There are different models you can use to describe the nucleus. Models such as the Shell or Collective models describe nuclear energy levels with three quantum numbers.
The existence of nuclear isomers is usually related to a large spin and parity change between excited and ground states. In the case of Ba-137, the isomer state has spin 11/2, odd parity, and the ground state has spin 3/2, even parity. The large spin change, plus the party change, hinder de-excitation and lead to a measurable lifetime.
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