Hi Margaret,
The Outside Diameter (OD) of AWG 4/0 is approximately 0.62 inches (15.75mm).
Definitely too large to accomodate an SCT013 CT.
US homes built before the late 60s were wired with Copper and typically had 100 Amp service, which used AWG 0 copper. An SCT013 would fit Service Entrance Wires in that particular scenario.
Sometime in the late 60s to early 70s, Copper Service Entrance Wires were replaced by Aluminum. Since Aluminum has more resistance per foot than Copper, the equivalent Aluminum wire is two gauges larger than its Copper counterpart. About that same time, 200 Amp service became the norm.
The term 200 Amp service causes much confusion as it’s the rating of the Load Center, (circuit breaker box)
and the Service Entrance Wires vice the maximum amount of continuously available current.
More info on that, here.