Rationality is scientific, rationalization is mythical.
Rationality uses as tools, calculation (induction) and logic (deduction) based on facts and/or human experience, and is based on the principle that science (or human reasoning) cannot define the Real (reality as a whole) but only can define concepts. For rationality, there’s a part of reality which is not possible to rationalize.
In the case of quantum mechanics, rationality uses the formal logical mathematics (deduction) based upon empirical data collected by means of physical measuring devices.
On the other hand, rationalization is based on the principle that the Real (reality) is forcibly and totally subject to a definition by the human Reason. It consists in a construction of a logical coherence based upon incomplete or erroneous data, or based upon a reductive discursive principle.
Rationality exists not only in the theoretical building ― i.e., in the structure of a specific scientific theory ― as well as it exists through and by means of a dialogue with human experience and with the external world, which is concrete and objective. As soon as facts and human experience denies, jeopardizes, or even put in doubt a given theory, rationality revises its previous standards based on evidence or auto-evidence.
On the contrary, rationalization imposes itself to the facts and makes them void by means of a excessive exercise of logic in relation to the sphere of the empiric, and by refusal of reality as it presents itself to us in all its complexity. Rationalization is a characteristic of the “illuminist philosophizing” by which the symbols acquire themselves an autonomous life and independent from human experience. Through rationalization [which led to the political religions] the reality is accommodated to a specific ideological vision of it.
Science depends upon human rationality which is the axiom (the principle) of science; before and beyond the axiom, there is nothing else and everything depends on it. Therefore, science cannot test rationality in a retrospective way, by putting its own principle in doubt or/and in a jeopardize position.
Human religiosity cannot be a subject of science unless science questions its own axiom (rationality) and therefore denies itself as science by adopting rationalization which moulds reality at someone’s subjective will.