3:55 PM -- The first photo of Jayme has surfaced ... showing her smiling with her aunt and godmother, Jennifer Naiberg Smith. As we told you ... they were reunited this afternoon at the hospital where Jayme was being evaluated. 1:57 PM -- Officials say cops recovered a shotgun consistent with what was used at the scene of the homicide. Cops say Patterson -- who shaved his head after allegedly killing Jayme's parents to hide from cops -- shot the door open. Cops say Patterson had a small connection to Jayme's parents -- working at the same turkey processing plant...