Radical line thickness

From this answer, I understand that radical chooses the thickness of the horizontal line as a function of the height of a character.

Is there a way to redefine radical so as we have control on the thickness? I would like end up with a slightly thicker line.

Edit: As a fallback solution, what if 1) we use LuaLaTeX, or 2) we just replace the “standard square root sign” (meaning, typeset in Computer Modern) with the square root sign of another font, e.g. STIX?