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This is because nuclear decay processes follow a exponential law. The time difference gamma 1 – gamma 2 measures the life time of the intermediate state and therefore this will have the shape of a exponential decay.
The number of 1-2 events is smaller than that of the 1-3 events because of the favoriign of sending gammarays in the direction of the nuclear spin. This is the peanut shape as seen many times before.
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