Vicinage effect for hydrogen clusters in Si3N4and SiO2

Abstract

We have measured the evolution with depth $z$ of the vicinage effect and Coulomb explosion for H${}_{2}{}^{+}$ and H${}_{3}{}^{+}$ molecular ions traversing thick, uniform amorphous targets of Si${}_{3}$N${}_{4}$ and SiO${}_{2}$. High depth resolution is achieved by scanning the energy per nucleus of the incoming molecules ${E}_{b}$ around the energy ${E}_{R}$ corresponding to narrow resonances in the cross sections of ${}^{18}$O${(p,\ensuremath{\alpha})}^{15}$N at 151 keV and in ${}^{15}$N${(p,\ensuremath{\alpha}\ensuremath{\gamma})}^{12}$C at 429 keV. The corresponding reaction yield $Y({E}_{b})$ is, to first order, inversely proportional to the stopping force ${S}_{\mathrm{mol}}$ on the molecular fragments, giving a direct image of the evolution of the vicinage effect and Coulomb explosion with $z$. At the target surface, the vicinage effect enhances the stopping force on the molecules by a factor $\ensuremath{\chi}>1$. As they penetrate the matter, the distance between the molecule nuclei increases, as a consequence of Coulomb explosion and multiple scattering lateral displacement, and the vicinage effect decreases with depth $z$. The experiment yields information on the screened Coulomb repulsive potential via the repulsion velocity ${V}^{\mathrm{lim}}$ observed at large $z$, where the distances ${R}_{ij}$ between the molecule nuclei are large compared to the adiabatic cutoff ${R}_{\mathrm{ad}}$ (no vicinage effect). We show that the first order view, that $Y(Eb)$ $\ensuremath{\propto}{S}_{\mathrm{mol}}^{\ensuremath{-}1}$, is profoundly modified by the energy fluctuations induced by the Coulomb explosion and lateral multiple scattering. Our observations are satisfactorily reproduced when modeled using a dynamic screening radius ${r}_{s}$ in the range ${R}_{\mathrm{ad}}$ (for H${}_{3}{}^{+}$) to $2{R}_{\mathrm{ad}}$ (for H${}_{2}{}^{+}$) for the Coulomb explosion and the evolution with ${R}_{ij}$ of $\ensuremath{\chi}$ given by the dielectric model for the interaction of the exploding molecules with the target electron gas.