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{{primary sources|date=October 2011}}

An '''electron bubble''' is the empty space created around a free [[electron]] in a cryogenic gas or liquid, such as [[neon]] or [[helium]].  They are typically very small, about 2&nbsp;nm in diameter at atmospheric pressure.

== Electron bubbles in helium ==

At room temperature, electrons in [[noble gas]]ses move about freely, limited only by collisions with the weakly interacting atoms.  Their [[electron mobility|mobility]], which depends on the gas density and temperature, is well described by classical [[kinetic theory of gases|kinetic theory]].  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.<ref>{{Cite journal |last1=Ramanan |first1=G. |last2=Freeman |first2=Gordon R. |date=September 1990 |title=Electron mobilities in low density helium and nitrogen gases: Momentum transfer cross sections at very low energies |url=http://aip.scitation.org/doi/10.1063/1.459675 |journal=The Journal of Chemical Physics |language=en |volume=93 |issue=5 |pages=3120–3126 |doi=10.1063/1.459675 |bibcode=1990JChPh..93.3120R |issn=0021-9606}}</ref>

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.<ref>{{Cite journal |last1=Ramanan |first1=G. |last2=Freeman |first2=Gordon R. |date=September 1990 |title=Electron mobilities in low density helium and nitrogen gases: Momentum transfer cross sections at very low energies |url=http://aip.scitation.org/doi/10.1063/1.459675 |journal=The Journal of Chemical Physics |language=en |volume=93 |issue=5 |pages=3120–3126 |doi=10.1063/1.459675 |bibcode=1990JChPh..93.3120R |issn=0021-9606}}</ref>  At low temperatures, electrons injected into [[liquid helium]] do not move freely as one might expect, but rather form small vacuum bubbles around themselves.

== Electron repulsion from the surface of helium ==

Electrons are attracted to liquid helium due to the difference in [[dielectric constant]]s between the gas and liquid [[phase (matter)|phase]] of helium.  The negative electron [[dielectric polarization|polarizes]] the helium at the surface, leading to an [[image charge]] which [[electron-on-helium qubit|binds it to the surface]].  The electron is forbidden from entering the liquid for the same reason [[hydrogen]] atoms are stable: [[quantum mechanics]].  The electron and image charge form a [[bound state]], just as an electron and [[proton]] do in a hydrogen atom, with a minimum average separation.  In this case, the minimum energy is about 1 [[Electronvolt|eV]] (a moderate amount of energy on an atomic scale)[[#Footnotes|[3]]].

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 [[surface tension]] term, and the pressure-volume term.  The confinement term is purely quantum mechanical, since whenever an electron is tightly confined, its [[kinetic energy]] goes up.  The surface tension term represents the [[surface energy]] 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.[[#Footnotes|[4]]]
: <math>E \approx \frac{h^2}{8 m R^2} + 4\pi R^2\alpha + \frac{4}{3}\pi R^3P</math>

Here ''E'' is the energy of the bubble, ''h'' is the [[Planck constant]], ''m'' is the [[electron mass]], ''R'' is the bubble radius, ''α'' is the surface energy, and ''P'' is the ambient pressure.

== 2S electron bubble ==

A theoretical prediction has been made based on the analysis of the equation above,[[#Footnotes|[5]]] that the 2S electron bubble exhibits a startling morphological instability under a wide range of ambient pressures. While its [[wave function]] is spherical, the stable shape of the bubble is nonspherical.

== References ==
{{reflist}}

== Footnotes ==

* 1. {{cite journal |author=G. Ramanan and Gordon R. Freeman |title=Electron Mobilities in Low Density Helium and Nitrogen Gases |journal=[[Journal of Chemical Physics]] |volume=93 |issue=5 |pages=3120 |year=1990 |doi=10.1063/1.459675|bibcode = 1990JChPh..93.3120R }}
* 2. {{cite journal |author=C. G. Kuper |title=Theory of Negative Ions in Liquid Helium |journal=[[Physical Review]] |volume=122 |issue=4 |pages=1007–1011 |year=1961 |doi=10.1103/PhysRev.122.1007|bibcode = 1961PhRv..122.1007K }}
* 3. {{cite journal |author=W. T. Sommer |title=Liquid Helium as a Barrier to Electrons |journal=[[Physical Review Letters]] |volume=12 |issue=11 |pages=271–273 |year=1964 |doi=10.1103/PhysRevLett.12.271|bibcode = 1964PhRvL..12..271S }}
* 4. {{cite journal |author=M. A. Woolf and G. W. Rayfield |title=Energy of Negative Ions in Liquid Helium by Photoelectric Emission |journal=[[Physical Review Letters]] |volume=15 |issue=6 |pages=235 |year=1965 |doi=10.1103/PhysRevLett.15.235|bibcode = 1965PhRvL..15..235W }}
* 5. {{cite journal |author=P. Grinfeld and H. Kojima |title=Instability of the 2S Electron Bubbles |journal=[[Physical Review Letters]] |volume=91 |issue=10 |pages=105301 |year=2003 |doi=10.1103/PhysRevLett.91.105301|bibcode = 2003PhRvL..91j5301G |pmid=14525485}}

== External links ==
* {{cite press release |date=25 November 2005 |url=http://www.eurekalert.org/pub_releases/2005-11/ns-qba112305.php |title=Quantum bubbles are the key |publisher=[[New Scientist]]}}

[[Category:Electron]]
[[Category:Cryogenics]]