Shakeoff Ionization near the Coulomb Barrier Energy

We measure the projectile $K$ x-ray spectra as a function of the beam energies around the Coulomb barrier in different collision systems. The energy is scanned in small steps around the barrier aiming to explore the nuclear effects on the elastically scattered projectile ions. The variation of the projectile x-ray energy with the ion-beam energies exhibits an unusual increase in between the interaction barrier and fusion barrier energies. This additional contribution to the projectile ionization can be attributed to the shakeoff of outer-shell electrons of the projectile ions due to the sudden nuclear recoil ($\sim {10}^{-21}\sec$) caused by the attractive nuclear potential, which gets switched on near the interaction barrier energy. In the sudden approximation limit, the theoretical shakeoff probability calculation due to the nuclear recoil explains the observed data well. In addition to its fundamental interest, such processes can play a significant role in dark matter detection through the possible mechanism of x-ray emissions, where the weakly interacting massive particle-nucleus elastic scattering can lead to the nuclear-recoil-induced inner-shell vacancy creations. Furthermore, the present work may provide new prospects for atomic physics research at barrier energies as well as provide a novel technique to perform barrier distribution studies for two-body systems.

Figure 1

Systematics of the analysis for a typical case of the 120 MeV ${}^{58}{\mathrm{Ni}}^{12+}$ beam on $80\mu \mathrm{g}/{\mathrm{cm}}^2$ ($\sim 113\mu \mathrm{g}/{\mathrm{cm}}^2$ at 45°) carbon foil: (a) x-ray spectrum showing the projectile x rays corresponding to $K_{\alpha }$, $K_{\beta }$, $K_{\gamma }$, and $K$-REC peaks. The Fe $K_{\alpha }$ and $K_{\beta }$ peaks due to the beam halo hitting the target frame are also shown. A schematic of the setup is shown in the inset. (b) Deconvolution of the $K_{\alpha }$ x-ray peak corresponding to different charge states (H-like to F-like). (c) CSD calculated using Eq. (1). The raw x-ray spectra, observed at different beam energies are shown in Supplemental Material [14].

Figure 2

Variation of projectile characteristic x-ray energy versus beam energy: (a) ${}^{56}\mathrm{Fe}$ $K_{\alpha }$, (a’) ${}^{56}\mathrm{Fe}$ $K_{\beta }$, (b) ${}^{58}\mathrm{Ni}$ $K_{\alpha }$, (b’) ${}^{58}\mathrm{Ni}$ $K_{\beta }$, (c) ${}^{63}\mathrm{Cu}$ $K_{\alpha }$, and (c’) ${}^{63}\mathrm{Cu}$ $K_{\beta }$. Error bars are tiny and smeared in the symbol size except the ${}^{63}\mathrm{Cu}$ $K_{\beta }$ curve. All solid lines are to guide the eye only. The dash-dot vertical lines represent the theoretical interaction barrier ($E_b^{\text{theor}}$) and theoretical fusion barrier ($E_f^{\text{theor}}$) of the corresponding systems [15], whereas the solid vertical line corresponds to the measured interaction barrier ($E_b^{\exp }$). The values of $E_f^{\text{theor}}$, $E_b^{\text{theor}}$, and $E_b^{\exp }$ for each system are given in Table 1. The distance of closest approach versus beam energy for the systems (a”) ${}^{56}\mathrm{Fe}$ on ${}^{12}\mathrm{C}$, (b”) ${}^{58}\mathrm{Ni}$ on ${}^{12}\mathrm{C}$, and (c”) ${}^{63}\mathrm{Cu}$ on ${}^{12}\mathrm{C}$ are also shown.

Figure 3

Variation of mean charge state versus beam energy: (a) ${}^{56}\mathrm{Fe}$, (b) ${}^{58}\mathrm{Ni}$, and (c) ${}^{63}\mathrm{Cu}$ beam on the carbon foil. Solid lines are to guide the eye only. Uncertainties are almost covered within the symbol size. See the text for other details.