N_{p} = (\frac{4π}{3} R^{3}) n_{p}

N_{recomb} = \frac{N_{p}}{t_{r}} = \frac{(\frac{4π}{3} R^{3}) n_{p}}{t_{r}}

N_{UV} = N_{recomb} = \frac{(\frac{4π}{3} R^{3}) n_{p}}{t_{r}}

R_{eq} = (\frac{3 N_{UV}}{4πn_{p}} )^{1/3} (t_{r})^{1/3}

volume swept = σv_{e}t_{r}

volume per electron = \frac{1}{n_{e}}

σv_{e}t_{r} = \frac{1}{n_{e}}

t_{r} = \frac{1}{σv_{e}n_{e}}

v_{e} = \sqrt{\frac{3kT}{m_{e}}}

σ ≃ 5.9 × 10^{−25} m^{2}

σ_{ionize} ≃ 6 × 10^{−22} m^{2}

mfp of ionizing photon = \frac{1}{σ_{ionize} n_{H}}

R_{Stromgren} = (\frac{3 N_{UV}}{4π} )^{1/3} (\frac{1}{σv_{e}} )^{1/3} n_{p}^{−2/3}