Punctuation with "and thus" in the middle of a sentence

This sentence has two independent clauses. They are connected by "and" with a comma before it. The "and" and the comma are correct. However, adding a comma after "thus" is not correct because it is an adverb; the comma after it is not necessary.

The sentence is fine this way:

"Accepted theories can provide satisfactory results, and thus experiments can be avoided."

If "thus" is used as a conjunctive adverb (without "and"), a semi-colon and a comma are necessary. This version of your sentence is also correct:

"Accepted theories can provide satisfactory results; thus, experiments can be avoided."

Both of these sentences are clearer than your sentence that has the comma after "thus."