In the table of nuclides, it shows that $\rm Ag$ 108 can go through either electron capture or beta- decay (though the branching ratio for electron capture decay is much lower). What determines that? Do nuclides try to maximize binding energy or binding energy per nucleon? And is decay into Palladium much rarer because of the conditions necessary for electron capture are hard to come by?
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"What determines that?"
You must mean "is there a theoretical model that determines that", otherwise the answer is "because that is what the data measurements show".
The theory that models nuclear physics is quantum mechanical. In principle the solution of the quantum mechanical equation , call it $Ψ$ should give the probability of the capture or the decay happening when $Ψ^*Ψ$ is calculated.
Because of the many particle complexity of nuclides, an over all quantum model is used, the shell model, when describing nuclei. It should be the one to use if one wants to describe electron capture and beta decay, but the proposed variations studied for astrophysical observations (example for electron capture)do not include Ag .
Maybe you will get a better answer by a specialist.
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