OK, firstly, I think this resource is really important. Please read it and take it to heart:
http://www.phillyspissed.net/sites/default/files/what%20to%20do%20when%20someone%20tells%20you.pdfIt's called: 'What to Do When Someone Tells you that you violated their boundaries, made them feel uncomfortable, or committed assault.'
Basically, your relationship / friendship now has to exist on the terms of your ex. Give her space now. Do not contact her. If she wants to get back in contact with you, ask what you can do if anything to help, but acknowledge that you raped her and that it was entirely your fault. If she contacts you, you could calmly offer to turn yourself in to the authorities if she so wishes - however, is she doesn't want to press charges, respect that. She has already given you an apology. You may not believe it, but you should not try to seek further confirmation.
You can't undo what you did, sadly. I think Hugo Schwyzer is a hypocrite and an unrepentant abuser (he tried to murder his ex and is also possibly a rapist, by admission) but, oddly enough, he has good advice to give to someone who wants to redeem themselves after committing past abuse:
Your goal is not to be loved by everyone; your goal is to pay a debt, to make amends, and to become a better human being.
http://www.hugoschwyzer.net/2009/03/19/an-open-letter-to-kyle-payne/If your ex does not desire to take legal action against you, then I would suggest that you dedicate yourself to volunteering. Do not volunteer at a shelter or a rape crisis line, because I think that would be inappropriate. However, you could volunteer regularly at a soup kitchen or an animal shelter or somewhere like that.
I also think it is important to be open with your friend and acquaintances about what you did - which is ######6 scary, but also necessary. Some people won't forgive you or want to remain your friend. Other people will respect your honesty. You just have to accept what does and who doesn't. Don't challenge or try to excuse yourself. Most importantly is to not push yourself upon any mutual friends for support. Your ex-girlfriend needs and deserves them around her more than you do right now and you have to respect that. Talk to any friends who are just friends with you and talk to your family. Maybe book yourself in to see a therapist. There are also people to talk to here.

You are still a human being, not a monster. Everyone of us is a human being. Also, you were pretty young. Too old for your act - which is a terrible thing to do to anyone - to be inexcusable, but not too old to change. Even at 20 your brain hasn't quite finished developing. You can ensure that you never do something like this ever again.
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When I was younger - actually, about your age - I assaulted my ex-partner. It was not penile rape (and may not have been recognised legally as rape at the time, though would according to the updated F.B.I. definition of rape) but it was certainly a sexual assault. She had said that she was not in the mood for being sexual and to just hold her. When we were spooning I moved my hands and ended up touching her in a violatory way. Because she didn't anything at the time I was able to convince myself for a couple of years that this was not sexual assault i.e. 'she didn't say NO and I didn't force or threaten her, so it was consensual'. I know now this was self-deception and though it is hard to continue living with that knowledge, I would rather be alive and anxious and full of regret, but living in truth, that alive and self-deceiving, living a happy lie. I might have remained dangerous and hurt more people. Also, then I would never have apologised, nor tried to take ownership for my crime.
I hope you now know that you must always have clear and enthusiastic consent before doing anything sexual, even with a partner you have done things with many times before. Hopefully this is being taught more and more in school. The rapes shown on television and films are generally obviously violent, with lots of physical force, restraint and a weapon. There must be many thousands and thousands of rapists who do not see themselves as rapists and will continue hurting people.
I am glad you will no longer hurt anyone else and I think you should continue to live, even if it is hard.
If you want to message me about this please feel free. It might not be a good idea to describe your crime too explicitly on these boards. It's tricky because part of accountability is taking ownership and part of that is not wanting people to have false illusions about who you are and what you have done. However, if there is even the tiniest risk that your ex-girlfriend might come across these forums and recognise her own story, do not do it, because that might re-traumatize her and it is really not your right to do so.