How are branching ratios determined? by experiment only?

  • #1

Main Question or Discussion Point

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
 

Answers and Replies

  • #2
blechman
Science Advisor
779
8
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.
 
  • #3
....

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
 
  • #4
blechman
Science Advisor
779
8
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!
 

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