Excitation of atoms and molecules by highly relativistic ions

We study the cross section for inelastic collisions of atoms and small molecules under the influence of highly relativistic charged ions as they occur in storage rings and accelerators. Starting from fully time-resolved calculations of the electronic dynamics, we study a set of complementing approximations, a sudden approximation for the extremely fast collision at low impact parameter combined with time-dependent perturbation theory for the weak and slow collisions at large impact parameters. This leads eventually to a simple, yet reliable, estimate in terms of the ion-hydrogen cross section and the variance of the dipole moment for the actual system. We discuss, in particular, the systems H, He, C, N, O, Ne, ${\mathrm{H}}_2$, and ${\mathrm{N}}_2$.

Figure 1

Detailed excitation probabilities ${\eta }_{nl}$ for excitation of a hydrogen atom by a fast proton with velocity $\beta =v∕c=0.99$ at various impact parameters $b$. We show specific transitions from the $1s$ state to the various excited states $nl$ in the hydrogen atom computed in sudden approximation. The results gather in bunches of same angular momentum $l$ and different $n$. The groups are indicated by embracing arrows labeled with the corresponding $l$.

Figure 2

Total inelastic transition probability $\eta$ (dashed) and sum of excitations to bound states only (solid) for excitation of a hydrogen atom by a fast proton with velocity $\beta =v∕c=0.99$ at various impact parameters $b$.

Figure 3

Probabilities for excitation of a Ne atom by a fast proton with velocity $\beta =v∕c=0.99$ at various impact parameters $b$. We show the probability for excitations from the valence $2s$-$2p$ shell (dashed) and from the deep lying $1s$-core state (solid).

Figure 4

Total inelastic transition probabilities for transitions from the ground state of different atoms (as indicated) by a fast proton with velocity $\beta =v∕c=0.99$ at various impact parameters $b$ computed with the sudden approximation.

Figure 5

Total inelastic transition probability for the collision of velocity $\beta =v∕c=0.99$ with a ${\mathrm{N}}_2$ molecule as function of the impact parameter $b$. Results are shown for various orientations of the molecular axis with respect to the $z$ axis ($=$ direction of propagation of the proton). All results are obtained with the sudden approximation.

Figure 6

Total inelastic transition probability for the proton-hydrogen collision with proton velocity $\beta =v∕c=0.99$ as a function of the impact parameter $b$. Results from various approximations are compared as indicated. The probabilities are scaled by $b^2$ to display them relative to the asymptotics of the sudden approximation.

Figure 7

Total inelastic transition cross sections for the collision of fast protons with atoms and molecules. The cross sections are shown as function of ionic $\gamma$ for a selection of typical atoms and molecules.

Figure 8

Total inelastic transition cross sections as in Fig. 7 but scaled by the relative dipole variances ${\Delta }^2{D}_{\mathrm{H}}∕{\Delta }^2{D}_X$, where H stands for hydrogen and $X$ for the actual atom or molecule.

Figure 9

The angular averaged dipole sum $G$ over the rms radius of the electron density for different systems under study.