How does the Gamow window change for different reactions?

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Discussion Overview

The discussion centers around the Gamow window in nuclear fusion reactions, particularly focusing on the relationship between the Gamow energy peak and the width of the Gamow window for reactions such as proton-proton and deuteron-proton interactions. Participants explore the implications of these concepts on reaction rates and the measurement of the window's width.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that a greater Gamow energy peak results in a smaller Gamow window, but expresses uncertainty about the factors influencing the width of the window for different reactions.
  • Another participant questions how the width of the Gamow window is measured, proposing various methods such as measuring width over a threshold or at half the maximum.
  • A different participant notes a lack of clarity on the measurement of width and seeks to understand the relationship between the peak and the drop-off around it.
  • One participant mentions that Wikipedia contains formulas that can be used to visualize the function for different parameters.
  • Another participant indicates that the formulas are beyond their current understanding, suggesting a gap in knowledge regarding the mathematical interpretation of these concepts.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the measurement of the width of the Gamow window and the relationship between the peak and the width. There is no consensus on how these concepts are defined or measured.

Contextual Notes

Participants highlight limitations in their understanding of the mathematical formulations related to the Gamow window and its implications for fusion reactions.

TheCelt
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I am learning about the gamow energy and saw a graph explaining the gamow peak - but i am not quite sure i understand the relationship about the overwall gamow window.

From what i think i understand so far for fusion if the gamow energy peak is greater the gamow window becomes smaller is this correct? Not quite sure what drives the width of the gamow window for something like proton-proton or the deuteron-proton reaction.Obviously one has a higher gamow peak but i am not sure what changes about the rest of the area under the curve.
 
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How do you measure the width? Width over some threshold? Width at half the maximum? Something else?
If the required energy for the reaction is higher you get much lower reaction rates at equal temperature - but typically these reactions will happen at higher temperatures where the thermal spectrum is broader (doesn't change that much with smaller changes in the energy).
 
I don't know how its measured I just saw the graph looking like a bell curve around the peak. Nothing else was really said about what happens to the width at different peak levels. So i don't have much insight to give with regards to what width is measured with here, i was curious to know the relationship was between the peak and the drop off around it.
 
Well we don't learn these formulas at high school its beyond my understand to interpret by just pure math at this stage...
 

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