Not using a ballscrew, it's a standard 3/8-10 LH acme screw. I did look into using a ballscrew, but opted to go with the acme screw because of price and simplicity (would love to have used a ballscrew though). Got the screw and delrin nut from user widgetmasterinc on ebay. Here's a link to the nut: LINK
The same seller also sells an 18" section of 3/8-10 LH acme threaded rod for $10.
It wouldn't be very difficult to adapt this design to use a ballscrew though. Would probably require some type of side plate off the Carriage Block.
Here's a pic showing the mounting of the nut. This pic also shows where the Lead Nut Plate is utilized.