  Using the H$\beta$ linewidth, we obtained the virial central supermassive
black hole masses and then the Eddington ratios in a sample of broad-line AGNs
and NLS1s observed by ASCA. Combined with the data from ROSAT and Chandra
observations, We found a strong correlation between hard/soft X-ray photon
index and the Eddington ratio. Such a correlation can be understood by a
two-zone accretion flow model, in which zone is a thin disk and the inner zone
is an advection-dominated accretion flow (ADAF) disk. The relation between
X-ray photon index and the Eddington ratio may account for NLS1s with not too
steep X-ray photon index founded by SDSS. If this relation is directly related
to the accretion disk, it may also exist in the accretion disk of different
scales (such as microquasar).
