After a death sentence is affirmed in state collateral review, the prisoner may file for federal habeas corpus, which is a unique type of lawsuit that can be brought in federal courts. Federal habeas corpus is a species of collateral review, and it is the only way that state prisoners may attack a death sentence in federal court (other than petitions for certiorari to the United States Supreme Court after both direct review and state collateral review). The scope of federal habeas corpus is governed by the Antiterrorism and Effective Death Penalty Act of 1996, which restricted significantly its previous scope. The purpose of federal habeas corpus is to ensure that state courts, through the process of direct review and state collateral review, have done at least a reasonable job in protecting the prisoner's federal constitutional rights. Prisoners may also use federal habeas corpus suits to bring forth new evidence that they are innocent of the crime, though to be a valid defense at this late stage in the process, evidence of innocence must be truly compelling.
Is there an answer to this question (If it cannot be answered, say "unanswerable"): What act restricted the scope of federal habeas corpus?
the Antiterrorism and Effective Death Penalty Act of 1996