This week's book giveaway is in the Other Open Source APIs forum. We're giving away four copies of Storm Applied and have Sean Allen, Peter Pathirana & Matthew Jankowski on-line! See this thread for details.
If you use dependency injection to get it using the @PersistenceContext annotation then you should not close it as this is handled for you. However if you are creating it from the factory as you are in your snippet then absolutely it is your responsibility to make sure it gets closed every time.