Observationally , it is found that there is a strong correlation between the hard X-ray photon index \Gamma and the Compton reflection scaling factor \Re in active galactic nuclei .
In this paper , we propose that the \Gamma - \Re correlation can be explained within the framework of the condensation of the hot corona onto the cold accretion disc around a supermassive black hole .
In the model , it is presumed that , initially , a vertically extended hot gas ( corona ) is supplied to the central supermassive black hole by capturing the interstellar medium and stellar wind .
In this scenario , when the initial mass accretion rate \dot { M } / \dot { M } _ { Edd } \gtrsim 0.01 , at a critical radius r _ { d } , part of the hot gas begins to condense onto the equatorial disc plane of the black hole , forming an inner cold accretion disc .
Then the matter is accreted in the form of the disc-corona structure extending down to the innermost stable circular orbits of the black hole .
The size of the inner disc is determined by the initial mass accretion rate .
With the increase of the initial mass accretion rate , the size of the inner disc increases , which results in both the increase of the Compton reflection scaling factor \Re and the increase of the hard X-ray photon index \Gamma .
By comparing with a sample of Seyfert galaxies with well-fitted X-ray spectra , it is found that our model can roughly explain the observations .
Finally , we discuss the possibility to apply our model to high mass X-ray binaries , which are believed to be fueled by the hot wind from the companion star .