Try the new scope on a different gun.
I too have seen that on Ruger rings.What rifle action did you put it on ? Does it make any difference if the rings are front or back rings , as they can cause pressure problems at times ? I have seen this with Browning actions where the rings look nearly the same but don't interchange front to back and work out well . Is the new scope touching the barrel ? Are the rifles action screws still tight ? What type of stock is the rifle mounted in , wood , synthetic , laminated ? What type of shooting platform are you using , bags , ect. ? Is the barrel still clean any carbon ring or other build up in it ? So many variables so many questions that need answers to figure it out .