Now that a former Hawaii-based soldier has been convicted of murder in the 2005 killing of his 5-year-old daughter, his defense team is trying to keep him from being sentenced to death by arguing that he suffers from a low level of intelligence.

The sentencing-eligibility phase began Tuesday for Naeem Williams in the Honolulu federal courtroom where jurors convicted him last week of murder in his daughter Talia’s beating death. The phase began with opening statements from the prosecution and the defense.

If jurors don’t agree that he can be sentenced to death, he will receive a life sentence without possibility for release.

Although Hawaii abolished capital punishment in 1957, Williams faces the death penalty because it’s a federal case. The fatal beating occurred on military property, allowing him to be tried in the federal justice system.

Defense attorney Michael Burt told jurors they will hear from several mental health experts who have evaluated Williams’ intelligence. Williams failed his first military aptitude test and, with help, later achieved the minimum score to get into the Army, Burt said.

Williams has an IQ score of 73, putting him in the fourth percentile and has a mental age of a 7- to 9-year-old, Burt said.

“The issue of punishment is now before you,” Burt said. “The question in this phase is no longer, ‘Is Mr. Williams responsible.’ “

The first witness, psychiatrist Pablo Stewart, testified that his opinion is that Williams suffers from intellectual impairment. The doctor said that during the time Talia lived with Williams in Hawaii, the former soldier suffered from a low IQ and functional brain impairment, made worse by alcohol abuse.

Prosecutors said that during this phase, they will rely on evidence presented during the trial that resulted in Williams’ conviction.

Assistant U.S. Attorney Darren Ching’s opening statement Tuesday echoed the one he delivered at the beginning of the trial, where he described months of abuse Williams inflicted on the girl before delivering a fatal blow that was so hard it left knuckle imprints on her chest.

“This blow was so hard Talia fell back and hit her head on the unforgiving concrete floor of her two-story prison,” Ching said. “Talia died a terrible death, but her death ended an even more horrific life.”

Williams testified that he and Talia’s stepmother, Delilah Williams, beat Talia almost daily, kept her home alone and didn’t feed her for days at a time.

Ching said the “frequency, severity and escalation” of the beatings show Williams’ intent. The prosecution argues the death penalty is warranted, partly because of the victim’s vulnerability.

U.S. District Judge J. Michael Seabright sustained Ching’s objection when Burt started to tell jurors about how historic it would be for someone to receive the death penalty in Hawaii.

Hawaii’s last recorded execution was in 1944.