What is the hebrew term for the rationalist approach of the Rambam, the Ran, the Rivash, Ralbag etc.?
A popular word used to be חוקר as in חוקרי טבע which loosely translates as philosopher or scientist.
Also popular is משכיל, meaning someone who tries to understand. But that has underlying connotations which may or may not be intentional.
Also on the subject though not what you are looking for, the phrase עסקן בדברים, or just עסקן according to Rashi, is used to describe someone who experiments to prove the science in psukim, as seen in Chulin 57b.
[Oddly, there he 'proved' the navi right(that ants don't have a king), got criticized for his need to prove it instead of simply relying on the navi, and in reality, based on our current knowledge, the navi was right on a technicality (they have a queen, not a king) which should have proven the test useless(as there would have been a leader in charge that the underlings should take counsel with).]