I am applying for graduate physics and I was wondering to work with a well-known professor in Caltech. He is a pioneer in the field that I am interested in. I have a kinda outstanding background, however, I am not sure if the professor is looking for exotic genius students who have completed their master at 18 or something! In this sense, I am very ordinary. How should I send an email to the professor and finally understand if I have any chance to do my PhD under his supervision or not?
P.S. I just want to know how one should contact a professor to make themselves sure that whether the professor is willing to accept them as a graduate student. I do not ask please decide on behalf of me.