In this work we propose a new diagnostic to segregate cool core (CC) clusters from non-cool core (NCC) clusters by studying the two-dimensional power spectra of the X-ray images observed with the Chandra X-ray observatory. Our sample contains 41 members ($z=0.01sim 0.54$), which are selected from the Chandra archive when a high photon count, an adequate angular resolution, a relatively complete detector coverage, and coincident CC-NCC classifications derived with three traditional diagnostics are simultaneously guaranteed. We find that in the log-log space the derived image power spectra can be well represented by a constant model component at large wavenumbers, while at small wavenumbers a power excess beyond the constant component appears in all clusters, with a clear tendency that the excess is stronger in CC clusters. By introducing a new CC diagnostic parameter, i.e., the power excess index (PEI), we classify the clusters in our sample and compare the results with those obtained with three traditional CC diagnostics. We find that the results agree with each other very well. By calculating the PEI values of the simulated clusters, we find that the new diagnostic works well at redshifts up to 0.5 for intermediately sized and massive clusters with a typical Chandra or XMM pointing observation. The new CC diagnostic has several advantages over its counterparts, e.g., it is free of the effects of the commonly seen centroid shift of the X-ray halo caused by merger event, and the corresponding calculation is straightforward, almost irrelevant to the complicated spectral analysis.
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