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When an electron is forced into liquid helium rather than floating on its surface, it forms a bubble rather than entering the liquid. The size of this bubble is determined by three main factors (ignoring small corrections): the confinement term, the
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Below a critical temperature, the mobility of the electrons drops quickly to a value much below what is expected classically. This discrepancy led to the development of the electron bubble theory. At low temperatures, electrons injected into
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154:. As the temperature is lowered, the electron mobility decreases, since the helium atoms slow down at lower temperature and do not interact with the electron as often.
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of the liquid helium; this is exactly like water and all other liquids. The pressure-volume term is the amount of energy needed to push the helium out of the bubble.
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term, and the pressure-volume term. The confinement term is purely quantum mechanical, since whenever an electron is tightly confined, its
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that the 2S electron bubble exhibits a startling morphological instability under a wide range of ambient pressures. While its
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456:"Electron mobilities in low density helium and nitrogen gases: Momentum transfer cross sections at very low energies"
409:"Electron mobilities in low density helium and nitrogen gases: Momentum transfer cross sections at very low energies"
32:
72:
187:
602:
M. A. Woolf and G. W. Rayfield (1965). "Energy of
Negative Ions in Liquid Helium by Photoelectric Emission".
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151:
54:
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G. Ramanan and Gordon R. Freeman (1990). "Electron
Mobilities in Low Density Helium and Nitrogen Gases".
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do in a hydrogen atom, with a minimum average separation. In this case, the minimum energy is about 1
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do not move freely as one might expect, but rather form small vacuum bubbles around themselves.
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333:{\displaystyle E\approx {\frac {h^{2}}{8mR^{2}}}+4\pi R^{2}\alpha +{\frac {4}{3}}\pi R^{3}P}
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move about freely, limited only by collisions with the weakly interacting atoms. Their
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134:. They are typically very small, about 2 nm in diameter at atmospheric pressure.
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A theoretical prediction has been made based on the analysis of the equation above,
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P. Grinfeld and H. Kojima (2003). "Instability of the 2S Electron
Bubbles".
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190:. The electron is forbidden from entering the liquid for the same reason
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Electrons are attracted to liquid helium due to the difference in
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W. T. Sommer (1964). "Liquid Helium as a
Barrier to Electrons".
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C. G. Kuper (1961). "Theory of
Negative Ions in Liquid Helium".
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is spherical, the stable shape of the bubble is nonspherical.
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454:Ramanan, G.; Freeman, Gordon R. (September 1990).
407:Ramanan, G.; Freeman, Gordon R. (September 1990).
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225:goes up. The surface tension term represents the
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182:the helium at the surface, leading to an
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198:. The electron and image charge form a
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126:in a cryogenic gas or liquid, such as
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178:of helium. The negative electron
142:At room temperature, electrons in
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460:The Journal of Chemical Physics
413:The Journal of Chemical Physics
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681:"Quantum bubbles are the key"
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44:secondary or tertiary sources
509:Journal of Chemical Physics
371:is the surface energy, and
174:between the gas and liquid
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202:, just as an electron and
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637:Physical Review Letters
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573:Physical Review Letters
188:binds it to the surface
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31:relies excessively on
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172:dielectric constants
687:. 25 November 2005.
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379:2S electron bubble
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707:Cryogenics
696:Categories
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394:References
66:newspapers
33:references
499:Footnotes
488:0021-9606
441:0021-9606
315:π
299:α
286:π
245:≈
180:polarizes
702:Electron
666:14525485
192:hydrogen
148:mobility
124:electron
646:Bibcode
614:Bibcode
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359:is the
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186:which
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128:neon
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