## 1 Introduction
\[Y_{\text{FD}}=\alpha A(E_{\text{P}}-\phi)^{2}/2k_{\text{B}}{}^{2}, \tag{4}\]  
where \(Y_{\text{FD}}\) is the quantum yield, \(E_{\text{P}}\) is the incident photon energy, and \(\phi\) is the photothreshold (photoelectric work function). Here, it should be noted that, previously, we examined the ratio of the magnitude of \(\pi^{2}/6\) (\(=1.64\)) to that of \(x^{2}/2\) in Equation (3) at the present experimental condition and verified that the ratio is small, reaching a conclusion that the approximate Equation (4) can be used [7]. It is seen that the plot of the square root of \(Y_{\text{FD}}\) against \(E_{\text{P}}\) in Equation (4) falls on a straight line, giving the values of both \((\alpha A/2k_{\text{B}}{}^{2})^{1/2}\) and \(\phi\). In fact, in the work, the values of \(\alpha A\) were obtained by fitting the PE data of the electron emission intensity, represented by the unit of counts\(\cdot\)min\({}^{-1}\), as a function of \(E_{\text{P}}\) to Equation (4). Typical plots of the PE data against \(E_{\text{P}}\) are presented in Figure 1 in Reference [7]. The PE experiments and results for the wavelength scan were summarized as follows [7]: (1) the wavelength was scanned in the 300-200 nm range at 25, 200, and 339 \({}^{\circ}\)C; (2) using the electron emission intensity, from which PE quantum yields can be estimated, as a function of wavelength of incident light, the values of electron photoemission probability, \(\alpha A\), and photothreshold, \(\phi\), were determined. Both \(\alpha A\) and \(\phi\) values increased with increasing temperature. This means that the factor governing the increase of PE with temperature is \(\alpha A\), but not \(\phi\); (3) in addition, the total number of emitted electrons during the wavelength scan, \(N_{\text{T}}\), and the emission intensity at a wavelength of 210 nm, \(I_{210}\), during the wavelength scan were obtained; (4) from the Arrhenius plots of the logarithm of \(\alpha A\), \(N_{\text{T}}\), and \(I_{210}\) values against the reciprocal of the above three temperatures in Kelvin, the activation energies \(\Delta E_{\alpha A}\)\(\Delta E_{\rm NT}\), and \(\Delta E_{210}\) were estimated. It was found that the values of \(\Delta E_{\rm\alpha A}\), \(\Delta E_{\rm NT}\), and \(\Delta E_{210}\) were almost independent of the environments. The purpose of the present PE study was to more quantitatively analyze the dependence of PE characteristics for scratched iron surfaces on scratching environments, particularly the surface oxygen, temperature, and photon energy. Firstly, we describe the dependence of XPS spectra of Fe 2\(p\), Fe 3\(p\), O 1s, and C 1s at three temperatures of 25, 200, and 339 \({}^{\circ}\)C for scratched iron samples on the scratching environments. The total number of the electrons counted in the XPS measurements of these spectra, called XPS intensity, was used as one of the XPS characteristics to feature the environments. Furthermore, the XPS intensity of oxygen components obtained from the resolution of O 1s spectrum was used as another feature of the XPS characteristics. Then, the activation energies were obtained from Arrhenius plots of the XPS characteristics such as the XPS intensity and the maximum peak intensity of the Fe 2\(p\), Fe 3\(p\), and O 1\(s\) spectra. Secondly, the relationship of PE characteristics during Up1 and Up2 temperature scans, that is, the total count of electrons emitted during Up1 and Up2 scans, \(N_{\rm Up1}\) and \(N_{\rm Up2}\), and the activation energies, \(\Delta E_{\rm aUp1}\) and \(\Delta E_{\rm aUp2}\), with the environments was examined. In addition, the relationship between the PE characteristics, \(\Delta E_{\rm aUp1}\) and \(N_{\rm Up1}\) and \(\Delta E_{\rm aUp2}\) and \(N_{\rm Up2}\), was described. Thirdly, the dependence of PE characteristics obtained from the light wavelength scan at the above three temperatures on the environments was examined.