Editing Classical electron radius (section)

{{Use American English|date = March 2019}}
{{Short description|Physical constant providing length scale to interatomic interactions}}
The '''classical electron radius''' is a combination of fundamental [[Physical quantity|physical quantities]] that define a [[length scale]] for problems involving an electron interacting with [[electromagnetic radiation]]. It links the classical electrostatic self-interaction energy of a homogeneous charge distribution to the electron's relativistic mass-energy.  According to modern understanding, the electron is a [[point particle]] with a [[Point particle#Point charge|point charge]] and no spatial extent.  Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems.  The classical electron radius is given as
: <math>r_\text{e} = \frac{1}{4\pi\varepsilon_0}\frac{e^2}{m_{\text{e}} c^2} = 2.817 940 3227(19) \times 10^{-15} \text{ m} = 2.817 940 3227(19) \text{ fm} ,</math>
where <math>e</math> is the [[elementary charge]], <math>m_{\text{e}}</math> is the [[electron mass]], <math>c</math> is the [[speed of light]], and <math>\varepsilon_0</math> is the [[vacuum permittivity|permittivity of free space]].<ref>[[David J. Griffiths]], ''Introduction to Quantum Mechanics'', Prentice-Hall, 1995, p. 155. {{ISBN|0-13-124405-1}}</ref>  This numerical value is several times larger than the [[proton radius|radius of the proton]].

The classical electron radius is sometimes known as the [[Hendrik Lorentz|Lorentz]] radius or the [[Thomson scattering]] length.  It is one of a trio of related scales of length, the other two being the [[Bohr radius]] <math>a_0</math> and the [[reduced Compton wavelength]] of the electron {{math|''ƛ''<sub>e</sub>}}.   Any one of these three length scales can be written in terms of any other using the [[fine-structure constant]] <math>\alpha</math>:
: <math>r_\text{e} = </math> {{math|''ƛ''<sub>e</sub>}} <math>\alpha = a_0 \alpha^2.</math>