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How are branching ratios determined? by experiment only?

  1. Jan 8, 2010 #1
    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
     
  2. jcsd
  3. Jan 8, 2010 #2

    blechman

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    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.
     
  4. Jan 8, 2010 #3
    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
     
  5. Jan 8, 2010 #4

    blechman

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    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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