How are branching ratios determined? by experiment only?

  • Context: Undergrad 
  • Thread starter Thread starter WarpedWatch
  • Start date Start date
  • Tags Tags
    Experiment Ratios
Click For Summary

Discussion Overview

The discussion revolves around the determination of branching ratios in nuclear reactions, specifically whether these ratios are derived solely from experimental data or if they can also be predicted through theoretical frameworks such as quantum mechanics and quantum field theory.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Mark inquires whether branching ratios are determined only by experiments or if there exists a fundamental theory that can predict these ratios.
  • One participant explains that the rate of a process can be computed and defines branching ratios in terms of decay widths, indicating that these calculations are based on quantum mechanics and quantum field theory.
  • Mark expresses interest in whether these phenomena could have been understood without direct experimental evidence.
  • Another participant confirms that partial widths can indeed be calculated using Fermi's Golden Rule and its relativistic extensions, suggesting a theoretical basis for these calculations.

Areas of Agreement / Disagreement

Participants generally agree that branching ratios can be computed theoretically, but there is an underlying inquiry about the necessity of experimental data for these determinations, leaving some aspects of the discussion unresolved.

Contextual Notes

The discussion does not resolve the extent to which theoretical predictions align with experimental results or the implications of relying on either approach for understanding branching ratios.

WarpedWatch
Messages
36
Reaction score
0
Greetings,

when I look up how nuclear reactions take place, I often see branching ratios listed as percentages. So I'm wondering: are those ratios determined only by experiment or is there some fundamental theory that can predict what those percentages will be?

many thanks,
Mark
 
Physics news on Phys.org
If you are studying a process X -> Y, the "rate" at which this process occurs is called [itex]\Gamma(X\rightarrow Y)[/itex]. This is computable. If we denote the TOTAL width (that is, the inverse lifetime, the sum of all possible decay widths for all possible Y, also computable) as [itex]\Gamma(X)[/itex], then a "branching ratio" is defined as:

[tex]\frac{\Gamma(X\rightarrow Y)}{\Gamma(X)}[/tex]

That is, it is the fraction of total decays of X that go into Y. So all this is computable, and it is always a fraction (percentage), since

[tex]\Gamma(X)=\sum_Y \Gamma(X\rightarrow Y)[/tex].

I'm not sure if that answers your question...

These things are all computable from quantum mechanics/quantum field theory.
 
blechman said:
...

These things are all computable from quantum mechanics/quantum field theory.

Yes, that is what I wanted to know. I was wondering if this kind of phenomenon is something that could have been figured out without running direct experiments.

many, many thanks for your help,
Mark
 
yes, one can calculate partial widths directly from Fermi's Golden Rule in Quantum Mechanics (and its relativistic generalizations in Quantum Field Theory) and compare to experiment.

Happy I was able to help!
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
4K
Replies
2
Views
3K
  • · Replies 4 ·
Replies
4
Views
4K
Replies
10
Views
225
  • · Replies 10 ·
Replies
10
Views
5K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 0 ·
Replies
0
Views
4K
  • · Replies 93 ·
4
Replies
93
Views
6K