\begin{table} \begin{center} \begin{tabular}{lll} \hline\\ $A_{H^+} $ & $8.4 \times 10^{-11} T^{-1/2} T_3^{-0.2} (1 + T_6^{0.7})^{-1}$ & RR for H$^{+}$ \\[.5em] $A_{d} $ & $1.5 \times 10^{-10} T^{-0.6353}$ & dielectronic RR for He$^{+}$ \\[.5em] $A_{He^+} $ & $1.9 \times 10^{-3} T^{-1.5} \mathrm{e}^{-470000/T} (1 + 0.3 \mathrm{e}^{-94000/T})$ & RR for He$^{+}$ \\[.5em] $A_{He^{++}} $ & $3.36 \times 10^{-10} T^{-1/2} T_3^{-0.2} (1 + T_6^{0.7})^{-1}$ & RR for He$^{++}$ \\[.5em] \hline\\ $\Gamma_{H^{0}} $ & $5.85 \times 10^{-11} T^{1/2} \mathrm{e}^{-157809.1/T} ( 1 + T_5^{1/2})^{-1}$& CIR for H$^{0}$ \\[.5em] $\Gamma_{He^{0}} $ & $2.38 \times 10^{-11} T^{1/2} \mathrm{e}^{-285335.4.1/T} ( 1 + T_5^{1/2})^{-1}$& CIR for He$^{0}$ \\[.5em] $\Gamma_{He^{+}} $ & $5.68 \times 10^{-12} T^{1/2} \mathrm{e}^{-631515/T} ( 1 + T_5^{1/2})^{-1}$& CIR for He$^{+}$ \\[.5em] \hline \end{tabular} \end{center} \caption{Temperature ($T$) dependent recombination rates (RR) and collisional ionization rates (CIR) for Hydrogen and Helium species, adapted from \citet{katzCosmologicalSimulationsTreeSPH1996}. All rates are in units of cm$^3$ s$^{-1}$. $T_n$ is shorthand for $T / 10^n$K.} \label{tab:coll-ion-rates-katz} \end{table}