 2). Evidently, only the
formation of multiatomic complexes (clusters or bubbles)
around the ions can be responsible for these low mobilities.
Table 2. Mobilities of negative impurity ions in liquid 4He at
= 1.3T K [14]
Ion e-bubble Cl − F − I − Ba − Ga −
μ , cm2/(V·s) 0.54 0.46 0.47 0.45 0.47 0.41
Properties of negative impurity ions in liquid helium
were investigated in [11,15–19]. In these studies, it was
found that the binding energy E of the outer-shell electron
in a negative ion (electron affinity) in a liquid dielectric
increases by about 1 eV and a spherical cavity is formed
around the ion. The radius of this cavity depends not only
on the thermodynamic parameters of the liquid but also on
the characteristics of the negative ion. The negative ion in
vacuo is formed by a long-range polarization attraction and
a short-range exchange repulsion between the outer-shell
electron and the ion core. The following simplest model
potential can be used as a potential for the interaction of an
electron with its atom:
2
4 , > ,( ) = 2
, ,
c
i
c
e r RV r r
r R
⎧ α
−⎪
⎨
⎪∞ ≤⎩
(1)
where α is the atomic polarizability, e is the electron
charge, and cR is the radius of the solid atomic core,
which occurs due to the exchange interaction of the outer-
shell electron with electrons of internal atomic shells. Ta-
ble 3 summarizes the solid core radii cR obtained by solv-
ing the Schrödinger equation for an electron in potential
(1) with known polarizability α and electron affinity E .
The asymptotic behavior of a wave function away from a
repulsion center has the form 1( ) = exp ( / )r r r−Ψ − λ . The
characteristic size of the region of the spatial electron loca-
lization depends on the attachment energy, 2 /2mEλ ≅ .
The electron affinity E is usually much lower than the
ionization potential I ; because of this, the value of λ is
much higher than the size of the corresponding atom or
molecule. A weakly bound electron spends the majority of
time away from the ion core and interacts with the atoms
of the surrounding liquid similarly to a free electron. The
exchange interaction results in the formation of a spherical
cavity of radius R around the ion. The electron potential
energy undergoes a jump of approximately 1 eV at the
boundary of a cavity. In our calculations we use the model
potential of the interaction of the outer-shell electron of a
negative ion with the atoms of the liquid lV proposed by
Stampfli [20]. The binding energy eE of the outer-shell
electron of a negative ion placed in a cavity of the liquid
was found by solving the Schrödinger equation with the
resulting potential ( ) = ( ) ( )i lV r V r V r+ , and an equilibrium
radius of the cavity R was found provided that the free
energy
2 3( ) = ( ) 4 (4 / 3)eF R E R R pR− + πσ + π (2)
reached a minimum (σ is the surface tension coefficient
and p is the pressure in the liquid). Table 3 summarizes
the results of the calculation.
Table 3. Atomic core polarizability α , electron affinity E ,
core ionization potential I , solid core radius cR , van der Waals
constant 6C for the interaction of the core with helium atoms,
and radius R of the cavity around the negative ion
Core 3
0, aα E , eV I , eV 0,cR a 6
6 0,C a 0,R a
e-bubble – – – – – 32.1
Cl 15 3.61 12.97 0.92 9.8 5.71
F 3.8 3.40 17.42 0.51 2.9 5.05
I 24 3.06 10.45 1.13 13.5 6.35
Ba 283 0.14 5.21 4.08 93.3 20.7
Ga 33.6 0.41 6.00 1.52 12.4 19.8
2
*He 316 0.18 4.77 1.79 67.0 15.4
O2 10.6 0.46 12.1 0.91 6.6 11.0
O 5.4 1.46 13.6 0.63 3.6 6.8
H 4.5 0.75 13.6 0.60 3.0 8.5
A.G. Khrapak and W.F. Schmidt
496 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5
One can see that the sizes of the cavities around the ha-
logen and alkaline-earth metal ions are significantly diffe-
rent. First, let us discuss properties of complexes formed
around the negative ions of halogens. In terms of our mo-
del, the radius of the cavities in which these ions are locali-
zed 0(5 6)a− is much smaller than the radii of solid clus-
ters formed around He+ ions ( 014.9a ) and alkali metal
positive ions ( 015.8a ) [5]. This suggests that clusters are
formed near the negative ions of halogens. In this case, the
presence or absence of a cavity within a cluster is of little
importance for the determination of the radius of these
clusters: as in the case of positive ions, the negative ions at
the center of a cluster can be considered as point ions. To
understand the reason for the considerable difference be-
tween the mobilities of the He+ ion, on the one hand, and
negative halogen ions, on the other hand, Khrapak [17]
invoke the reasoning that was used to explain the small
differences in the mobilities of positive helium and alkali
metal ions [8]. It was noted that, although the polarization
interaction of an ion with helium atoms outside the cluster
is equal for all the ions, the additional van der Waals inte-
raction of helium atoms with the ion core depends on its
atomic number. An excess pressure results in an increase
in the cluster radius and a decrease in the cluster mobility.
This effect is even more important in the case of negative
ions. The potential energy of the interaction of a helium
atom arranged near the surface of a cluster with a point ion
placed at the center of the cluster takes the form
2
He 6 He
6 He4 6
He
3( ) = , .
22
a
a a
a
e C I I
V r C
I Ir r
α
− − ≅ α α
+
(3)
Here 6C is the van der Waals constant of the interaction of
helium atoms with the atom of the ion core, which was
evaluated using the London formula [21]. Table 3 summa-
rizes the constants 6C thus calculated. With growth of the
constant 6C the cluster radius has to increase and the mo-
bility has to decrease in agreement with small mobility
changes observed in experiment [14]. However, this effect
can decrease the mobility of negative halogen ions by (5–
10)% as compared to the mobility of the He+ ion but hard-
ly by a factor of 2.
In the case of alkaline-earth metal ions Ba− and Ga− ,
which exhibit a low electron affinity E in the vacuum, the
bubble radius is large enough and creation of the solid
shell around the bubbles is unlikely. According to our esti-
mations, the electron binding energies eE for these ions in li-
quid helium at = 1.3T K are similar and equal to 1.42 and
1.46 eV, respectively. The difference between the charac-
teristic size of wave functions λ for these ions is small;
this fact is ultimately responsible for the observed similarity
of the ion mobilities. At first glance, the fact that the mobi-
lity decreases with decreasing bubble radius (Ba Ga )− −→
is surprising. However, note that, at = 1.3T K on the satu-
ration line of liquid 4He, the mobility of ion complexes
depends on scattering by rotons [1]. Bondarev [22] had
shown that the density of rotons increases with decreasing
distance to the ion complex as result of the polarization
attraction. In the case of the electron bubbles this effect
does not play a significant role because of the large value
of their radius. In the case of Ba− and Ga− ions the polari-
zation interaction of the helium atoms situated in the vicin-
ity of the bubble surface plays an important role
2 4( / 2 =1.2e Rα K for Ba− and 1.4 K for Ga− ) and results
in significant increase of the roton concentration near the
ion bubbles. This effect can be responsible for difference
of the mobilities of Ba− and Ga− ions. However, a ques-
tion why mobilities of alkaline-earth metal ions are less
than the mobility of the e-bubble is still open.
3. Fast and exotic ions
In addition to “usual” electron bubbles in superfluid he-
lium two kinds of negative charge carriers were observed:
“fast” [23–27] and “exotic” [24–27] ions. The mobility of
the fast ions was about 7 times higher than the electron
bubble mobility and mobilities of several different exotic
ions lay in between. For production of ions different me-
thods were used: the α source placed in liquid [23], the β
source and gas discharge placed above the liquid [24,25],
and only the gas discharge above the liquid [26,27]. Mobil-
ity of the electron bubbles at temperature around 1 K is
determined by collisions with rotons and is proportional to
square of the bubble radius R . If one suggests, that around
fast and exotic ions, voids or clusters are created, then one
may estimate the radius of these complexes assuming that
their mobility is proportional to the radius square [3,25]. It
lies between 030.4a (electron bubbles) and 011.8a (fast
ions). At low electric fields electron bubbles are in the
thermal equilibrium with the gas of scatters (rotons) and
the bubble drift velocity is proportional to the electric field.
Under increasing the electric field the bubble energy is also
increased and the field dependence of the drift velocity
became weaker. Finally, at some critical electric field the
drift velocity demonstrates an abrupt change, known as
giant fall or giant discontinuity (see, for example, [28]). It
is the result of the creation of a charge-carrying quantized
vortex rings in the superfluid. The same effect is observed
with the exotic ions but not with the fast ions [26]. This
may be an evidence for the different nature of fast and ex-
otic ions. The measurements show that the critical velocity
cv for the nucleation of vortex rings by exotic ions is larg-
er than for electron bubbles, and that amongst the different
exotic ions, cv increases as the mobility increases. Theory
predicts that the critical velocity of an ion should increase
with decreasing of the ion radius [29]. Thus, the measure-
ments of the critical velocity also indicate that the exotic
ions are smaller than the normal electron bubbles.
It is strange, but the nature of the fast and exotic ions is
still unknown. Several models were proposed for these
Negative ions in liquid helium
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 497
negative charge carriers [24,30] but none of them could
interpret all experimental data [3,31]. Below we suggest a
new model. It follows from experiments that fast and exot-
ic ions have different nature. Both kinds of ions were not
observed in usual experiments, both kinds were observed
in gas discharge experiments, and exotic ions were not
observed in experiments with radioactive sources. Let us
consider their properties separately.
We suggest that fast ions represent a bubbles created
around negative ions of the excimer 2
*He in the triplet
state. In contrast to “usual” experiments, in which elec-
trons are photo-injected in liquid helium with an energy of
the order of 1 eV, using of radioactive sources or gas dis-
charges produces not only ionization but also excited
atoms and molecules as well. Both the singlet atomic and
molecular excitations decay rapidly to the ground electron-
ic state, but the long-living triplet species quickly thermal-
ize and form bubbles around themselves. With 15 μs time
constant the triplet *He combines with another helium
atom to produce 2
*He in a highly excited vibrational state
( = 16)v . This state relaxes to its ground vibrational state
with time constant about 30 μs [32]. The lowest electroni-
cally excited state in liquid helium is the triplet excimer
2
*He ( ua +Σ ) which lies at 17.8 eV above the ground state.
Due to the very weak spin-orbit coupling in He, this state
is metastable with a large intrinsic lifetime of about 15 s
[33–35]. Spectroscopic studies result in a conclusion that
excimers occur in bubble states. The bubble model was
employed by Hickman et al. to analyze spectral shifts of
*He [36] and 2
*He [37] in liquid He. Results of early stu-
dies have been validated in the later spectroscopic studies
[38–40]. Theoretical estimations of the bubble radius give
about 012a for *He [41] and 013a for 2
*He [42].
The long-lived metastable negative excimer ion He 2
−
was first observed in 1984 [43] and now its properties in
vacuum are well known. The 4
gΠ state has electronic
configuration 21 1 2 2g u g uσ σ σ π , the electron affinity E is
0.18 0.03± eV, the lifetime is 135 15± μs, only = 0v
vibrational state is responsible for this long-lived state
[44]. This ion can exist in liquid helium as result of excita-
tion by α or β particles, or as result of the diffusion
through the surface from the gas-discharge plasma. How-
ever properties of He 2
− ions in condensed helium are quite
unknown. It is sufficiently evident that like excimer 2
*He ,
the ion He 2
− is localized inside empty void. Size of the
void can be estimated in frames of the model used in pre-
vious section for impurity negative ions. For this, it is ne-
cessary to estimate parameters α , cR , and 6C of the inte-
raction potential. The main contribution to the
polarizability of the excimer 2
*He gives the excited atom
*He ,
2
* *He Heα α . The atomic polarizability can be es-
timated from its ionization potential, 3 3a I −α∼ ∼ , where
a is the radius of the atom. The excitation energy of the
helium atom is 19.82 eV and the ionization potential
*He = 24.59 19.82 = 4.77I − eV. Thus
2
3
3He
* He 0He *He
204 .
I
a
I
⎛ ⎞
α α ⎜ ⎟
⎜ ⎟⎝ ⎠
(4)
The core radius cR is determined by solution of the Schrö-
dinger equation with known E and
2
*He
α . This gives =cR
0= 1.79a . The constant of the van der Waals interaction
of the core ( *He ) with helium atoms can be estimated by
the London formula
*He He 6
*6 He 0He*He He
3 67 .
2
I I
C a
I I
α α
+
(5)
Figure 1 shows the free energy of a spherical bubble
created around He 2
− ion as a function of its radius. The
equilibrium bubble radius is equal 015.4a , more than
twice smaller than the radius of the e-bubble. Notice that
the wave function of the 4
gΠ state of He 2
− does not
posses spherical symmetry. As a result a form of the bub-
ble has to obtain a characteristic two-lobe peanut structure
similar to the excited e-bubble in 1P state [45]. This effect
could reduce the roton scattering cross-section of the bub-
ble and explain observed rise of the fast ions mobility.
The issue remains open about the lifetime of the He 2
−
ion in condensed helium. The drift time in the experiments
[24–27] is about 1 ms, several times greater than the va-
cuum lifetime of the ion. However the wave function of the
outer electron of the He 2
− ion undergos significant alterna-
tions which can result in increasing of the ion lifetime.
Another possibility to adjust the difference between the
short lifetime and long drift time consists in following:
during the drift time between electrodes electrons have a
possibility several times to escape from the ionic complex
with subsequent capture by another excited molecule. Af-
ter escaping from the ion with an energy of about 19 eV,
the electron is thermalized during approximately 1 ps [2]
and after that it can be captured by a next excitation or it
can create an e-bubble. If concentration of the excimer
molecules 2*He in liquid helium is high enough, then elec-
trons practically all time will be localized in He 2
− inside
Fig. 1. Free energy of the He2
− bubble as a function of radius in
superfluid helium.
,R a0
He bubble2
–
–1.30
–1.35
–1.40
–1.45
10 15 20 25 30
F
,
eV
A.G. Khrapak and W.F. Schmidt
498 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5
bubble. These complex problems need special considera-
tion exceeding the frames of the present work.
Exotic ions were observed in superfluid helium only
when ionization of helium was produced by gas discharge
above the liquid surface. There is good reason to believe
that these ions are stable negative impurity ions, which are
always present in small amounts in the gas discharge plas-
ma. Despite the fact that in superfluid helium all impurities
are frozen out, atomic and molecular impurities may be
present in the discharge plasma as a consequence of the et-
ching from the experimental cell walls and electrodes. Un-
fortunately the plasma composition in experiments [24–27]
is unknown and below we present results of our estima-
tions for several most probable candidates for the role of
the exotic ions, such as O 2
− , O − , and H−. All these ions
are localized inside bubbles. Dependencies of the free
energy on the bubble radius for these ions are shown in
Fig. 2. Values of the equilibrium radii of these ions are
listed in Table 3. The size of the O 2
− bubble is three times
less the radius of the e-bubble and this ion can be responsi-
ble for mobility of one of the fastest exotic ions. The size
of O − bubble or cavity is much smaller than the radius of
cluster usually formed around positive helium ion. As in
the case of negative ions of halogens, this points to the
formation of a solid cluster around the O − ion, with a void
inside. The size of this complex has to be closed to that of
He + cluster 0(14.9 )a , and its mobility has to exceed about
two or three times the e-bubble mobility. The ion H −
represents an intermediate case: the bubble is surrounded
by a layer of dense but probably not solid helium. For the
determination of its structure and that of similar exotic ions
more detailed and complex investigations are needed.
4. Conclusions
In this work we have addressed the properties of differ-
ent negative impurity ions in liquid helium. With help of a
simple model it was found that owing to the strong ex-
change interaction of the outer electron of a negative ion a
void is always created around the ion. In the case of ions
with a large enough electron affinity a layer of solid heli-
um can be formed around the void, and the complex repre-
sents a cluster rather than a bubble. It was demonstrated
that complexes formed around negative alkaline-earth met-
als and halogens have qualitatively different structure
(bubbles and clusters, correspondingly), although the
measured values of their mobility were similar. It was
substantiated that the “fast” ions represent negative ions of
the excimer 2
*He localized in non-spherical bubble. Con-
cerning the “exotic” ions, an assumption was made that
they are formed in the gas discharge plasma as result of the
etching of the cell walls and electrodes and are then in-
jected into the liquid.
Additional experimental and theoretical investigations
are necessary for better understanding of properties of im-
purity negative ions in superfluid helium and other dielec-
tric liquids.
In the experiment by Kasimov et al. [14] the mobility of
negative impurity ions injected in liquid helium was small-
er than the mobility of the e-bubbles. But in this work the
well known mobility of e-bubbles (see, for example,
[1,46]) was not measured. According to our estimations the
radius of these charged complexes is about 015a (halogen
negative ion clusters) or 020a (alkaline-earth metal nega-
tive ion bubbles). As a result the mobility of impurity ions
has to be several times higher than the e-bubble mobility in
contradiction with the experiment. Additional experiments
with simultaneous measurement of the ion and e-bubble
mobility as well as with more wide nomenclature of ions
are desirable. The measurements of the critical velocity for
nucleation of vortex rings by impurity ions could also give
important information about size of these ionic complexes.
The interest to the theoretical investigations of the pro-
perties of He 2
− ions in liquid helium is self-evident. It
would be rewarding to perform density-functional calcula-
tions of the equilibrium shape of the non-spherical bubble
similar to the recent calculations for excited e-bubbles
[19,42,45]. Knowledge of the bubble shape and of the out-
er electron wave function will give the possibility to esti-
mate the lifetime of the He 2
− ion in liquid helium. Kinetics
of the bubble formation around He 2
− and possible electron
trapping by excimer 2
*He are worthy of investigation.
We thank E. Gordon, E. Illenberger, B. Smirnov, and L.
Vasilyak for helpful discussions. This work was supported
in part by the Russian Foundation for Basic Research,
project No. 09-08-01063.
1. V. Shikin, Usp. Fiz. Nauk 20, 226 (1977).
2. A.G. Khrapak, W.F. Schmidt, and E. Illenberger, in:
Electronic Excitations in Liquid Rare Gases, W.F. Schmidt
and E. Illenberger (eds.), American Scientific Publishers,
Stevenson Ranch (2005), p. 239.
3. H.J. Maris, J. Phys. Soc. Jpn. 77, 111008 (2008).
Fig. 2. Free energy F normalized to its minimum value minF of
some negative impurity ions as a function of the bubble radius in
superfluid helium.
–0.97
–0.98
–0.99
–1.00
5 10 15 20
F
F
/|
|
m
in
,R a0
O
–
O2
–
H
–
Negative ions in liquid helium
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 499
4. W.W. Johnson and W.I. Glaberson, Phys. Rev. Lett. 29, 214
(1972).
5. W.I. Glaberson and W.W. Johnson, J. Low Temp. Phys. 20,
313 (1975).
6. M. Foerste, H. Guenther, O. Riediger, J. Wiebe, and G. zu
Putlitz, Z. Phys. B104, 317 (1997).
7. R.R. Atkins, Phys. Rev. 116, 1339 (1959).
8. M.W. Cole and R.A. Bachman, Phys. Rev. B15, 1388
(1977).
9. H.T. Davis, S.A. Rice, and L. Meyer, J. Chem. Phys. 37,
2470 (1962).
10. O. Hilt, W.F. Schmidt, and A.G. Khrapak, IEEE Trans.
Dielectrics Electr. Insul. 1, 648 (1994).
11. A.V. Berezhnov, A.G. Khrapak, E. Illenberger, and W.F.
Schmidt, High Temp. 41, 425 (2003).
12. Y. Sakai, E.H. Böttcher, and W.F. Schmidt, J. Jpn. Inst.
Electr. Eng. A61, 499 (1983).
13. A.A. Levchenko and L.P. Mezhov-Deglin, J. Low Temp.
Phys. 89, 457 (1992).
14. A. Kasimov, C. Zuhlke, K. Jungmann, and G. zu Putlitz,
Physica B329, 352 (2003).
15. K.F. Volykhin, A.G. Khrapak, and V.F. Schmidt, JETP 81,
901 (1995).
16. P.D. Grigor’ev and A.M. Dyugaev, JETP 88, 325 (1999).
17. A.G. Khrapak, JETP Lett. 86, 252 (2007).
18. A.G. Khrapak and V.F. Schmidt, Int. J. Mass Spectrom. 277,
236 (2008).
19. F. Ancilotto, M. Barranco, and M. Pi, Phys. Rev. B80,
174504 (2009).
20. P. Stampfli, Phys. Rep. 255, 1 (1995).
21. F. London, Z. Phys. Chem. B11, 222 (1930).
22. V.N. Bondarev, JETP Lett. 18, 693 (1973).
23. C.S.M. Doake and P.W.F. Gribbon, Phys. Lett. A30, 252
(1969).
24. G.G. Ihas and T.M. Sanders, Jr., Phys. Rev. Lett. 27, 383
(1971).
25. G.G. Ihas, Ph. D. Thesis, University of Michigan (1971).
26. V.L. Eden and P.V.E. McClintock, Phys. Lett. A102, 197
(1984).
27. C.D.H. Williams, P.C. Hendry, P.V.E. McClintock, J. Appl.
Phys. 26, Supplement 26-3, 105 (1987).
28. A.F. Borghesani, in: Electronic Excitation in Liquefied Rare
Gases, W.F. Schmidt and E. Illenberger (eds.), American
Scientific Publishers, Stevenson Ranch (2005), p. 133.
29. C.M. Muirhead, W.F. Vinen, and R.J. Donnelly, Philos.
Trans. R. Soc. London A311, 433 (1984).
30. T.M. Sanders, Jr. and G.G. Ihas, Phys. Rev. Lett. 59, 1722
(1987).
31. D. Jin, W. Guo, W. Wei, and H.J. Maris, J. Low Temp. Phys.
158, 307 (2010).
32. H. Buchenau, J.P. Toennies, J.A. Northby, J. Chem. Phys.
95, 8134 (1991).
33. C.F. Chabalowski, J.O. Jensen, D.R. Yarkony, and B.H.
Lengsfield III, J. Chem. Phys. 90, 2504 (1989).
34. D.B. Kopeliovich, A.Ya. Parshin, and S.V. Pereverzev, Sov.
Phys. JETP 69 638, (1989).
35. D.N. McKinsey, C.R. Brome, J.S. Butterworth, S.N.
Dzhosyuk, P.R. Huffman, C.E. H. Mattoni, and J.M. Doyle,
Phys. Rev. A59, 200 (1999).
36. A.P. Hickman and N.F. Lane, Phys. Rev. Lett. 26, 1216
(1971).
37. A.P. Hickman, W. Steets, and N.F. Lane, Phys. Rev. B12,
3705 (1975).
38. V.B. Eltsov, S.N. Dzhosyuk, A.Ya. Parshin, and I.A.
Todoshchenko, J. Low Temp. Phys. 110, 219 (1998).
39. S.G. Kafanov, A.Ya. Parshin, and I.A. Todoshchenko, JETP
118, 1143 (2000).
40. A.Ya. Parshin, I.A. Todoshchenko, and S.G. Kafanov,
Physica B284-288, 91 (2000).
41. J.P. Hansen and E.L. Pollock, Phys. Rev. A5, 2214 (1972).
42. J. Eloranta, N. Schwentner, and V.A. Apkarian, J. Chem.
Phys. 116, 4039 (2002).
43. Y.K. Bae, M.J. Coggiola, and J.R. Petersom, Phys. Rev. Lett.
52, 747 (1984).
44. T. Andersen, Phys. Scripta T59, 230 (1995).
45. D. Mateo, M. Pi, and M. Barranco, Phys. Rev. B81, 174510
(2010).
46. K.W. Schwarz, Phys. Rev. A6, 837 (1972).
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