I'm contacting a professor for getting possibly a research fund or to start a collaboration. Before sending the whole application and the proposal (which is a long document), I would like to send an email to her to share the general idea about my proposal so see if its boundary and criteria are matched with her future plan and research interest. So after a generic explanation, I want to ask if she has any interest in the subject and..., I could send them the complete proposal document. Currently, I've written, "if you are interested I can provide you more details", which I don't think is the best way. What is a more polite and formal expression for such a situation?
I would say the sentence already looks polite enough. You could change it to
Should you be interested in my research project, I would be happy to send you the complete research proposal and answer any questions you might have.
But I do not expect this sentence to have any effect on the chances of success of your application. The content of your proposal and how you write the summary are much more important.