How are branching ratios determined? by experiment only?

[WarpedWatch]

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

 

[blechman]

If you are studying a process X -> Y, the "rate" at which this process occurs is called \Gamma(X\rightarrow Y). 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 \Gamma(X), then a "branching ratio" is defined as:

\frac{\Gamma(X\rightarrow Y)}{\Gamma(X)}

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

\Gamma(X)=\sum_Y \Gamma(X\rightarrow Y).

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

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

 

[WarpedWatch]

...

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

 

[blechman]

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!