Abstract <p>The α-shape factor of the real epithermal neutron spectrum, characterized by the 1/E^{1+ α} dependence, at the sample irradiation positions of the neutron production chamber installed at the IREN facility, was experimentally determined using the dual monitor method based on cadmium ratios. Two monitor sets, consisting of gold and copper foils, were employed for the determination of the α-shape factor. A revised equation for the determination of the α-shape factor was derived, which explicitly accounts for the effects of thermal and epithermal neutron self-shielding, as well as cadmium transmission of epithermal neutrons, in a logical and transparent manner. The arrangement of the correction factors for these effects in our proposed equation differs from that in the equations commonly used by other authors. The α-shape factor obtained using the proposed equation was compared with those calculated using several alternative equations employed by other research groups. The discrepancies observed among the values of the α-shape factor determined by solving different equations indicate that the placement of the correction factors within the equation significantly affects the result. Therefore, particular attention should be paid to this aspect when applying the dual monitor method for determining the α-shape factor.</p>