Integral Representation of the Random-Phase Approximation Correlation Energy

Using the spectral function ${\phi }^{\prime }\left(z\right)/\phi \left(z\right)$, the random-phase approximation correlation energy and other properties of a finite system can be written as a contour integral in a compact way. This yields a transparent expression and reduces drastically the numerical efforts for obtaining reliable values. For illustration the method is applied to pairing vibrations in rotating nuclei.