There's been changes Ann. A. longifolia is a synonym, check out the links above if you dare.
Asimina spatulata is the only one which fits for Alabama, Asimina angustifolia isn't listed there. The two do look different as mentioned on the biodiversity library (look at the snip).
http://www.floraofalabama.org/...
Yours could be Asimina angustifolia, not certain though, should check the location.
http://florida.plantatlas.usf....