Populations of2pand3pterms in hydrogen excited byH+,H2+, andH3+ions passing through thin carbon foils

Relative beam-foil populations of the $2p$ term in hydrogen have been measured as a function of the proton energy ($0.015\lesssim E\lesssim 1.10$ MeV). For $E\gtrsim 0.1$ MeV, these populations are found to be proportional to the equilibrium neutral fractions of protons emerging from a carbon foil. At lower energies ($E<\mathrm{}0.1\mathrm{}$ MeV), the behavior of the excitation function of the $2p$ term is compatible with a decrease of the ratio of the $2p$ population to the ground-state population with respect to that ratio at higher energies. The first precise measurements of the dependence on the projectile energy ($0.1<E<\mathrm{}1.8\mathrm{}$ MeV) of the population of the $2p$ term excited by the passage of $\mathrm{H}_2^{}{}_{}{}^{+}$ and $\mathrm{H}_3^{}{}_{}{}^{+}$ ions through carbon foils of various thicknesses (2.5-22 μg/${\mathrm{cm}}^2$) are reported. Only the long-dwell-time region ($t\gtrsim 1.5$ fs) is considered in this work. The variation of $R=\frac{I^{\mathrm{molec}}}{I^{\mathrm{atom}}}$ ($I^{\mathrm{molec}}$ and $I^{\mathrm{atom}}$ are the $\mathrm{L}\mathrm{y}-\alpha$ intensities per incident proton observed with molecular and atomic projectiles of the same velocity, respectively) with the projectile energy per nucleon ($\frac{E}{M}$) and the thickness ($T$) of the foil is well described by the following relation: $R=R_{\infty }[1-C\exp (\frac{-kE}{M}\left)\right]$, where $R_{\infty }$, $C$, and $k$ are parameters depending only on $T$, and on the number of protons in the cluster. A qualitative explanation of the $R\left(\frac{E}{M,T}\right)$ behavior is proposed. Values of $R$ have also been measured for $\mathrm{L}\mathrm{y}-\beta$ radiation and are found to be significantly smaller than those obtained for $\mathrm{L}\mathrm{y}-\alpha$ radiation, for foils of thickness $T\lesssim 6$ μg/${\mathrm{cm}}^2$.