integration – how solve a double integral analytically or numerically

can someone help me to solve this integral or explain me how to set it on mathematica?

begin{equation}
int_{-infty}^{+infty} dk_alpha dk_phi frac{1}{2pi} e^{-frac{k_alpha^2}{2}} e^{-frac{k_phi^2}{2}} e^{ik_alpha alpha} e^{ik_phi phi} xi^{ik_alpha} e^{2isqrt{k_alpha^2 – xi k_phi^2}} e^{-2i k_alpha arctanh{ Big( frac{sqrt{k_alpha^2 – xi k_phi^2}}{k_alpha}} Big) }
end{equation}

I’ve tried both analytically and numerically but I couldn’t solve it.
Analytically the calculation doesn’t seem to go on, while numerically it returns several error messages.
Thank you all!