Interesting integral involving modulus of difference of vectors, how to solve?

[omg!]

Hi guys,

Homework Statement

how do i solve (or approximate if not solvable) this integral

$$\int\int e^{-\alpha(|\vec{r}_1-\vec{r}_2|-r_0)^2} d^3\vec{r}_1 d^3\vec{r}_2$$

$$\alpha>0$$

Homework Equations

none

The Attempt at a Solution

none

 

[hunt_mat]

Compute:
$$|r_{1}-r_{2}|^{2}=(r_{1}-r_{2}).(r_{1}-r_{2})$$
What do you get? Or take an easier example, can you compute:
$$\int\int e^{-\alpha (|x-y|-a)^{2}}dxdy$$