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Probably the first step towards applying for a PhD program is to find a professor who has enough interest/resource(s)/willing for the supervision. I know some of the rules (including attaching CV and research interests plus recommendation letters) for a letter to professors but is there any specific information that should be included in the letter to make it more efficient?
In other word, how to write an email to persuade the professor to accept my application?
Professors get two kinds of emails from "prospective" students. The first kind is serious. But the other is just a mass mailing in which it becomes quickly obvious (first sentence or so) that the student has no real interest and no knowledge of the professor or their specific interests and research trajectory. For example, I'm in computer science with very specific interests, but I used to get (retired now) a lot of mail, often from China, from people wanting to "join my research group (which didn't exist)" and giving their background as something like Petroleum Engineering. Well. Those don't get answered.
So, you want your letter to clearly be viewed as a serious attempt to connect and that you have serious interest and appropriate knowledge and background.
Before you write such a letter, first learn something about that professor. Find their CV and their stated interests. Obtain and read a few of their papers, or at least the abstracts. Now you have a basis on which to know if you want to work with them (really) and a basis for describing your background and how it fits.
Then, in a letter or email, you can mention that you have at least a bit of understanding of what they do and that you would be interested in working along those same lines. Discuss your specific background that might be relevant. I think it is less important that you give things like GPA or awards than it is that you, perhaps, have a bit of relevant research experience or have otherwise worked closely with a professor or two.
Express interest in working with them, but also that you really know what that is.
