The burden of proof is always on the state to prove their case beyond all reasonable doubt. When it's a he said/she said case with no corroborating evidence, it comes down only to the credibility of the witness, and that credibility is challenged if someone is intoxicated. Obviously, it's a high burden to meet, but not impossible. Convictions are possible under this circumstance.
To be honest, this comes across as more of an "I have a girl saying this about me, oh no!" situation than any sort of legal research. I don't intent to be rude any more than I think Mr. Lehn did, but your question really DOES seem bizarre. If you really are researching for a paper, I think you should be good if you focus on constitutional protections for the accused.
You're doing "general research to become a lawyer" and you're asking "how hard is it to prove...that a person has been raped"...huh? Am I missing something here? Are you kidding? This is absolutely one of the most ridiculous posts I've ever seen on here. Still, I'll answer your question as best I can. So-called "he said, she said" crimes are always a challenge for the state if there's no corroborating evidence.
The above is for academic purposes and is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
If a woman believes she was raped law enforcement will advise her to and/or accompany her to the hospital for a rape kit so he said she said is not an issue.
Many cases are prosecuted on a he said she said basis. That's the nature of the law. Consider a man that is a victim of a car jacking and he is the only witness - does that mean the case should be thrown out?
There is no crystal ball. Each case has it's own life and own facts. Best of luck in your studies.
My comments are not intended to establish an attorney-client relationship, are not confidential, and are not intended to constitute legal advice. Proper legal advice can only be given by an attorney who agrees to represent you, who reviews the facts of your specific case, who does not have a conflict of interest preventing the representation, and who is licensed to practice in the appropriate jurisdiction where the legal issue may be filed or in the state where the law applies