Retrieving the norm of an unstored field in Lucene

Question

I have an existing Lucene index with an indexed, unstored field. Let's name the field longText. I need the norm of longText for a specific calculation. Not all the documents in the index have a longText field. When I try to get the norm for longText from a document that does not have this field, I always get 1.0, which is the default, but very wrong, value.

Is there a way to get the norm only for documents that have this field?

Alternatively, is there a way to get an indication whether a document has this field? Using getField() won't work as the field is, well, unstored.