  Recently, diffuse and extended sources in TeV gamma-rays as well as in X-rays
have been detected in the direction of the Galactic globular cluster (GC)
Terzan 5. Remarkably, this is among the brightest GCs detected in the GeV
regime. The nature of both the TeV and the diffuse X-ray signal from Terzan 5
is not settled yet. These emissions most likely indicate the presence of
several non-thermal radiation processes in addition to these giving rise to the
GeV signal.
  The aim of this work is to search for diffuse X-ray emission from the GeV
detected GCs M 62, NGC 6388, NGC 6541, M 28, M 80 and NGC 6139 to compare the
obtained results with the signal detected from Terzan 5. This study will help
to determine whether Terzan 5 stands out amongst other GC or whether a whole
population of globular clusters feature similar properties.
  None of the six GCs show significant diffuse X-ray emission on similar scales
as observed from Terzan 5 above the particle and diffuse galactic X-ray
background components. The derived upper limits allow to assess the validity of
different models that were discussed in the interpretation of the
multi-wavelength data of Terzan 5. A scenario based on synchrotron emission
from relativistic leptons provided by the millisecond pulsar population can not
be securely rejected if a comparable magnetic field strength as in Terzan 5 is
assumed for every GC. However, such a scenario seems to be unlikely for NGC
6388 and M 62. An inverse-Compton scenario relying on the presence of a
putative GRB remnant with the same properties as the one proposed for Terzan 5
can be ruled out for all of the six GCs. Finally, the assumption that each GC
hosts a source with the same luminosity as in Terzan 5 is ruled out for all GCs
but NGC 6139. (abridged)
