  We report the results of the spatial two-point correlation function xi(r) for
the new X-ray galaxy cluster survey REFLEX, which comprises of 452 X-ray
selected clusters (449 with redshifts) detected by the ROSAT satellite during
the ROSAT All-Sky-Survey. The REFLEX cluster sample is flux limited to
3x10^{-12} erg s^{-1} cm^{-2} in the ROSAT energy band (0.1-2.4 keV) and spans
3 decades in X-ray luminosity (10^{42} - 10^{45} h^{-2} erg s^{-1}), containing
galaxy groups and rich clusters out to a redshift z~0.3. Covering a contiguous
area of 4.24 sr REFLEX is the largest X-ray cluster sample to date for which
spatial clustering has been analysed. Correlation studies using clusters
selected on the basis of their X-ray emission are particularly interesting as
they are largely free from the projection biases inherent to optical studies.
For the entire flux-limited sample we find that the correlation length (the
scale at which the correlation amplitude passes through unity) r_0~20
h^{-1}Mpc. For example, if a power-law fit is made to xi(r) over the range 4-40
h^{-1} Mpc then r_0=18.8+-0.9. An indication of the robustness of this result
comes from the high degree of isotropy seen in the clustering pattern on scales
close to the correlation length. On larger scales xi(r) deviates from a
power-law, crossing zero at ~45h^{-1} Mpc. From an examination of 5
volume-limited cluster sub-samples we find no significant trend of r_0 with
limiting X-ray luminosity. A comparison with recent model predictions for the
clustering properties of X-ray flux-limited samples, indicates that Cold Dark
Matter models with the matter density Omega_m=1 fail to produce sufficient
clustering to account for the data, while Omega_m~0.3 models provide an
excellent fit.
