Determining partial photoemission cross sections of methane with dedicated uncertainties

Photoemission spectroscopy is used to quantitatively determine the partial cross section of the $1t_2$ and $2a_1$ subshells of methane. Photoelectron spectra are recorded using a hemispherical electron analyzer and monochromatized synchrotron radiation. The corresponding emission peaks are analyzed to calculate the partial cross sections with the associated uncertainties in a photon energy range from 16.5 to 70 eV. The presented results cover this broad energy range with corresponding uncertainties and belong to the framework of photoemission orbital tomography, aiming to bridge the experimental gap between simple single atoms and complex molecular monolayers.

Figure 1

Energy scale calibration, using Eq. (1) to fit the peaks from neon $2p$ and $2s$ for different photon energies $h\nu$, represented by markers $\blacksquare$ and $⧫$, respectively. The lines mark the fit function (1).

Figure 2

PESs of ${\mathrm{CH}}_4 2a_1$ and $1t_2$, measured at $h\nu =45$ eV. The peaks $1t_2$ and $2a_1$ show an underlying structure, assigned to vibrational modes [35, 36].

Figure 3

Normalized PESs of the ${\mathrm{CH}}_4$ peaks $2a_1$ and $1t_2$ for different photon energies $h\nu$.

Figure 4

Example of the pressure $p$ during the acquisition of the PES. The solid line gives the mean value, while the shaded area denotes the standard deviation.

Figure 5

(a) Spectrum and fit of the ${\mathrm{CH}}_4 1t_2$ peak, assessed at $h\nu =19$ eV. (b) Absolute deviation ${\mathrm{\Delta }}_C$ of the measured counts to the fit.

Figure 6

Relative spectrometer transmission function $T\left(E_{\text{kin}}\right)$ for kinetic electron energies up to 65 eV with uncertainties.

Figure 7

Angular distribution for different values of the asymmetry parameter $\beta$, presented by the solid curved line. The arrows mark the direction of the linear polarization. The scaling is such that 1 equals the PCS ${\sigma }_i\left(h\nu \right)/4\pi$. The straight lines mark angles of ${45}^{\circ }$ ($\cdots$) and $54.7^{\circ }$ (- - -).

Figure 8

Parameter $\beta$ for ${\sigma }_{1t2}$ as taken from Marr and Holmes [45] up to 30 eV ($•$) with uncertainties. Above 30 eV we extrapolate $\beta =1\pm 0.25$ (— and shaded area). The calculated values from Stener and Decleva [46] are included for comparison ($\cdots$).

Figure 9

PCS results for ${\mathrm{CH}}_4 1t_2$ ($+$) with error bars representing the expanded uncertainties $(k=2)$. Literature data from Backx and Wiel [24] ($◂$), Wiel et al. [23] ($\times$) and ${\sigma }_{\text{tot}}^{\text{lit}}$ [28] (shaded area) are shown for comparison. The data of $2a_1$ are added for photon energies $h\nu \ge 28$ eV ($•$) as the sum ${\sigma }_{1t2}+{\sigma }_{2a1}$. (a) A log-log plot of cross sections. (b) Difference $\mathrm{\Delta }\sigma$ plotted with ${\sigma }_{\text{tot}}^{\text{lit}}$ as reference.

Figure 10

PCS results for ${\mathrm{CH}}_4 2a_1$ ($•$) with expanded uncertainties $(k=2)$. Literature data from Backx and Wiel [24] ($◂$) and Wiel et al. [23] ($\times$) are shown for comparison.