Water-equivalent material

A water-equivalent material is a material whose relevant interaction with ionizing radiation approximates that of water under specified conditions. For a water phantom, the comparison concerns energy absorption and scattering in the measurement geometry. It is not a statement that the material merely has a density near that of water, or that equivalence at one energy applies at every other energy.^[ref]

For a narrow monoenergetic photon beam, the linear attenuation coefficient satisfieswhere $\rho$ is the mass density and $\mu /\rho$ the mass attenuation coefficient. Equal densities leave the mass interaction coefficients unconstrained. Predicting absorbed dose also involves how transferred energy is deposited, for which the mass energy-absorption coefficient is relevant; the attenuation of primary photons alone is not the complete scattering and deposition problem. For charged particles, the corresponding comparison also involves stopping power.

For an original toy calculation, stipulate equal densities but linear attenuation coefficients ${\mu }_w=0.05\mathrm{c}{\mathrm{m}}^{-1}$ and ${\mu }_m=0.08\mathrm{c}{\mathrm{m}}^{-1}$ at one chosen photon energy. For $t=10\mathrm{cm}$, the unscattered fractions in the Beer-Lambert law areThe substitute transmits only $e^{-0.3}\approx 0.74082$ times the unscattered intensity of the reference, despite identical density. These coefficients are stipulated model inputs, not tabulated data for real water or a named plastic. Matching even this transmission at one energy would not establish equal absorbed dose throughout a larger scattering object. Energy dependence of water equivalence is therefore part of any meaningful equivalence specification.

A focused physical comparison places the same characterized detector in reference water and in a candidate slab assembly, with controlled material thickness, irradiation geometry and detector position. Record density and composition as well as detector response over the intended radiation conditions. Slab gaps and changes in surrounding scattering material can confound the comparison; the primary IAEA discussion explicitly treats material variability and the approximate nature of plastic-to-water scaling.^[ref]