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Polarizability is an important fundamental property of subatomic particles. Polarizabilities determine the dynamical response of a bound system to external perturbations, and provide insight into the internal strong interaction structure.^[1]

Electronic polarizability

Electronic polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field, which may be caused by the presence of a nearby ion or dipole.

The electronic polarizability $\alpha$ is defined as the ratio of the induced dipole moment ${\boldsymbol {p}}$ of an atom to the electric field ${\boldsymbol {E}}$ that produces this dipole moment.

${\boldsymbol {p}}=\alpha {\boldsymbol {E}}$

Polarizability has the SI units of C·m²·V⁻¹ = A²·s⁴·kg⁻¹ but is more often expressed as polarizability volume with units of cm³ or in Å³ = 10⁻²⁴ cm³.

$\alpha {\boldsymbol {(cm^{3})=}}{\frac {10^{6}}{4\pi \varepsilon _{0}}}\alpha {\boldsymbol {(C\cdot m^{2}\cdot V^{-1})}}$ where $\epsilon _{0}$ is the vacuum permittivity.

The polarizability of individual particles is related to the average electric susceptibility of the medium by the Clausius-Mossotti relation.

Note that the polarizability $\alpha$ as defined above is a scalar quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the $x$ -direction can only produce an $x$ component in ${\boldsymbol {p}}$ . However, it can happen that an electric field in the $x$ -direction, produces a $y$ or $z$ component in the vector ${\boldsymbol {p}}$ . In this case $\alpha$ is described as a tensor of rank 2, which is represented with respect to a given system of axes (frame of reference) by a $3\times 3$ matrix.

Magnetic polarizability

Template:Expert-subject-multiple Magnetic polarizability defined by spin interactions of nucleons is an important parameter of deuterons and hadrons. In particular, measurement of tensor polarizabilities of nucleons yields important information about spin-dependent nuclear forces.^[2]

The method of spin amplitudes uses quantum mechanics formalism to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin $S \geq 1$ are specified by the unit polarization vector ${\boldsymbol {p}}$ and the polarization tensor P_`. Additional tensors composed of products of three or more spin matrices are needed only for the exhaustive description of polarization of particles/nuclei with spin $S ≥ .mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}3⁄2$ .^[2]

References

^ L. Zhou (2002). "Magnetic polarizability of hadrons from lattice QCD" (PDF). European Organization for Nuclear Research (CERN). Retrieved 25 May 2010. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ ^a ^b A. J. Silenko (18 Nov 2008). "Manifestation of tensor magnetic polarizability of the deuteron in storage ring experiments". Springer Berlin / Heidelberg. doi:10.1140/epjst/e2008-00776-9. Retrieved 25 May 2010.

External links

[CERN-1] L. Zhou (2002). "Magnetic polarizability of hadrons from lattice QCD" (PDF). European Organization for Nuclear Research (CERN). Retrieved 25 May 2010. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[Silenko-2] A. J. Silenko (18 Nov 2008). "Manifestation of tensor magnetic polarizability of the deuteron in storage ring experiments". Springer Berlin / Heidelberg. doi:10.1140/epjst/e2008-00776-9. Retrieved 25 May 2010.

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[2]

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-{{Unreferenced|date=December 2009}}
+{{More footnotes|date=May 2010}}
+'''Polarizability''' is an important fundamental property of subatomic particles.  Polarizabilities determine the dynamical response of a bound system to external perturbations, and provide insight into the internal strong interaction structure.<ref name="CERN">{{cite web |author=L. Zhou |coauthors=F. X. Lee, W. Wilcox, J. Christensen |title=Magnetic polarizability of hadrons from lattice QCD |url=http://cdsweb.cern.ch/record/581347/files/0209128.pdf |publisher=European Organization for Nuclear Research ([[CERN]]) |date=2002 |format=[[PDF]] |accessdate=25 May 2010}}</ref>
-'''Polarizability''' is the relative tendency of a charge distribution, like the [[electron cloud]] of an [[atom]] or [[molecule]], to be distorted from its normal shape by an external [[electric field]], which may be caused by the presence of a nearby [[ion]] or [[Dipole#Field_from_an_electric_dipole|dipole]].
+==Electronic polarizability==
+Electronic polarizability is the relative tendency of a charge distribution, like the [[electron cloud]] of an [[atom]] or [[molecule]], to be distorted from its normal shape by an external [[electric field]], which may be caused by the presence of a nearby [[ion]] or [[Dipole#Field_from_an_electric_dipole|dipole]].
 The electronic polarizability <math>\alpha</math> is defined as the ratio of the induced dipole moment <math>\boldsymbol{p}</math> of an atom to the electric field <math>\boldsymbol{E}</math> that produces this dipole moment.
@@ Line 14: / Line 17: @@
 Note that the polarizability <math>\alpha</math> as defined above is a [[scalar (physics)|scalar]] quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the <math>x</math>-direction can only produce an <math>x</math> component in <math>\boldsymbol{p}</math>. However, it can happen that an electric field in the <math>x</math>-direction, produces a <math>y</math> or <math>z</math> component in the vector <math>\boldsymbol{p}</math>. In this case <math>\alpha</math> is described as  a [[tensor]] of rank 2, which is represented with respect to a given system of axes (frame of reference) by a <math>3 \times 3</math> [[Matrix (mathematics)|matrix]].
+=={{anchor|Magnetic polarizability}}Magnetic polarizability==
+{{Expert-subject-multiple|Physics|Electromagnetism|type=section|date=May 2010}}
+Magnetic polarizability defined by spin interactions of nucleons is an important parameter of deuterons and hadrons.  In particular, measurement of tensor polarizabilities of nucleons yields important information about spin-dependent nuclear forces.<ref name="Silenko">{{cite web |author=A. J. Silenko |title=Manifestation of tensor magnetic polarizability of the deuteron in storage ring experiments |url=http://www.springerlink.com/content/m2744373305l24m7/ |publisher=Springer Berlin / Heidelberg |date=18 Nov 2008 |doi=10.1140/epjst/e2008-00776-9 |accessdate=25 May 2010}}</ref>
+The method of spin amplitudes uses quantum mechanics formalism to more easily describe spin dynamics.  Vector and tensor polarization of particle/nuclei with spin {{math|<big>S</big> ≥ 1}} are specified by the unit polarization vector <math>\boldsymbol{p}</math> and the polarization tensor ''P''<sub><small>`</small></sub>.  Additional tensors composed of products of three or more spin matrices are needed only for the exhaustive description of polarization of particles/nuclei with spin {{math|<big>S</big> ≥ {{frac|3|2}}}} .<ref name="Silenko"/>
 ==See also==
-*[[Polarization density]]
+* [[Polarization density]]
+==References==
+{{reflist}}
+==External links==
+* [http://books.google.com/books?id=bI-ZmZWeyhkC&pg=PA290&lpg=PA290&dq=Magnetic+polarizability&source=bl&ots=G5kn6PLhSr&sig=ZJKTzwW-YZhTKtOLjbEHcRzdVfA&hl=en&ei=13z8S8HGG8KBlAfbx-nGDw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBQQ6AEwATgK#v=onepage&q=Magnetic%20polarizability&f=false The theory of the electromagnetic field] by David M. Cook
+* [http://arxiv.org/abs/hep-ph/9309211 Consistent Calculation of the Nucleon Electromagnetic Polarizabilities in Chiral Perturbation Theory Beyond Next-to-Leading Order]
+* [http://bearspace.baylor.edu/Walter_Wilcox/www/LHPCPresentation-Dell.pdf Hadron polarizabilities and magnetic moments with background field methods] ([[PDF]])
+{{particles}}
 [[Category:Atomic physics]]