Charge Equilibrium of Helium Ions in Helium Gas from 60 to 840 keV

Charge equilibrium fractions corresponding to the components ${\mathrm{}\left(\mathrm{He}\right)\mathrm{}}^0$, ${\mathrm{}\left(\mathrm{He}\right)\mathrm{}}^{+}$, and ${\mathrm{}\left(\mathrm{He}\right)\mathrm{}}^{++}$ of a helium beam in helium gas have been measured. Singly ionized beams of ${\mathrm{He}}^4$ and doubly ionized beams of ${\mathrm{He}}^3$ were used. Ion velocities covered the range corresponding to energies of ${\left({\mathrm{He}}^4\right)}^{+}$ ions from 60 to 840 keV. The charge-equilibrated beam was magnetically separated and charge spectra were recorded by means of a movable detector of equal sensitivity for all three charge components. In the energy interval where they overlap, namely between 60 and 200 keV, the measured equilibrium fractions are in excellent agreement with those of Barnett and Stier. No systematic discrepancy between the equilibrium fractions obtained at equal velocities with beams of the isotopes ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ was observed. The results were discussed in terms of the probabilities $M_{\mathrm{I}}$ for presence of any one of the two electrons in ${\mathrm{}\left(\mathrm{He}\right)\mathrm{}}^0$ and $M_{\mathrm{II}}$ for presence of the one electron in ${\mathrm{}\left(\mathrm{He}\right)\mathrm{}}^{+}$ as a function of the beam velocity $v$. Similarity of the curves for $M_{\mathrm{I}}$ and $M_{\mathrm{II}}$ allows for their superposition by a translation transformation on the velocity scale by a constant approximately equal to the "orbital" velocity $u_{\mathrm{I}}$ of either electron in ${\mathrm{}\left(\mathrm{He}\right)\mathrm{}}^0$ as calculated from its first ionization energy. This is in disagreement with Dmitriev's assumption that the presence probabilities $M_i$ can be described by a universal function $M\left(\frac{v}{u_i}\right)$.