Electron bubbles and light
T. V. Prevenslik
11F Greenburg Court
Discovery Bay, Hong Kong
The splitting of electron bubbles into a pair of electrino bubbles has been
proposed to explain the increased photoconductivity of liquid helium upon light
illumination. The new explanation given here
asserts ththat light induced
electron bubbles produced
by the ionization of impurities in the liquid helium. But the visible (VIS)
light in photoconductivity experiments lacks the Planck energy to reach the
vacuum ultraviolet (VUV) levels necessary for impurity ionization, and
therefore a mechanism initiated by VIS light that produces VUV light needs to
be identified. To this end, a cavity quantum electrodynamics (QED) induced
photoelectric mechanism is proposed that implicitly assumes the liquid helium
contains both coarse and fine size impurities. Rapid thermal expansion of
coarse impurities upon absorption of IR-VIS light causes the separation of
liquid helium from the surface of the impurity, the separation nucleating a
bubble containing the impurity. Prior to separation, each atom in the impurity
emits 3 x ˝ kT of thermal energy as
far infrared (IR) radiation. But at the instant of separation, the IR radiation
from the impurity is momentarily suppressed by cavity QED because the bubble
has a high electromagnetic EM resonant frequency. To conserve energy, the
suppressed IR radiation is promptly released as coherent multi-IR photons that
combine to VUV levels at the bubble surface. Fine impurities in the bubble
surface are ionized by the VUV light and produce electrons by the photoelectric
effect, the electrons promptly localizing to form the light induced electron
bubbles that yield the increased photoconductivity.
Over 30 years ago, Northby and Sanders  studied the mobility of electron bubbles in liquid helium under an electric field. Electrons introduced into the liquid helium from a radioactive source promptly localized to electron bubbles, or ions. Mobility was inferred by measuring the time for the electron bubbles to move between grids in the liquid helium under an electric field. Photoconductivity experiments were performed with infrared (IR) and visible (VIS) light having Planck energy from 0.7 to 3 eV. The photoconductivity was expected to increase because the IR light would eject the electrons from the electron bubbles, and indeed, the photocurrent did increase upon illumination with the peak occurring in the IR light at a Planck energy of 1.21 eV.
Subsequently, light induced mobility of electron bubbles was found in other experiments. Instead of a radioactive source, Ihas and Sanders  used a glow discharge struck above the surface of liquid helium in a container. Voltage applied to the grids in the liquid helium provided the electric field by which electrons in the discharge were drawn into the liquid helium, the glow discharge itself providing the source of light illumination. Mobility inferred from the time for the electron bubbles to traverse the space between the grids suggested that in addition to the electron bubbles or normal ions, the liquid helium contained a wide range of exotic ions, the exotic ions having drift velocities greater than that of the normal ions. Thereafter, Eden and McClintock  confirmed the finding of a continuum of exotic ions while explaining the exotic ions by charged vortex rings.
Recently, Maris [4,5] in an another explanation of the exotic ions proposed the photocurrent [1-3] should not have increased by contending the electrons ejected from the electron bubbles by the IR light would promptly localize to form new electron bubbles without any increase in mobility or photoconductivity. Rather, Maris proposed that the IR light excited the electrons from the ground state to their dumb-bell shape excited state, whereupon the electrons split to form a pair of electrons, called electrinos. Although the total electron charge remained the same, the smaller electrinos having less drag moved faster and consequently the mobility or photocurrent increased. Today, the light induced splitting of the electron into electrinos is a subject of great controversy in that the implication is made that the electron is divisible - contrary to the fundamental thinking  of quantum physics.
However, the explanation of light induced exotic ions need not invoke vortex rings or the divisibility of the electron, as the exotic ions can be explained by the photoelectric effect. If the illuminating light has Planck energy in the vacuum ultraviolet (VUV) of at least 4.9 eV, impurities in the liquid helium can be made to produce photoelectrons, which after localization form light induced electron bubbles that yield the increased photoconductivity.
But IR-VIS and not VUV light is employed in the experiments. Indeed, Lezak et al.  tested the photoelectron hypothesis that the light induced electron bubbles were nucleated in liquid helium from the electrons liberated from the surface of a bismuth heater upon illumination. The photoconductivity was not found to increase, but the results are inconclusive, as the Planck energy of the light was limited to about 4 eV. Yet, photoconductivity  was observed with light limited to Planck energy of about 3 eV. These experiments suggest that if photoconductivity increases, a mechanism is at play that somehow increases the Planck energy of IR-VIS light to VUV levels to produce photoelectrons from which the light induced electron bubbles are formed.
If such a VUV conversion mechanism exists, light induced electron bubbles may be considered produced by IR-VIS light anywhere in the field of illumination. If so, the normal, exotic, and fast ions observed by Ihas  may be readily explained. Light induced electron bubbles produced near the collector grid having short time of flight are inferred to be fast ions having high mobility; whereas, normal ions having the lowest mobility formed by the radioactive source or the glow discharge are located farthest from the collector grid. Exotic ions having mobility between the normal and fast ions are light induced electron bubbles formed by photoelectrons at various distances from the collector grid.
The purpose of this paper is to explain how the photoelectric effect can increase the mobility of electron bubbles in photoconductivity experiments.
BACKGROUND AND THEORY
Mechanisms by which VUV light is produced by cavity QED are those in which bubbles are nucleated in liquid helium from the absorption of the IR-VIS light by either the electron bubbles or impurities. However, absorption of IR light by the electron bubbles is excluded here, as even if electrons are ejected they promptly localize [4,5] without producing the electrons necessary to explain the observed increases in photoconductivity.
Bubble nucleation by impurities
Light induced electron bubbles may explain the observed increase in photoconductivity providing there is a coarse and fine distribution of impurities in the liquid helium. Coarse size impurities have dimensions of microns and are likely to be metallic remnants (Fe,Cr,etc.) of vessel walls specific to the experiment; whereas, fine size impurities are atoms or clusters of gases (N,Ar,etc.) having dimensions of nanometers adsorbed to vessel surfaces.
IR-VIS light having an energy flux Q illuminating a coarse impurity of spherical radius RO in an otherwise uniform distribution of fine impurities is depicted in Fig. 1 (a). Provided the impurity is absorptive at the wavelength of the light, the light induces the impurity to undergo a rapid expansion, the expansion imparting a velocity to the liquid interface that causes a gap g to form as the liquid separates from the impurity surface. A helium bubble containing the impurity nucleates as shown in Fig. 1(b).
Figure 1 - Production of Light Induced electron bubbles from fine impurities on bubble wall by VUV radiation from the illumination of coarse impurity by IR-UV light
Of interest is the initial thermal response at temperatures near liquid helium temperatures where heat loss by radiation may be neglected. Treating the impurity as spherical of radius Ro , the 1-D lumped mass energy balance is:
where, T is the temperature, t is time, a is the fractional absorption of the light by the impurity, and r and C are the density and specific heat of the impurity. The convective film coefficient H ~ K/g, where K is the thermal conductivity of the He vapor in the gap.
At steady state, (3)
For helium vapor at 2 K, thermal conductivity K ~ 0.004 W m-1K-1. Taking the gap thickness g ~ 0.1Ro ~ 1 mm, the impurity radius Ro ~ 10 mm and H ~ 4000 W m-2K-1. For an iron impurity, r ~ 7879 kg m-3 and C ~ 449 J kg-1K-1. Assuming a XeCl laser at 308 nm and a repetition rate of 150 Hz, Q ~ 7.5 MW m-2. For a ~ 1, the time to reach 67% of the steady state temperature difference (T - TO ~ 468 K) is about 3 ms. This suggests the impurities are heated during the mobility experiments  having times of flight from 1 to 3 ms. With the liquid helium at 2 K, the light induces a thermal shock that is sufficient to briefly separate the liquid helium from the impurity - an important consideration in the cavity QED induced photoelectric effect.
The cavity QED induced photoelectric effect relies on the the thermal kT energy of the atom, the average energy Eavg of which may be represented by a harmonic oscillator with a broad range of wavelengths. Fig. 2 shows the thermal energy saturates at a liquid helium temperature of 2 K to about 0.00017 eV, far less than that at ambient temperature of 300 K. The QED effect in the nucleation of bubbles in water at ambient temperature is discussed in Appendix A.
Figure 2 – Average harmonic oscillator energy at 2 and 300 K
At liquid helium temperatures, each atom in the impurity emits low frequency IR radiation of magnitude 3 x ˝ kT. But at the instant the liquid separates from the impurity, the bubble is a high frequency QED cavity, and therefore the low frequency IR emission from all atoms in the impurity is suppressed, a condition referred  to as inhibited cavity QED. The suppressed IR energy UIR is,
where, Y is the IR energy density, Y ~ Ndof x ˝ kT / D3, k is Boltzmann’s constant, Ndof is the number of degrees of freedom of the atoms in the impurity, which is 3, and D is the solid density spacing between atoms in the impurity, which is about 0.3 nm.
Energy conservation requires the suppressed EM energy be promptly released to the surroundings in the form of coherent multi-IR photons. The IR photons collectively combine to VUV levels to excite fine impurities in the bubble surface as shown in Fig. 1. The Planck energy E,
The number Ne of electrons produced by the fine impurities depends on the number Np of photons, the fraction gimp of impurities in the surface of the bubble wall, and the impurity photoelectric yield gP of electrons per photon,
Since the released EM radiation is coherent and comprised of multi-IR photons, the number Np of VUV photons having Planck energy EVUV may be written,
Concentrations of coarse and fine impurities in liquid helium are not known. Fractions of coarse impurities need not be large, say a few tens. Fine impurities are expected to be of the order of the solubility of gases in water, say gimp<10-4. Most impurity atoms illuminated with VUV light have low electron yields, gP < 10-3. Fig. 3 shows the Planck energy E at the bubble surface R ~ Ro as a function of impurity radius Ro at liquid helium temperatures of 2 K. For gP ~ 0.001 and gimp ~ 10-5, the number Ne of electrons produced at 2 K with multi-IR photons that combine to a Planck energy EVUV ~ 4.9 eV are shown. Large coarse impurity radii Ro > 10 mm are necessary because the low thermal kT energy at liquid helium temperatures requires more impurity atoms to reach VUV levels, e.g., an impurity having Ro ~ 17 mm produces only about 400 electrons.
Figure 3 - No. of Electrons Ne and Planck energy E versus impurity radius Ro
SUMMARY AND CONCLUSIONS
IR-VIS Light and Photocurrent
The cavity QED induced photoelectric effect provides a reasonable explanation of how IR-VIS light  enhances the photocurrent providing a concentration of a few tens of coarse 20-50 mm impurities in an otherwise fine distribution of 1-10 nm atomic cluster impurities. Impurity concentrations are not known and are likely to be specific to the experimental system.
The cavity QED induced photoelectric effect relies on an evacuated gap to isolate the IR radiation from the impurity from the bubble wall. Direct contact or helium vapor in the gap negates the conversion of IR radiation from the coarse impurity to VUV radiation. Since the vapor pressure of liquid helium increases rapidly above 1.5 K, the light induced photocurrent is expected to diminish rapidly consistent with the fact  that the photocurrent is only observed below about 1.7 K.
Glow Discharge and Exotic Ions
Normal, exotic, and fast ions only appear [2,3,7] in experiments where a glow discharge is struck near the surface of liquid helium. Since glow discharge itself produces VUV radiation, there may not be any need to invoke the cavity QED induced photoelectric effect to explain how the IR-VIS light produces light induced photoconductivity. Experimental resolution of the importance of VUV in glow discharge is indicated.
Electrinos and Vortex Rings
Light induced photoconductivity may be explained by the irradiation of impurities in the liquid helium either directly from the VUV light in glow discharge by the photoelectric effect, or indirectly by IR-VIS light in the cavity QED induced photoelectric effect. Either way, there is no need to propose vortex rings and electrinos to explain light induced photoconductivity.
 Northby, J.A. and Sanders, T.M. "Photoejection of Electrons from Bubble States in Liquid Helium" , Phys. Rev. Lett. Vol. 18, 1967, pp. 1184-6.
 Ihas, G.G. and Sanders, T.M. “Exotic Negative Carriers in Liquid Helium”, Phys. Rev. Lett. Vol. 27, 1971, pp. 383-6.
 Eden, V.L. and McClintock, P.V.E. “The Effect of Strong Electric Fields on Exotic Negative ions in He II: Possible Evidence for the Nucleation of Charged Vortex Rings”, Phys. Lett. Vol. 102A, 1984, pp. 197-200.
 Maris, H.J. "On the Fission of Elementary Particles and the Evidence for Fractional Electrons in Liquid Helium", J. Low Temp. Phys. Vol. 120, 2000, pp.173-204.
 Chown, M. “Double or Quit”, New Scientist 14 October 2000, pp. 25-7.
 Lezak, L.C., Brodie, L.C. and Semura, J.S. "Light induced nucleation of vapor bubbles at the interface of solid and superheated liquid helium I: test of the photoelectron hypothesis", Cryogenics, April 1984, pp.211-3.
 Ihas, G.G. Ph.D. thesis, University of Michigan, 1971.
 Harouche, S. and Raimond, J-M. "Cavity quantum electrodynamics" , Scientific American, 1993, pp. 54-62.
Sonoluminescence (SL) is the VIS light from the cavitation of bubbles in water. SL in the cavitation of water may be explained with the EM radiation produced in the nucleation of bubbles by cavity QED.
Consider a spherical water volume of radius R0 in a state of hydrostatic compression at ambient pressure P0 as shown in Fig. A-1(a). At ambient temperature T, all water molecules in the continuum emit IR radiation. If the continuum is perturbed to produce a state of hydrostatic tension, a bubble nucleates as shown in Fig A-2(b).
Because of surface tension S, the expanding liquid bubble wall of radius R separates from a tightly bound core of water molecules, the core depicted by the radius R0 = 2S / P0, where R > R0. Briefly, an annular space isolates the core from the bubble wall. Since the bubble is a high EM resonant cavity, the low frequency IR radiation from the core is momentarily suppressed. To conserve EM energy, the suppressed IR energy is promptly released as coherent multi-IR photons that accumulate to VUV levels in the bubble wall surface water molecules.
Figure A-1 - Bubble nucleation in water with surface tension
For a spherical core of water molecules of radius R0, the EM energy UEM released is,
where, Y is the EM energy density, Y ~ Ndof x ˝ kT / D3. For a water molecule, Ndof is 6. If all the available EM energy UEM suppressed during nucleation is conserved with the Planck energy UPlanck of the bubble surface molecules,
The number NVUV of VUV photons having Planck energy EVUV may be written,
Consider a bubble at T ~ 300 K having a core radius R ~ R0 = 1.44 mm corresponding to surface tension S ~ 0.072 Nt / m. The EM radiation accumulated in the bubble surface water molecules in the VUV has a Planck energy E ~ 120 eV, and is more than sufficient for dissociating the water molecule.
Taking EVUV ~ 4.9 eV for the dissociation of the water molecule, NVUV ~ 7.3x109 photons. The mole fraction solubility of Ar in water at 300K gives the fraction of Ar atoms in the bubble surface as about 2.75x10-5. Since every VUV photon produces a hydroxyl OH ion, the most likely number of Ar*OH excimers formed is about 2x105. Upon bubble collapse, SL is observed as the Ar*OH excimers decompose under the high collapse pressure, the SL response dominated by the *OH band at 310 nm. Hence, the number of SL photons produced is about 2x105.
The cavity QED induced photoelectric effect is consistent with the experimentally * derived standard unit of SL that asserts about 2x105 SL photons are produced for the collapse of bubbles in water.
* Hiller, R.T., Weninger, K, Putterman, S.J., and Barber, B. P. "Effect of Noble gas doping on single bubble sonoluminescence", Science, 266, 1994, pp. 248-250.