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	<title>Spin pumping - Revision history</title>
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	<updated>2026-08-17T11:25:42Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<id>https://en.formulasearchengine.com/w/index.php?title=Spin_pumping&amp;diff=14074&amp;oldid=prev</id>
		<title>en&gt;A13ean at 22:09, 2 May 2013</title>
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		<updated>2013-05-02T22:09:02Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Context|date=May 2011}}&lt;br /&gt;
The &amp;#039;&amp;#039;&amp;#039;Axilrod–Teller potential&amp;#039;&amp;#039;&amp;#039; is a three-body [[potential]] that results from a third-order perturbation correction to the attractive [[van der Waals force|London dispersion interactions]] (instantaneous induced dipole-induced dipole)&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
V_{ijk}= E_{0} \left[&lt;br /&gt;
\frac{1 + 3 \cos\gamma_{i} \cos\gamma_{j} \cos\gamma_{k}}{\left( r_{ij} r_{jk} r_{ik} \right)^3}&lt;br /&gt;
\right]&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;r_{ij}&amp;lt;/math&amp;gt; is the distance between atoms &amp;lt;math&amp;gt;i&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;j&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;\gamma_{i}&amp;lt;/math&amp;gt; is the angle between the vectors&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{r}_{ij}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;\mathbf{r}_{ik}&amp;lt;/math&amp;gt;.  The coefficient &amp;lt;math&amp;gt;E_{0}&amp;lt;/math&amp;gt;  is positive and of the order &amp;lt;math&amp;gt;V\alpha^{3}&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the ionization energy and &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt; is the mean atomic polarizability; the exact value of &amp;lt;math&amp;gt;E_{0}&amp;lt;/math&amp;gt; depends on the magnitudes of the dipole matrix elements and on the energies of the &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; orbitals.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
*{{cite journal&lt;br /&gt;
 |last1=Axilrod |first1=B. M.&lt;br /&gt;
 |last2=Teller |first2=E.&lt;br /&gt;
 |year=1943&lt;br /&gt;
 |title=Interaction of the van der Waals Type Between Three Atoms&lt;br /&gt;
 |journal=[[Journal of Chemical Physics]]&lt;br /&gt;
 |volume=11 |issue=6 |pages=299&lt;br /&gt;
 |doi=10.1063/1.1723844&lt;br /&gt;
|bibcode = 1943JChPh..11..299A }}&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Axilrod-Teller potential}}&lt;br /&gt;
[[Category:Chemical bonding]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{physics-stub}}&lt;br /&gt;
{{chemistry-stub}}&lt;/div&gt;</summary>
		<author><name>en&gt;A13ean</name></author>
	</entry>
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