What Happens When a Spherical Square Well Approaches 2mc2?

[sean_mp]

Homework Statement

I'm dealing with a dirac particle in an attractive spherical square well. I've solved for the transcendental equation to find energy, found the normalized wave function, and now I'm trying to explain what happens when the well becomes very deep, when V₀ ≥ 2mc². If I plug V₀=2mc² into my equations, nothing dramatic really sticks out. I have the same equation as Greiner on page 220, Eq.(27).

Homework Equations

I'm trying to get the values in the left hand side of table 9.2 on page 222 (V₀(κ=-1)), but I'm not sure how to go about it. If I can't solve for this, I need to come up with another consequence of the well depth approaching 2mc².

The Attempt at a Solution

 

[member 553083]

I've tried plugging in V0=2mc2 into Eq.(27), but this doesn't really seem to get me anywhere. I'm not sure what else to do. Any help would be greatly appreciated!