To obtain ${\ensuremath{\gamma}}_{e}$ for ${\mathrm{H}}_{2}^{+}$ ion bombardment on metal targets, an expression for the secondary electron emission coefficient by fast positive ion bombardment is obtained after adopting a method of calculation similar to that employed by Sternglass. It is shown that the experimental values of ${\ensuremath{\gamma}}_{e}$ for ${\mathrm{H}}_{2}^{+}$ ion bombardment agree with the calculated values provided it is assumed that inside the target a hydrogen molecular ion is dissociated into a proton and a hydrogen atom, each having half the energy of the molecular ion. The dissociation cross section of a hydrogen molecular ion inside the target may be given by ${\ensuremath{\sigma}}_{d}=K\ensuremath{\surd}T$, where $K=1.2$, ${\ensuremath{\sigma}}_{d}$ is expressed in units of ${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$, and $T$ is in Mev.The secondary electron emission coefficient ${\ensuremath{\gamma}}_{e}$ for high-energy hydrogen atom bombardment on a metal surface is also calculated and compared with experimental data. In the calculation, a neutral beam of hydrogen atoms is treated inside the target as composed of protons and electrons in addition to hydrogen atoms. Each of these three kinds of particles are capable of producing internal secondaries.A fair agreement between the calculated and observed values of ${\ensuremath{\gamma}}_{e}$ for ${\mathrm{H}}^{+}$, ${\mathrm{D}}^{+}$, ${\mathrm{H}}_{2}^{+}$, and ${\mathrm{H}}^{0}$ bombardments has been obtained.
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