A federal prohibition would exist for any person who:

Has been convicted in any court of a crime punishable by imprisonment for a term exceeding one year
Is a fugitive from justice
Is an unlawful user of or addicted to any controlled substance
Has been adjudicated as a mental defective or committed to a mental institution
Is an alien illegally or unlawfully in the United States or who has been admitted to the United States under a non-immigrant visa
Has been discharged from the Armed Forces under dishonorable conditions
Having been a citizen of the United States, has renounced U.S. citizenship
Is subject to a court order that restrains the person from harassing, stalking, or threatening an intimate partner or child of such intimate partner
Has been convicted in any court of a misdemeanor crime of domestic violence
Is under indictment for a crime punishable by imprisonment for a term exceeding one year