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Concept# Fine-structure constant

Summary

In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.
It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field, by the formula 4πε_0ħcα = e^2. Its numerical value is approximately 0.0072973525693 ≃ 1/137.035999084, with a relative uncertainty of
The constant was named by Arnold Sommerfeld, who introduced it in 1916 when extending the Bohr model of the atom. α quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Michelson and Morley in 1887.
Why the constant should have this value is not understood, but there are a number of ways to measure its value.
In terms of other fundamental physical constants, α may be defined as:
where
e is the elementary charge ();
h is the Planck constant ();
ħ is the reduced Planck constant, ħ = h/2π (1.054571817×10−34 J⋅Hz−1)
c is the speed of light ();
ε_0 is the electric constant ().
Since the 2019 redefinition of the SI base units, the only quantity in this list that does not have an exact value in SI units is the electric constant.
The electrostatic CGS system implicitly sets 4πε_0 = 1, as commonly found in older physics literature, where the expression of the fine-structure constant becomes
A nondimensionalised system commonly used in high energy physics sets where the expressions for the fine-structure constant becomes
As such, the fine-structure constant is just a quantity determining (or determined by) the elementary charge: e = ≈ 0.30282212 in terms of such a natural unit of charge.
In the system of Hartree atomic units, which sets e = m_e = ħ = 4πε_0 = 1, the expression for the fine-structure constant becomes
The 2018 CODATA recommended value of α is
α = e^2/ 4πε_0ħc = 0.0072973525693.

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