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The constant epsilon is the nuclear efficiency and is related to the strong nuclear force. It's value is 0.007, which is pretty critical.
If it was less than 0.006 then Deutirium would be unstable due to proton / neutron bonds, and we would not get any helium being produced.
If it was greater then 0.008 then protons would be able to bind to each other directly, so there would be no hydrogen after the big bang.
A clear and detailed explanation of why it must have this value is given in the book Just Six Numbers by Martin J Rees.
last modified 18:26 2005/02/17