On the Momentum Loss of Heavy Ions

In the calculation of the momentum loss of a heavy ion in its passage through matter, an estimate is needed of the charge of the ion as a function of its velocity. The process of capture and loss of electrons in collisions is characterized by the velocity within the ion of the electron or electrons participating. This velocity is roughly proportional to the ion velocity. The factor of proportionality is introduced as a convenient parameter $\gamma$. Two methods are used to estimate the charge of the ion: (1) It is supposed that the characteristic velocity is that of the energetically most easily removable electron, which is determined from the Thomas-Fermi model. Under this assumption $\gamma$ tends to increase with atomic number ($\gamma =1.3\mathrm{}$ for $Z=6\mathrm{}$ to $\gamma =1.8\mathrm{}$ for $Z=55\mathrm{}$). (2) It is supposed that the characteristic velocity is that of the outermost electron, which is also calculated from the Thomas-Fermi model. $\gamma$ is found to decrease with atomic number ($\gamma =0.6\mathrm{}$ for $Z=6\mathrm{}$ to $\gamma =0.35\mathrm{}$ for $Z=55\mathrm{}$). The characteristic velocity probably lies between these extremes.