After arriving at the family business in Douglas, Ga., and finding his wife fatally shot on Sept. 20, 2006, Jon Worrell called 911 and crumpled to the ground in sobs.

His wife, Doris Worrell, was 39 when she was killed. The couple had three children who at the time were under the age of 12.

She died of a gunshot to the head at their business, Jon’s Sports Park, amid its arcade, batting cage, go-kart track and mini-golf course. It was a recreational destination for families in that rural part of southern Georgia, about 130 miles southwest of Savannah.

With such a backdrop, investigators and others in the city of about 12,000 first thought that Mr. Worrell was as he appeared, a devastated husband.

The authorities said they initially believed that Ms. Worrell died in a bungled robbery attempt or by someone in retaliation for being barred from the amusement park by Mr. Worrell.

But on Friday they said they had no doubts that he was behind her death.

“Jon instigated a conspiracy to commit this murder,” said Jason Seacrist, the lead agent on the case for the Georgia Bureau of Investigation.