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I am trying to find an old science fiction short story in which the police monitor people's emotional levels. The climax of the story is a scene where the police prevent something fairly horrific, possibly a child murder, as a result of the police monitoring a person whose emotional level over the course of a day(?) gradually climbs to some extraordinary level.

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The sounds a lot like "The Circuit Riders" by R. C. FitzPatrick from the April 1962 Analog. It fits every fact you provide in the question.

You can read the story on Project Gutenberg

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