Equation 1 · The Resonance That Selected Carbon, and the Universes That Couldn't
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Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol σ
σ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol v
v is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol Gamma
Gamma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol k_B
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Symbol T
T occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Denominator: k_BT
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction.
What the article says around this equation
The underlying reaction-rate dependence that ties the Hoyle-state’s radiative width directly to the resonance’s position above threshold is the same relation used throughout the modern literature on this reaction, of the schematic resonant form . where and are the alpha-decay and radiative partial widths, their sum, and 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, two views of the…
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The underlying reaction-rate dependence that ties the Hoyle-state’s radiative width directly to the resonance’s position above threshold is the same relation used throughout the modern literature on this reaction, of the schematic resonant form . where and are the alpha-decay and radiative partial widths, their sum, and 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, two views of the same quantity’s grip on the same exponent.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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