Suddenly, everyone who dies becomes a Zombie and a Ghost.
A Zombie will, so long as it has an intact head, continue to function until it starves "back" to death. Any meat it eats is perfectly converted to energy, and it need not sleep or rest as a result. It retains all capability it had in life, including intelligence, and will not rot any further. However, it no longer heals from injury except by absorbing radiation and loses all emotions not related desire to eat or immediate self preservation. As a result, it will not speak or act unless it directly serves it's immediate purposes, making it a rather dull conversationalist.
No preference is expressed for human meat, but on the other hand there's also no aversion to the idea. Zombies left unattended for too long might try to spead radiation by any means open to them.
As for the Ghost: Ghosts are glowy blue transparent upper torsos, with a tail tethering them to within ten feet of the Zombie they were once part of. A Ghost experiences all emotions except for those a Zombie retains, can talk normally and can lift roughly the weight of a hardback novel. They are completely intangible and indestructible, but will dissipate if the Zombie "dies".