While doing a problem in quantum mechanics, I came across this integral: $$\int_V d^3\vec k\frac{1}{z-\frac{k^2}{2\mu}+i0^+}.$$Where the region $V$ is the intersection of two spheres centered on $\vec p_1$ and $\vec p_2$ with common radius $\lambda$(assuming $|\vec p_1-\vec p_2|<2\lambda$). I simply cannot see how to evaluate the integral as the bounds are defined piecewise and the pieces also depend on the orientation of $(\vec p_1-\vec p_2)$. Can someone help me?
Any comments/hints will be also helpful.
Thanks in advance.