Questions on psp8 pseudopotential and BKB projector

Hello Abinit Users,

I am trying to understand and use Abinit pseudopotential for some computation. I have read a few lecture notes/tutorials on pseudopotential, and got really confused after I read this page. Hope that you can help me clarify my confusion.

In equation (2) for constructing the projector on a real-space mesh, why there is a $1/r$ factor in the radial part? I did not see this factor in other notes/tutorial that I had read. How to deal with the points as $r$ approaches 0? Is this for the psp8 format only? Or is it also for other formats, like psp6?

I might have a completely misunderstanding of pseudopotential in KB form (after I read the above page). Any replies will be highly appreciated.

Thank you.