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Equation 1 · Part 7 · The Resonance That Selected Carbon, and the Universes That Couldn't

Symbol E_R

⟨σv⟩3α  ∝  ΓαΓ Γrad  exp⁡ ⁣(−ERkBT)\langle \sigma v \rangle_{3\alpha} \;\propto\; \frac{\Gamma_\alpha}{\Gamma}\,\Gamma_{\mathrm{rad}}\; \exp\!\left(-\frac{E_R}{k_{B}T}\right)
ERE_R

What this part means

the resonance energy above the reacting threshold [ 5 ].

Its job in the formula

ERE_R occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

where Γα\Gamma_\alpha and Γrad\Gamma_{\mathrm{rad}} are the alpha-decay and radiative partial widths, Γ\Gamma their sum, and ERE_R the resonance energy above the reacting threshold [ 5 ] .

The passage around this formula

…throughout the modern literature on this reaction, of the schematic resonant form ⟨σv⟩3α  ∝  ΓαΓ Γrad  exp⁡ ⁣(−ERkBT)\langle \sigma v \rangle_{3\alpha} \;\propto\; \frac{\Gamma_\alpha}{\Gamma}\,\Gamma_{\mathrm{rad}}\; \exp\!\left(-\frac{E_R}{k_{B}T}\right). where Γα\Gamma_\alpha and Γrad\Gamma_{\mathrm{rad}} are the alpha-decay and radiative partial widths, Γ\Gamma their sum, and ERE_R the resonance energy above the reacting threshold [ 5 ] . The exponential term is why a shift in the resonance’s position has outsized leverage on the reaction rate, and why the disputed radiative-width measurements of the previous section and the sensitivity calculations here are, in the end,…

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Sources cited in the surrounding passage

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