Journal of Electron Spectroscopy and Related Phenomena最新文献

{"title":"Unravelling Tungsten atom ionization at high energies: A relativistic electron impact study","authors":"Munendra Jain ,&nbsp;Ghanshyam Purohit ,&nbsp;Wolfgang Quint","doi":"10.1016/j.elspec.2025.147552","DOIUrl":"10.1016/j.elspec.2025.147552","url":null,"abstract":"<div><div>The high-energy electron impact ionization of atoms is a significant phenomenon in understanding atomic behaviour, and it can provide valuable information related to electron-atom scattering. In the case of the nuclear fusion process, electron and atom scattering done at high energy can provide precious information. In the present study, we report triple differential cross-sections (TDCS) and spin asymmetry for tungsten atoms’ electron impact K shell ionization at relativistic energies regime. The relativistic distorted wave Born approximation (rDWBA) formalism has been used with the coplanar asymmetric geometrical arrangement to calculate TDCS and spin asymmetry. The TDCS and spin asymmetry have been calculated for the high incident energy from 250 keV to 700 keV, for various scattering angles <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span>, <span><math><msup><mrow><mn>5</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span>, <span><math><msup><mrow><mn>8</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span> and <span><math><mrow><mn>1</mn><msup><mrow><mn>4</mn></mrow><mrow><mi>o</mi></mrow></msup></mrow></math></span> to create consistent with findings of (e, 2e) experiments of Schule and Nakel.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"281 ","pages":"Article 147552"},"PeriodicalIF":1.8,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Theoretical investigation of the triple differential cross section in the nitrogen molecule ionization by electron and positron impact","authors":"Sana Mekhalfa ,&nbsp;Salim Houamer ,&nbsp;Abdelaziz Mansouri ,&nbsp;Imene Khiat ,&nbsp;Ayoub Tamin ,&nbsp;Claude Dal Cappello ,&nbsp;Paul-Antoine Hervieux","doi":"10.1016/j.elspec.2025.147545","DOIUrl":"10.1016/j.elspec.2025.147545","url":null,"abstract":"<div><div>Calculations of the triple differential cross section (TDCS) for positron and electron impact ionization have been performed for the inner as well as the outer orbitals of nitrogen molecule, within a model developed for molecular targets and called M3CWZ. In this model, a full Coulomb wave scheme with variable charges to describe the continuum particles is used, taking into account the post collision interaction (PCI). Experiments performed in asymmetric geometries at large and lower recoil momentum have been investigated for the outer (<span><math><mrow><mn>2</mn><msub><mrow><mi>σ</mi></mrow><mrow><mi>u</mi></mrow></msub></mrow></math></span>, <span><math><mrow><mn>1</mn><msub><mrow><mi>π</mi></mrow><mrow><mi>u</mi></mrow></msub></mrow></math></span>and<span><math><mrow><mn>3</mn><msub><mrow><mi>σ</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></math></span>) as well as the inner <span><math><mrow><mn>2</mn><msub><mrow><mi>σ</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></math></span> orbitals, comparison is then made between experimental data and theory. At intermediate impact energies (up to 700 eV), it is found that the M3CWZ model is able to predict the general trends of the TDCS for the outer orbitals at large recoil momentum when the residual ion plays substantial role, better than other sophisticated models. For the inner <span><math><mrow><mn>2</mn><msub><mrow><mi>σ</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></math></span> orbital the large intensity of the TDCS observed in the recoil region is not correctly reproduced by the present calculations. At lower 250 eV impact energy, a moderate agreement with the data is achieved for outer <span><math><mrow><mn>3</mn><msub><mrow><mi>σ</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></math></span>orbital.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"281 ","pages":"Article 147545"},"PeriodicalIF":1.8,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Recoil effects in high energy photoemission of solids − Revisited","authors":"F. Roth ,&nbsp;D. Potorochin ,&nbsp;A. Gloskovskii ,&nbsp;C. Schlueter ,&nbsp;L. Wenthaus ,&nbsp;S. Molodtsov ,&nbsp;W. Drube ,&nbsp;W. Eberhardt","doi":"10.1016/j.elspec.2025.147544","DOIUrl":"10.1016/j.elspec.2025.147544","url":null,"abstract":"<div><div>This study systematically investigates core level recoil in photoemission from crystalline silicon (Si) and silicon carbide (4H-SiC), within the X-ray range of 2.45–9.5 keV. By examining the Si 2p, 2s, and C 1s core levels, we observe that SiC exhibits energy shifts exceeding single-atom recoil predictions, along with a lineshape change at higher photon energies attributed to being phonon-induced. In contrast, pure Si shows more modest shifts and line broadening, consistent with expected recoil effects. These observations imply that especially compound materials, such as SiC, exhibit an enhanced interplay of recoil and phonon dynamics, underscoring the necessity for refined photoemission models that accommodate these effects.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"281 ","pages":"Article 147544"},"PeriodicalIF":1.8,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relativistic theory of 2PPE","authors":"J. Braun","doi":"10.1016/j.elspec.2025.147542","DOIUrl":"10.1016/j.elspec.2025.147542","url":null,"abstract":"<div><div>Various apparative developments extended the potential of angle-resolved photoemission spectroscopy tremendously during the last decades. Modern experimental arrangements consisting of new photon sources, analyzers and detectors supply not only extremely high angle and energy resolution but also spin resolution. This provides an adequate platform to study in detail new materials like low-dimensional magnetic structures, Rashba systems, topological insulator materials or high T<span><math><msub><mrow></mrow><mrow><mi>C</mi></mrow></msub></math></span> superconductors. The interest in such systems has grown enormously not only because of their technological relevance but even more because of exciting new physics. Furthermore, the use of photon energies from few eV up to several keV makes this experimental technique a rather unique tool to investigate the electronic properties of solids and surfaces. The following article presents a recent theoretical development in the field of angle-resolved photoemission with a special emphasis on time-resolution. In detail, a theoretical frame for two-photon photoemission spectroscopy is introduced. The approach is based on a general formulation using the Keldysh formalism for the lesser Green’s function to describe the real-time evolution of the electronic degrees of freedom in the initial state after a sufficiently weak pump pulse drives the system out of equilibrium. Assuming that not only the probe but also the pump pulse is relatively weak, a perturbative approach can be formulated that allows to compute the lesser Green function explicitly for real systems in terms of the corresponding retarded and advanced Keldysh Green functions. The final state is represented by a time-reversed low-energy electron diffraction state. This so called two-photon photoemission spectroscopy is a widely used analytical tool to study non-equilibrium phenomena in solid materials. The theoretical approach presented here aims at a material-specific, realistic and quantitative description of the time-dependent spectrum based on a picture of effectively independent electrons as described by the local-density approximation in band-structure theory.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"281 ","pages":"Article 147542"},"PeriodicalIF":1.8,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating the stability and conductivity of Li₂CuO₂ for high-temperature LIB applications","authors":"Osman Murat Ozkendir","doi":"10.1016/j.elspec.2025.147543","DOIUrl":"10.1016/j.elspec.2025.147543","url":null,"abstract":"<div><div>The development of high-performance cathode materials for lithium-ion batteries (LIBs) is crucial for advancing energy storage technologies. The electronic and thermal properties of lithium cuprate (Li₂CuO₂, LCO), a promising cathode material with mixed ionic and electronic conductivity were investigated. Using a two-step computational approach, Density Functional Theory (DFT) was employ to calculate the band structure and density of states (DOS) at room temperature, revealing a direct bandgap of 1.61 eV and semiconductor-like behavior. Additionally, X-ray Absorption Fine Structure (XAFS) spectroscopy utilized to probe the temperature-dependent electronic and structural dynamics of LCO, ranging from 253 K to 473 K. The results demonstrate the stability of the Cu-O blocks under elevated temperatures, highlighting their resilience during charge-discharge cycles. The Debye-Waller factor (DWF) analysis further confirms the material's moderate thermal conductivity and structural integrity, making LCO a viable candidate for high-temperature LIB applications. This comprehensive study provides valuable insights into the electronic and thermal behavior of LCO, paving the way for the design of next-generation cathode materials with enhanced electrochemical performance and thermal stability.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"280 ","pages":"Article 147543"},"PeriodicalIF":1.8,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental determination of L-subshells x-ray yields and production cross sections of thick lead (Z=82) element by impact of 15–30 keV electrons","authors":"Kailash Verma ,&nbsp;Hitesh Rahangdale ,&nbsp;Kumar Ankit Upadhayay ,&nbsp;Raj Singh ,&nbsp;Bhupendra Singh ,&nbsp;Namita Yadav","doi":"10.1016/j.elspec.2025.147541","DOIUrl":"10.1016/j.elspec.2025.147541","url":null,"abstract":"<div><div>We present experimental results on the impact energy dependence of L-subshell x-ray yields and production cross sections for the thick lead target (Pb, Z = 82) under impact of 15–30 keV electrons. Results are compared with the simulation data from the Monte Carlo Penelope code with the Distorted Wave Born Approximation (DWBA) formulations. The comparison yields fairly good agreement for the L-shell x-ray yields within the experimental uncertainties. Furthermore, the present results of the intensity ratio of <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span> lines to the intensity of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> and their corresponding x-ray production cross sections are compared with available experimental and theoretical data; the agreement is found to be satisfactory. X-ray production cross sections for L-shell x-rays are derived by employing the thick target method (An et al., 2006). Furthermore, we have presented for the first time the experimental results on yield and x-ray production cross sections of the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span> line and have compared the results with the simulation data; the agreement between two results is found to be good within the error bars of the measurements.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"280 ","pages":"Article 147541"},"PeriodicalIF":1.8,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Electronic, magnetic and thermal behavior near the Invar compositions of Fe-Ni alloys","authors":"Ananya Sahoo ,&nbsp;Ayusa Aparupa Biswal ,&nbsp;S.K. Parida ,&nbsp;V.R.R. Medicherla ,&nbsp;Soumya Shephalika Behera ,&nbsp;M.N. Singh ,&nbsp;A. Sagdeo ,&nbsp;Sawani Datta ,&nbsp;Abhishek Singh ,&nbsp;Kalobaran Maiti","doi":"10.1016/j.elspec.2025.147540","DOIUrl":"10.1016/j.elspec.2025.147540","url":null,"abstract":"<div><div>The structural, magnetic and electronic properties of Fe<span><math><msub><mrow></mrow><mrow><mn>1</mn><mo>−</mo><mi>x</mi></mrow></msub></math></span>Ni<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> (<span><math><mi>x</mi></math></span> = 0.32, 0.36, 0.40, 0.50) alloys have been investigated using synchrotron based x-ray diffraction (XRD), superconducting quantum interference device (SQUID) magnetometer and the high resolution x-ray photoelectron spectroscopy (XPS) measurements. The XRD measurement was done down to 50 K temperature. The XRD studies suggest a single phase with fcc structure for <span><math><mi>x</mi></math></span> = 0.36, 0.40, and 0.50 alloys and a mixed phase for <span><math><mi>x</mi></math></span> = 0.32 alloy containing both bcc and fcc structures. The lattice parameter of the alloys exhibits a linear dependence on temperature giving rise to a temperature independent coefficient of thermal expansion (CTE). The lowest CTE is observed for <span><math><mi>x</mi></math></span> = 0.36 Invar alloy as expected while <span><math><mi>x</mi></math></span> = 0.50 alloy exhibits the highest CTE among the alloys studied. The CTE of the fcc component of mixed phase alloy is close to that of Invar alloy. The temperature dependence of magnetization of the alloys down to 2 K reveals an overall antiferromagnetic interactions within the ferromagnetic phase causing the magnetization decreasing with lowering temperature. The field cooled and zero field cooled data show larger differences for the Invar compositions; this is also manifested in the magnetic hysteresis data at 2 K and 300 K. The Fe 2<span><math><mi>p</mi></math></span> and Ni 2<span><math><mi>p</mi></math></span> core level spectra exhibit spin–orbit split features along with a satellite feature in the Ni 2<span><math><mi>p</mi></math></span> spectra. The spectral line shapes are almost similar for all the compositions studied. Interestingly, the spin–orbit splitting for Fe 3<span><math><mi>p</mi></math></span> spectra is larger than that observed for Ni 3<span><math><mi>p</mi></math></span> suggesting additional contributions due to the exchange interaction between the Fe 3<span><math><mi>p</mi></math></span> core hole with the Fe 3<span><math><mi>d</mi></math></span> moment. This suggests large magnetic moment contribution from Fe as expected. The core level and valence band spectra, and the magnetization data suggest significant role of disorder for the Invar compositions.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"280 ","pages":"Article 147540"},"PeriodicalIF":1.8,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fine structure of spectra for secondary electron excited by electron impact – Novel spectrum data analysis and application to nearly free electron metals","authors":"Satoshi Hashimoto ,&nbsp;Tsuguo Sakurada ,&nbsp;Shigeo Tanuma ,&nbsp;Keisuke Goto ,&nbsp;Takaharu Nagatomi","doi":"10.1016/j.elspec.2025.147539","DOIUrl":"10.1016/j.elspec.2025.147539","url":null,"abstract":"<div><div>In order to analyze the fine structure of the energy distribution of secondary electrons generated through the cascade process, we measured the electron spectra of NFE metals (Li, Mg, Al, Ca, Ga, In), their compounds (Al₂O₃ and GaAs) and Fe as transition metal with a CMA-type analyzer with absolute gain. We propose that the spectrum obtained by differentiating the energy spectrum in a logarithmic representation (defined as DLS) can be used to evaluate the excitation function that generates the fine structure of the secondary electron energy distribution. We found that the fine structure of the energy distribution of secondary electrons in NFE metals is mainly due to emission through a cascade process generated by the electrons from plasmon decay, which was obtained from analyses of the DLS, the excitation function, the energy distribution of secondary electrons <em>N(E)</em>, and the EELS spectra. In addition, slow Auger electrons also generate secondary electrons through the cascade process. In Al₂O₃, a fine structure of secondary electrons was generated by electrons excited to unoccupied states by inter-band transitions and inner-shell excitation. In GaAs, both contributions from plasmon decay and electrons excited to unoccupied states by inter-band transitions and inner-shell excitation were observed. Based on these findings, it is concluded that the fine structure of the energy distribution of the secondary electrons emitted in the cascade process is due to the following electrons: 1) electrons from plasmon decay, 2) slow Auger electrons, and 3) electrons excited to unoccupied states by inter-band transitions or inner-shell excitation. These fine structures are superimposed on the structure of the individual excitation by primary electrons.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"280 ","pages":"Article 147539"},"PeriodicalIF":1.8,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometry-dependent analysis of 2p3d- and 2p3s-partial fluorescence yield spectra for high-spin 3d5 systems","authors":"Saki Imada ,&nbsp;Frank M.F. de Groot","doi":"10.1016/j.elspec.2025.147538","DOIUrl":"10.1016/j.elspec.2025.147538","url":null,"abstract":"<div><div>Geometry dependences of partial fluorescence yield (PFY) spectra at the L_2,3-edge of 3d transition metals are discussed theoretically and experimentally for high-spin 3d⁵ systems in O_h and T_d point symmetries. Firstly, linear polarized light's propagation direction selection rules for a two-photon process are applied to 2p3d-PFY spectroscopy. Then, the 2p3d-PFY spectra were analyzed by comparison with spectra obtained as partial integration of 2p3d-resonant inelastic X-ray scattering (RIXS) signals, utilizing the relationship between PFY and RIXS spectroscopies: the former is an integration of yield of emitted light at each excitation energy, and the latter is a dispersion of emitted light as a function of emission energy at each excitation energy. Thus, a PFY spectrum can be divided into super PFY (sPFY) spectra using partial integrations of signals on a RIXS map, such as sPFY spectra from elastic and inelastic signals. It is suggested that the origin of the large deviation of 2p3d-PFY spectral shape in a linear-horizontal geometry from a true X-ray absorption spectrum is due to the lack of elastic signals, i.e., the lack of signals emitted when the system returns to its ground state. Contrary to a 2p3d-PFY spectrum, a 2p3s-PFY spectrum is often assumed to have a one-to-one correspondence with true XAS; however, 2p3s-PFY spectroscopy is also a two-photon process that abides by the propagation direction selection rules. We will show theoretically that 2p3s-PFY spectral shapes show a geometry dependence and offer a way to obtain a true X-ray absorption structure from a combination of 2p3s-PFY spectra in linear-vertical and linear-horizontal geometries.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"280 ","pages":"Article 147538"},"PeriodicalIF":1.8,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Attosecond dynamics of electron scattering by an absorbing layer","authors":"R.O. Kuzian ,&nbsp;E.E. Krasovskii","doi":"10.1016/j.elspec.2025.147535","DOIUrl":"10.1016/j.elspec.2025.147535","url":null,"abstract":"<div><div>Attosecond dynamics of electron reflection from a thin film is studied based on a one-dimensional jellium model. Following the Eisenbud–Wigner–Smith concept, the reflection time delay <span><math><mrow><mi>Δ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></math></span> is calculated as the energy derivative of the phase of the complex reflection amplitude <span><math><mi>r</mi></math></span>. For a purely elastic scattering by a jellium slab of a finite thickness <span><math><mi>d</mi></math></span> the transmission probability <span><math><mi>T</mi></math></span> oscillates with the momentum <span><math><mi>K</mi></math></span> in the solid with a period <span><math><mrow><mi>π</mi><mo>/</mo><mi>d</mi></mrow></math></span>, and <span><math><mrow><mi>Δ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></math></span> closely follows these oscillations. The reflection delay averaged over an energy interval grows with <span><math><mi>d</mi></math></span>, but in the limit of <span><math><mrow><mi>d</mi><mo>→</mo><mi>∞</mi></mrow></math></span> the amplitude <span><math><mi>r</mi></math></span> becomes real, so <span><math><mrow><mi>Δ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></math></span> vanishes. This picture changes substantially with the inclusion of an absorbing potential <span><math><mrow><mo>−</mo><mi>i</mi><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math></span>: As expected, for a sufficiently thick slab the reflection amplitude now tends to its asymptotic value for a semi-infinite crystal. Interestingly, for <span><math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≠</mo><mn>0</mn></mrow></math></span>, around the <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> maxima, the <span><math><mrow><mi>Δ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mtext>r</mtext></mrow></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> curve strongly deviates from <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span>, showing a narrow dip just at the <span><math><mrow><mi>Δ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mtext>r</mtext></mrow></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> maximum for <span><math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>. An analytical theory of this counterintuitive behavior is developed.</div></div>","PeriodicalId":15726,"journal":{"name":"Journal of Electron Spectroscopy and Related Phenomena","volume":"280 ","pages":"Article 147535"},"PeriodicalIF":1.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}