Average energy expended per ion pair in liquid argon

The measurement of the $W$ value, the average energy expended per ion pair, in liquid argon for internal conversion electrons emitted from ${}_{}{}^{207}{}_{}{}^{}\mathrm{Bi}$, is carried out by the electron-pulse method. Comparing with the $W$ value (26.09 eV) for $\alpha$ particles in a gas mixture of argon (95%) and methane (5%), the $W$ value in liquid argon is determined to be ${23.6}_{-0.3\mathrm{}}^{+0.5\mathrm{}}$ eV. This value is clearly smaller than that in gaseous argon (26.4 eV). Such a reduction of $W$ value in liquid argon can be explained by assuming the existence of the conduction band in liquid argon as in solid argon. Under this assumption, the $W$ value in liquid argon is estimated by applying the energy-balance method, which was used for the rare gases by Platzman. The calculated value thus obtained is in good agreement with the experimental result. Following the same method, the $W$ values for liquid krypton and liquid xenon are also estimated.