= 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>.<Absorbed Dose Determination in External Beam Radiotherapy by the International Atomic Energy Agency (2000)>[§4.2.3, printed pp. 39–40, absorption and scattering properties and water substitutes]{ref}
For a narrow monoenergetic <photon> beam, the <linear attenuation coefficient> satisfies
$$
\mu(E)=\rho\left(\frac{\mu}{\rho}\right)(E),
$$
where $\rho$ 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 $\mu_w=0.05\,\mathrm{cm^{-1}}$ and $\mu_m=0.08\,\mathrm{cm^{-1}}$ at one chosen <photon> energy. For $t=10\,\mathrm{cm}$, the unscattered fractions in the <Beer-Lambert law> are
$$
\frac{I_w}{I_0}=e^{-\mu_wt}=e^{-0.5}\approx0.60653,\qquad
\frac{I_m}{I_0}=e^{-\mu_mt}=e^{-0.8}\approx0.44933.
$$
The substitute transmits only $e^{-0.3}\approx0.74082$ 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.<Absorbed Dose Determination in External Beam Radiotherapy by the International Atomic Energy Agency (2000)>[§4.2.3, printed pp. 39–40, batch density, slab thickness and air gaps]{ref}
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