= Ionization-chamber charge-loss model
{title2=$q=(Cs-I_{\rm leak})/(e\eta\mathcal V)$}
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, then
$$
Q=CU,\qquad s=-\frac{dU}{dt},\qquad Cs=e\eta\mathcal Vq+I_{\rm leak},\qquad q=\frac{Cs-I_{\rm leak}}{e\eta\mathcal V}.
$$
Here $e$ is the <elementary charge> and $I_{\rm leak}$ 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 $6.00\,\mathrm{V\,h^{-1}}$, and a separately determined leakage-equivalent fall of $0.60\,\mathrm{V\,h^{-1}}$. The leakage-subtracted fall is $5.40\,\mathrm{V\,h^{-1}}$, so
$$
I_{\rm ion}=2.00\times10^{-12}\frac{5.40}{3600}\,\mathrm A=3.00\times10^{-15}\,\mathrm A,\qquad q\approx9.36\,\mathrm{cm^{-3}\,s^{-1}}.
$$
This is about $1.87\times10^4$ 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 correction
$$
q_{\rm ref}=q\frac{\rho_{\rm ref}}{\rho}=q\frac{p_{\rm ref}}p\frac{T}{T_{\rm ref}},
$$
where $T$ 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.
Back to article page
