Experimental and theoretical study of the elastic-electron–indium-atom scattering in the intermediate energy range

The results of experimental and theoretical studies on elastic-electron scattering by indium atom are presented. The measurements are performed at incident electron energies of $E_0=10$, 20, 40, 60, 80, and 100 eV within the scattering angles ranging from $10°$ to $150°$. Theoretical calculations have been carried out using both complex and real optical potentials and cover the energy range up to $E_0=350\text{eV}$. We report on relative differential cross sections (DCSs), integral $\left({\sigma }_{\text{el}}\right)$, momentum-transfer $\left({\sigma }_m\right)$, and viscosity $\left({\sigma }_v\right)$ cross sections for elastic-electron scattering. The energy dependence of the angular positions of DCS minima is also determined. Two data sets were calculated, with and withoutt an absorption potential being compared to the experimental results.

Figure 1

(Color online) (a) Radial electron density $4\pi r^2\rho \left(r\right)/N$ in indium atom reduced to electron number $N=49$. The solid line is the calculation with $\rho \left(r\right)$ from Eq. (A1) and the dashed line is $\rho \left(r\right)$ taken from Ref. [21] [Eq. (12)]. (b) Energy dependence of parameters $W_3\left(E\right)$ for absorption potential $V{A}_3\left(r,E\right)$. (c) Energy dependence of parameters $\beta \left(E\right)$ for absorption potential $V{A}_3\left(r,E\right)$.

Figure 2

(Color online) Differential elastic-electron–indium-atom scattering cross sections (in units of ${10}^{-20}{\text{m}}^2{\text{sr}}^{–1}$) at (a) 10 eV, (b) 20 eV, (c) 30 eV, and (d) 40 eV. The dashed line shows the results obtained by SEPSo theory (without absorption). The solid line shows the results obtained by the SEPASo theory (Eq. (1) with absorption potential $V{A}_3$ [Eq. (4)]). The dotted line at 20 eV shows DCSs calculated by the SEPSo theory with $\rho \left(r\right)$ from [21]. The dash-dotted line at 40 eV shows the results obtained by the SEPASo with potential $V{A}_2$ [Eq. (3)]. Circles with error bars represent the experimental results normalized at $20°$ to the SEPASo calculation (with $V{A}_3$).

Figure 3

(Color online) Differential elastic-electron–indium-atom scattering cross sections (in units of ${10}^{-20}{\text{m}}^2{\text{sr}}^{–1}$) at (a) 60 eV, (b) 80 eV, (c) 100 eV impact energies. The dashed line shows the results obtained by SEPSo theory (without absorption). The results of SEPASo theory [with absorption, Eq. (1)] are represented with potentials $V{A}_1$ [Eq. (3)], $V{A}_2$ [Eq. (3)], and $V{A}_3$ [Eq. (4)]. The dotted line, dash-dotted line, and the solid line denotes, respectively, $V{A}_1$, $V{A}_2$, and $V{A}_3$ potentials of the SEPASo theory. Circles with error bars represent the experimental results normalized at $20°$ to the SEPASo calculation (with $V{A}_3$). The results in (d) are represented by SEPASo theory only. The dash-dot-dotted (red), short-dashed (blue), short-dotted (green), and short-dash-dotted (black) lines denote, respectively, 150 eV, 200 eV, 250 eV, and 300 eV impact energies.

Figure 4

(Color online) Energy dependence of angular positions of minima in the differential elastic-electron–indium-atom cross sections. The dashed and solid lines show the results obtained by SEPSo and SEPASo theories, respectively. The stars and open triangles are critical minima calculated without and with absorption, respectively. The down triangles, rectangles, and circles are the first, second, and third experimentally obtained minima, respectively.

Figure 5

(Color online) Energy dependence of differential cross sections (in units of ${10}^{-20}{\text{m}}^2{\text{sr}}^{–1}$) for the elastic-electron scattering by the indium atom at fixed angle (a) $80°$, (b) $100°$, (c) $110°$, and (d) $140°$. Notations are the same as for Fig. 3.

Figure 6

(Color online) Integral elastic ${\sigma }_{\text{el}}$ (a), momentum-transfer ${\sigma }_m$ (b), and viscosity ${\sigma }_v$ (c) cross sections (in units of ${10}^{-20}{\text{m}}^2$) for elastic-electron scattering by indium atoms. Notations are the same as for Fig. 3.