Energy dependence of W values for protons in hydrogen

The mean energy $W$ required to produce an ion pair in molecular hydrogen has been obtained for protons in the energy range between 1 MeV and 4.5 MeV. The W values were derived from the existing experimental data on elastic {\it $\pi^-$p} scattering at the beam energy of 40 GeV. In the experiment, the ionization chamber IKAR filled with hydrogen at a pressure of 10 at served simultaneously as a gas target and a detector for recoil protons. For selected events of elastic scattering, the ionization yield produced by recoil protons was measured in IKAR, while the energy was determined kinematically through the scattering angles of the incident particles measured with a system of multi-wire proportional chambers. The ionization produced by $\alpha$-particles from $\alpha$-sources of $^{234}$U deposited on the chamber electrodes was used for absolute normalization of the W values. The energy dependence of $W$ for protons in H$_2$ shows an anomalous increase of $W$ with increasing energy in the measured energy range. At the energy of 4.76 MeV, the ionization yield for alpha particles is by 2\% larger than that for protons.