Which term describes a semi-conscious state of deep relaxation typically induced by narcotics?

The term "on the nod" refers specifically to a semi-conscious state of deep relaxation that is commonly seen in individuals who have consumed narcotics, particularly opioids. This state can be characterized by drowsiness and a tendency to appear as if one's head is nodding off due to the overwhelming sedation caused by these substances. It represents a unique physiological and psychological response associated with narcotic use, reflecting the drug's impact on the central nervous system.

The other terms listed do not capture the same meaning. "Overlapping Effect" relates to drug interactions and is not a specific state of relaxation induced by narcotics. "Pallor" refers to an unusual lack of color in the skin, which is more associated with certain medical conditions or shock than a drug-induced state of relaxation. "Nystagmus" describes involuntary eye movement, which is often an indicator of intoxication but does not connote the deep relaxation associated specifically with narcotics. Thus, "on the nod" stands out as the correct definition for the state described in the question.