language

When I wrote that it is not often heard, I just meant that I personally don't remember hearing the phrase. It seems like I have only heard and read phrases about relaxing the mind, calming the mind, etc. because the mind is the source of emotions. Think of the mind as an ocean and the waves as emotion. The waves on the shore are relative to the storm over the ocean. When the storm stops, the waves calm.
As far as one phrase you mentioned being written more than the other, my guess is that it is because "emotional relaxation" would be the subject of a sentence.

relax emotionlly is a verb/adverb

emotional relaxation is adjective/ noun

Look at the entire sentence to determine best structure to use.

Thanks so much! I realize that in this context of relaxing, we Chinese are prone to express in "relax+adv. ” , totally different from the English way of "relax+noun".

You're welcome. I understand.