Enhancement of electron-impact ionization induced by warm dense environments

Studies have shown significant discrepancies between the recent experiment [Berg et al., Phys. Rev. Lett. 120, 055002 (2018)] and current theoretical calculations on the electron-impact ionization cross section of ions in warm dense magnesium. Here, we present a systematic study the effects of the ionic correlations and free-electron screening on the electron-impact ionization of ions in warm dense matter. The ionic correlation and the free-electron screening effects yield additional Hermitian terms to the calculation of the ionic central-force-field potential, which significantly change the electronic structure compared with that of the isolated ion. In calculating the electron-impact ionization, we describe the impact and ionized electrons using a damped-distorted wave function, which considers the momentum relaxation of free electrons due to collisions with other free electrons and ions. We reproduce the electron-impact ionization process for ${\mathrm{Mg}}^{7+}$ in the solid-density plasma and increase the ionization cross section by one order of magnitude compared with that of the isolated ion, which excellently agrees with the experimental result of Berg et al.

Figure 1

The central-force-field potential of ${\mathrm{Mg}}^{7+}$ ion at a temperature of 75 eV. The black solid line represents the result at the boundary condition of the isolated ion, brown dot-dot-dashed, red long-dashed, orange dot-dashed, and blue short-dashed lines represent the results, including the ionic and free-electron correlation effects on the central-force-field potential at four free-electron number densities, namely, $3\times {10}^{21}$, $3\times {10}^{22}$, $3\times {10}^{23}$, and $9\times {10}^{23}{\text{cm}}^{-3}$, respectively. The dotted lines represent the positions of the ion-sphere radius, $R_{ws}={(3/4\pi n_i)}^{1/3}$, for different densities, including 15.56, 7.22, 3.35, and 2.32 in atomic units, respectively.

Figure 2

Radial wave functions of $1s$, $2p$, $3s$, and $3d$ electrons of ${\mathrm{Mg}}^{7+}$, as shown in panels (a)–(d), respectively. The black solid lines are computed at the boundary condition of the isolated ion, the other results are calculated from the central-force-field potential, as shown in Fig. 1.

Figure 3

The free-electron wave function with the energy of 75 eV are given using three models at a temperature of 75 eV and different densities of $3\times {10}^{21}$, $3\times {10}^{22}$, and $3\times {10}^{23}{\text{cm}}^{-3}$, as shown in panels (a)–(c), respectively.

Figure 4

IPD results of ${\mathrm{Mg}}^{n+}$ at the free-electron density of $3\times {10}^{23}{\text{cm}}^{-3}$ and temperature of 75 eV. The black solid line with circles is present results calculated by two-step model based on the modified FAC. The red dashed, blue dot-dashed, and orange dot-dot-dashed lines are the results of the SF, EK, and SP models, respectively.

Figure 5

Electron-impact ionization total cross-section for $e+1s2s^{2}2p^2{}^{2}P_{1/2}-1s2s^{2}2p+2e$ of ${\mathrm{Mg}}^{7+}$, occurs in solid-density magnesium plasma at a free-electron density of $3\times {10}^{23}{\text{cm}}^{-3}$ and electron temperature of 75 eV. Three methods are used to calculate the cross section, and results are compared with other theoretical calculations and experimental data of Berg et al. in Ref. [15].