I have that exact crossbar, and the ones for the 1/4" and 1/2" breaker bars too. They are not for sale, but I did measure the 3/8" crossbar. It's about 6 & 63/64" long and about 0.3100" in diameter.
I assume it's supposed to be 7" long, but I call it like I see it. I measured the diameter in a few places using a digital caliper. That's the most accurate diameter number for it. I have no idea what it works out to in fractions of an inch.
Also, I tried the all three crosssbars in their respective breaker bars. They all fit about the same. In other words, the crossbar for the 3/8" breaker bar was not significantly looser or tighter than the ones for the 1/4" or 1/2" breaker bar.
Let me know if you need more information.
Bernie
Thanks Bernie, that helps!
My 1/4" crossbar seems way too loose, the 1/2" fits as I would expect.

set of U-Circle 12 pt 1/2" shallow sockets from 7/16 to 1-1/8 including a 19/32. I've also got a Sliding T-bar in really great condition as well as a 10" and 5" extension. I didn't scan the extensions.