The value of the normalization is

(1)

The tested value of H is

(2)

so that the normalization is

(3)

After our variable changes to r1, r2, and r12

(4)

Which is equal to the normalization for n=0.   For beta also zero see betazero.doc .htm.

 

For n=0, the inner integral is

(5)

The integral over r₂ is

 

(6)

The uv term simplifies to zero, the integral becomes

(7)

then separate the two terms into two integrals and let z = the argument in each.

(8)

A bit more simplification yet

(9)

Then finally

 

(10)

Note that we can turn the work of finding the normalization around to find