The purpose of a process is not to document all the details. Processes are defined to make clear how the project members should work, they can also be used to make the process measurable. A process also guarantees a certain quality of the product.
The best course of action in my opinion is to use the UML and a process in order to document all of the details including the user needs and the scope. A process assists construction, they are using an interative and incremental approach these days, much better than the waterfal methodology.