The main problem in radiation dosimetry is the determination of the absorbed dose in a medium material m, at a point where a detector (different composition and atomic number) is placed. This detector is called “cavity”, c, and its response is proportional to the absorbed dose in the cavity material.
The ratio between the absorbed dose measurement at the detector, D_c, and the absorbed dose at the medium, D_m, (at the place where the detector is located) is defined as the factor f.

The theoretical determination of the factor f, independent on the detector size and composition, represents the general cavity theory problem. If the ionizing radiation is a photon field, we refer it as the general cavity theory for photon beams. Factor f expressions have been proposed by Burlin(1966) and Kearsley(1984). Burlin ignored backscattering effects at the interfaces detector-medium, and Kearsley regarded them.
In this work, a modification to Kearsley model is introduced by considering scattering effect not only in the interfaces but on each of the planes within the cavity. As a result, a new expression for the factor f is obtained which did not introduce any new parameter. Although the new expression differs in form with the Kearsley one, numerically they are very similar. The Kearsley and new theories were compared with experimental data from Ogunleye (1982, 1987). Good agreement for all media and for Cobalt-60 is found. Poor agreement for 10 MV photon beams and only very mismatched medium and cavity material is observed. This last result may be due to uncertainties in other parameters involved in the factor f calculation, such as the “mass attenuation coefficient for secondary electrons" at that energy. It is therefore concluded that Kearsley theory does not need any improvement and represent the general expression of the cavity theory for photon beams.

References

Burlin (1966), “A General Theory of Cavity Ionization”, British Journal of Radiology, 39, pp 727-734.
Kearsley (1984), “A new General Cavity Theory”, Phys. Med. Biol., 29, 10, pp1179-1187.
Ogunleye O. (1982), “Influence of Electron Path Lenght on the Evaluation of Burlin´s Cavity Theory”, British Journal of Radiology, 55, pp 588-590.
Ogunleye O. (1987), A comparison of the Burlin and Kearsley general theories with LiF TLD measurements for 10 MV x-ray, Phys. Med. Biol., 32, 7, pp 901-904.