 Ionization-chamber charge-loss model

An elementary ionization-chamber charge-loss model makes the inference explicit. Let a positively charged electrode and its electrometer have effective capacitance $C$, electric potential difference $U$, and enclosed gas volume $\mathcal{V}$. Assume constant $C$, a short enough interval that collection conditions remain stable, and no multiplication of charge in the gas. If ionization produces $q$ ion pairs per unit volume per unit time and a fraction $\eta$ is collected, thenHere $e$ is the elementary charge and $I_{\mathrm{leak}}$ is the parasitic electric current through imperfect insulation. Each fully collected ion pair transfers one elementary charge through the measuring circuit; counting its two opposite carriers as two transfers would introduce a factor-of-two error. The relation follows from charge conservation, rather than from a model of the incoming particle's identity.

For an invented example, take $C=2.00\mathrm{pF}$, $\mathcal{V}=2.00\mathrm{L}$, $\eta =1$, a measured fall of $6.00\mathrm{V}{\mathrm{h}}^{-1}$, and a separately determined leakage-equivalent fall of $0.60\mathrm{V}{\mathrm{h}}^{-1}$. The leakage-subtracted fall is $5.40\mathrm{V}{\mathrm{h}}^{-1}$, soThis is about $1.87\times 10^4$ collected ion pairs per second throughout the chamber, not that many primary cosmic rays. Unknown collection losses make $\eta <1$ another uncertainty; changes in capacitance would require differentiating $Q=CU$ with both factors variable.

Gas density is a separate issue. Under a fixed radiation field, fixed gas composition and approximately constant energy deposited per unit gas mass, the volume-based ionization rate scales as $q\propto \rho$. For a vented ionization chamber, the ideal gas law gives the illustrative correctionwhere $T$ is absolute temperature. A pressure-only correction presumes equal temperature. A sealed rigid chamber instead fixes gas number density as it rises: its internal pressure may change with temperature without losing gas. This does not make its insulation, electrometer calibration or collection efficiency insensitive to temperature. Nor can dividing by gas density correct arbitrary radiation from the vessel walls or changing particle energies. Those are distinct effects, not a universal normalization recipe.