I'm running a 7970 with an i7 and 16Gb RAM getting a stable 40+ frames.
Few things to do:
-As always, Make sure you're running the latest drivers for your card
-Turn down Anti-aliasing (2x or 4x is enough)
-Turn down your view distance (This will take tweaking to meet a good view > Good FPS ratio)
If you're still not getting good frames you may need to optimize settings in the CCC (Catalyst Control Center) such as:
"Performance - Quality" sliders, Ensuring the program controls how AA is dealt with rather than CCC.
If all that fails you may be able to squeeze some extra frames with a slight overclock (There are dozens of guides for this) and don't forget to turn the fan speed up.