Electron scattering from ${\mathrm{H}}_2\mathrm{O}$: Elastic scattering

Differential cross sections for elastic electron scattering from gaseous water are reported. The measurements are obtained using the relative flow method with He as the standard gas and a thin collimating aperture source of gas instead of a conventional needle source. Differential cross sections were measured at incident energies of 1, 2, 4, 6, 8, 10, 15, 20, 30, 50, and $100\mathrm{eV}$ for scattering angles ranging from 5° to 130° and integrated over angles to obtain integral cross sections. Corresponding calculations of the differential cross section are carried out using the Schwinger multichannel method, employing extensive basis sets and considering polarization and dipole-scattering effects. Whereas excellent qualitative agreement with past measurements of differential cross sections is observed, our measurements are found to be consistently in significant quantitative disagreement with these measurements. The present calculations, on the other hand, generally agree in magnitude with previous results.

Figure 1

(Color online) (●) Scattered electron signal rate (background corrected) vs gas flow rate for He and ${\mathrm{H}}_2\mathrm{O}$ at $E_0=20\mathrm{eV}$ and $\theta =30°$ and (solid line) linear fit to data. Note that while He displays a linear dependence, ${\mathrm{H}}_2\mathrm{O}$ shows a nonlinear dependence at higher pressures. The arrow in the figure for ${\mathrm{H}}_2\mathrm{O}$ is approximately the upper limit in flow rate region of operation of our experiment.

Figure 2

(Color online) Elastic electron scattering DCSs for ${\mathrm{H}}_2\mathrm{O}$ at various $E_0$. Experiments: (●) (red), present experiment, (▲) (blue), Danjo and Nishimura [13]; (◆) (green), Shyn and Cho [15] up to $20\mathrm{eV}$ ($2.2\mathrm{eV}$ data shown at $2\mathrm{eV}$) and Shyn and Grafe [17] at $30\mathrm{eV}$; (○) (violet), Johnstone and Newell [16]; ◼ (cyan), Cho et al. [18]. Calculations: solid line (black), present; short dashed line (short green dashes), Rescigno and Lengsfield [25]; dotted line (maroon dots), Varella et al. [30, 31]; long dashed line (long magenta dashes), Faure et al., rotationally summed DCS at $E_0=4\mathrm{eV}$ [37] and $E_0=6\mathrm{eV}$ [38]; and dot-dashed line (orange chain curve), Born-dipole approximation. See text for discussion.

Figure 3

(Color online) Experimental elastic electron scattering DCSs for ${\mathrm{H}}_2\mathrm{O}$ at $E_0=1\mathrm{eV}$ and $2\mathrm{eV}$. Legend: Experiments (●) (red) ${\mathrm{H}}_2\mathrm{O}$. Present results; (○) (black) methanol and (△) ethanol [52], (◇) (black) propanol and (◻) butanol, unpublished, in progress [64]. Theory: (-⋅-⋅-) Born-dipole approximation for ${\mathrm{H}}_2\mathrm{O}$. See text for discussion.

Figure 4

(Color online) Integral elastic cross sections (ICS) and total scattering cross sections (TCS) for low-energy electron collisions with ${\mathrm{H}}_2\mathrm{O}$. ICS measurements: (●) (red), present, obtained with Born-dipole extrapolation to 0° at $20\mathrm{eV}$ and below and $4.6\mathrm{meV}$ inelasticity assumed; (▲) (blue), Danjo and Nishimura [13]; (◆) (green), Shyn and Cho [15] to $20\mathrm{eV}$ and Shyn and Grafe [17] at $30\mathrm{eV}$ and above; (○) (violet), Johnstone and Newell [16]; (◼) (cyan), Cho et al. [18]; (△) (green), recommended ICS of Itikawa and Mason [1]. ICS calculations: (solid line) (black), present, with $10\mathrm{meV}$ inelasticity assumed; (dot-dashed line) (red), Varella et al. [30]; (dashed line) (magenta), rotationally summed result of Faure et al. [37]. TCS measurements: (▽) (green), recommended values of Itikawa and Mason [1], based on data of Kimura et al. [5] and Zecca et al. [8]; (×) (orange), Szmytkowski [3].

Figure 5

(Color online) Momentum-transfer cross sections for low-energy electron collisions with ${\mathrm{H}}_2\mathrm{O}$. Experiments: (●) (red), present; (▲) (blue), Danjo and Nishimura [13]; (◆) (green), Shyn and Cho [15] to $20\mathrm{eV}$ and Shyn and Grafe [17] at $30\mathrm{eV}$ and above; (○) (violet), Johnstone and Newell [16]; (◼) (cyan), Cho et al. [18]. Calculations: (solid line) (black), present; (dot-dashed line) (red), Varella et al. [30]; (dashed line) (magenta), Faure et al. [37]. (△) (green), recommended values of Itikawa and Mason [1].

Figure 6

(Color online) Comparison of the present (●) (red) elastic scattering DCSs at $\theta =90°$ with the relative (excitation function) DCSs of Seng and Linder [11] (×), normalized to present DCSs at $E_0=8\mathrm{eV}$ (arrow); (△) (blue), later elastic scattering (excitation function) measurement taken by us at fixed $\theta$ of 90°. See text for discussion.