Background: The energy weighted sum rules of the single-particle spectral functions provide a quantitative understanding of the fragmentation of nuclear states due to short-range and tensor correlations. Purpose: The aim of this paper is to compare on a quantitative basis the single-particle spectral function generated by different nuclear hamiltonians in symmetric nuclear matter using the first three energy-weighted moments. Method: The spectral functions are calculated in the framework of the self-consistent Greens function approach at finite temperature within a ladder resummation scheme. We analyze the first three moments of the spectral function and connect these to the correlations induced by the interactions between the nucleons. In particular, the variance of the spectral function is directly linked to the dispersive contribution of the self-energy. The discussion is centred around two- and three-body chiral nuclear interactions, with and without renormalization, but we also provide results obtained with the traditional phase-shift-equivalent CD-Bonn and Av18 potentials. Results: The variance of the spectral function is particularly sensitive to the short-range structure of the force, with hard-core interactions providing large variances. Chiral forces yield variances which are an order of magnitude smaller and, when tamed using the similarity renormalization group, the variance reduces significantly and in proportion to the renormalization scale. The presence of three-body forces does not substantially affect the results. Conclusions: The first three moments of the spectral function are useful tools in analysing the importance of correlations in nuclear ground states. In particular, the second-order moment provides a direct insight into dispersive contributions to the self-energy and its value is indicative of the fragmentation of single-particle states.
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