The Strange Relationship between the Momentum of a Photon Emitted from an Electron and the Momentum Acquired by the Electron

In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in the state where n=0has zero rest mass energy. However, a hydrogen atom has an energy level even lower than the n=0state. This is hard to accept from the standpoint of common sense. Thus, the author has previously pointed out that an electron at the energy level where n=0has zero energy because the positive energy mec2and negative energy −mec2cancel each other out. This paper elucidates the strange relationship between the momentum of a photon emitted when a hydrogen atom is formed by an electron with such characteristics, and the momentum acquired by the electron.

Electron Momentum Spectroscopy Investigation on Electronic Structure of Iso-dichloroethylene Valence Shell

Here an electron momentum spectroscopy study on the electronic structure of valence shell of iso-dichloroethylene molecule is reported. The experiment is carried out with a binary (e, 2e) spectrometer at incident electron energy of 1200 eV, employing noncoplanar symmetric arrangement. The binding energy spectra and electron momentum distributions (EMDs) of iso-dichloroethylene valence shell have been obtained. Theoretical EMDs are predicted with both Hartree-Fock and density functional theory methods, generally indicating good agreements with the measurement results. The interference effect is observed to significantly influence the EMDs of 2a2 and 5b2 Cl lone-pair orbitals.

Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

Electron Momentum Spectroscopy of Outer Valence Orbitals of 2-Fluoroethanol

The binding energy spectra and electron momentum distributions for the outer valence molecular orbitals of gaseous 2-fluoroethanol have been measured by the non-coplanar asym- metric （e, 2e） spectrometer at impact energy of 2.5 keV plus binding energy. The quantitative calculations of the ionization energies and the relevant molecular orbitals have been carried out by using the outer-valence Green＇s function method and the density functional theory with B3LYP hybrid functional. The observed ionization bands in binding energy spectra, as well as the previous photoelectron spectrum which was not assigned, have been assigned for the first time through the comparison between experiment and theory. In general, the the- oretical electron momentum distributions calculated by B3LYP method with aug-cc-pVTZ basis set are in line with the experimental ones when taking into account the Boltzmann- weighted thermo-statistical abundances of five conformers of 2-fluoroethanol.

Electron Momentum Spectroscopy of Valence Orbitals of n-Propyl Iodide： Spin-Orbit Coupling Effect and Intramolecular Orbital Interaction

The binding energy spectrum and electron momentum distributions for the outer valence orbitals of n-propyl iodide molecule have been measured using the electron momentum spectrometer employing non-coplanar asymmetric geometry at impact energy of 2.5 keV plus binding energy. The ionization bands have been assigned in detail via the high accuracy SACCI general-R method calculation and the experimental momentum profiles are compared with the theoretical ones calculated by Hartree-Fock and B3LYP/aug-cc-pVTZ（C,H）6-311G？？（I）. The spin-orbit coupling effect and intramolecular orbital interaction have been analyzed for the outermost two bands, which are assigned to the iodine 5p lone pairs, using NBO method and non-relativistic as well as relativistic calculations. It is found that both of the interactions will lead to the observed differences in electron momentum distributions. The experimental results agree with the relativistic theoretical momentum profiles, indicating that the spin-orbit coupling effect dominates in n-propyl iodide molecule.

Improvements on the third generation of electron momentum spectrometer

The significant modifications to our recently constructed electron momentum spectrometer have been implemented. Compared with our previous report, the energy and the angle resolutions are significantly improved and reach △E = 0.45 eV, △θ = ±0.53° and △φ = ±0.84°, respectively. Moreover, the details of data reduction and the relation between azimuthal angle range and the sensitivity are discussed.

Electron Momentum Spectroscopy of Ethanethiol Complete Valence Shell

The binding energy spectra and electron momentum distributions for the complete valence orbitals of ethanethiol were measured for the first time by binary （e, 2e） electron momentum spectroscopy employing non-coplanar symmetric kinematics at an impact energy of 1200 eV plus binding energy. The experimental results are generally consistent with the theoretical calculations using density functional theory and Hartree-Fock methods with various basis sets. A possible satellite line at 17.8 eV in binding energy spectrum was observed and studied by electron momentum spectroscopy.

Experimental and calculated momentum densities for the complete valence orbitals of the antimicrobial agent diacetyl

The first electronic structural study of the complete valence shell binding energy spectra of the antimicrobial agent diacetyl, encompassing both the outer and inner valence regions, is reported. The binding energy spectra as well as the individual orbital momentum profiles have been measured by using a high resolution （e, 2e） electron momentum spectrometer （EMS） at an impact energy of 1200eV plus the binding energy, and using symmetric noncoplanar kinematics. The experimental orbital electron momentum profiles are compared with self-consistent field （SCF） theoretical profiles calculated using the Hartree-Fock approximation and Density Functional theory predictions in the target Kohn-Sham approximation which includes some treatment of correlation via the exchange and correlation potentials with a range of basis sets. The pole strengths of the main ionization peaks from the inner valence orbitals are estimated.

Electron Momentum Distributions for 4a1 Orbitals of CFxCl4-x in Low Momentum Region： a Possible Evidence of Molecular Geometry Distortion

Electron momentum distributions for 4a1 orbitals of serial freon molecules CFaC1, CF2Cl2, and CFCl3 （CFxC14-x, x=1-3） have been reanalyzed due to the severe discrepancies between theory and experiment in low momentum region. The tentative calculations using equilibrium geometries of molecular ions have exhibited a great improvement in agreement with the experimental data, which suggests that the molecular geometry distortion may be responsible for the observed high intensities at p〈0.5 a.u.. Further analyses show that the severe discrepancies at low momentum region mainly arise from the influence of molecular geometry distortion on C-Cl bonding electron density distributions.

High Resolution Electron Momentum Spectroscopy Study on Ethanol： Orbital Electron Momentum Distributions for Individual Conformers

The outer-valence binding energy spectra of ethanol in the energy range of 9-21 eV are mea- sured by a high-resolution electron momentum spectrometer at an impact energy of 2.5 keV plus the binding energy. The electron momentum distributions for the ionization peaks cor- responding to the outer-valence orbitals are obtained by deconvoluting a series of azimuthal angular correlated binding energy spectra. Comparison is made with the theoretical calcu- lations for two conformers, trans and gauche, coexisting in the gas phase of ethanol at the level of B3LYP density functional theory with aug-cc-pVTZ basis sets. It is found that the measured electron momentum distributions for the peaks at 14.5 and 15.2 eV are in good agreement with the theoretical electron momentum distributions for the molecular orbitals of individual conformers （i.e., 8a＇ of trans and 9a of gauche）, but not in accordance with the thermally averaged ones. It demonstrates that the high-resolution electron momentum spectrometer, by inspecting the molecular electronic structure, is a promising technique to identify different conformers in a mixed sample.

Electron Momentum Spectroscopy of Valence Orbitals of Cyclopentene:Nuclear Dynamics and Distorted Wave Effect

We report a measurement of electron momentum distributions of valence orbitals of cyclopentene employing symmetric noncoplanar(e,2e)kinematics at impact energies of 1200 and 1600 eV plus the binding energy.Experimental momentum profiles for individual ionization bands are obtained and compared with theoretical calculations considering nuclear dynamics by harmonic analytical quantum mechanical and thermal sampling molecular dynamics approaches.The results demonstrate that molecular vibrational motions including ring-puckering of this flexible cyclic molecule have obvious influences on the electron momentum profiles for the outer valence orbitals,especially in the low momentum region.Forπ^(*)-like molecular orbitals 3a′′,2a′′,and 3a′,the impact-energy dependence of the experimental momentum profiles indicates a distorted wave effect.

Electron momentum spectroscopy of NF_3

The electronic structure of nitrogen trifluoride was investigated by combining the high-resolution electron momentum spectroscopy with the high-level calculations. The experimental binding energy spectra and the momentum distributions of each orbital were compared with the results of Hartree-Fock, density functional theory （DFT）, and symmetry-adapted- cluster configuration-interaction （SAC-CI） methods. SAC-CI and DFT-B3LYP with the aug-cc-pVTZ basis set can well reproduce the binding energy spectra and the observed momentum distributions of the valence orbitals except 1 a2 and 4e orbitals. It was found that the calculated momentum distributions using DFT-B3LYP are even better than those using the high-level SAC-CI method.

Electron Momentum Spectroscopy Study on Inner Orbitals of Methyl iodide

The binding energy spectrum and electron momentum profiles of the inner orbitals of methyl iodide have been measured using an electron momentum spectrometer at the impact energy of 1200 e V plus binding energy.Two peaks in the binding energy spectrum,arising from the spin-orbit splitting,are observed and the corresponding electron momentum profiles are obtained.Relativistic density functional calculations are performed to elucidate the experimental electron momentum profiles of two spin-orbit splitting components,showing agreement with each other except for the intensity in low momentum region.The measured high intensity in the low momentum region can be further explained by the distorted wave calculation.

Investigation of outer valence orbital of CF2Cl2 by a new type of electron momentum spectrometer

Electronic states of CF2Cl2 （dichlorodifluoromethane, Freon 12） have been studied using a new type of electron momentum spectrometer with a very high efficiency at an impact energy of 1200 eV plus binding energy. The experimental electron momentum profiles are compared with the density functional theory （DFT） and Hartree-Fock （HF） calculations. The relationship between orbital assignments in different coordinate systems is discussed. A new method of difference analysis based on the new type of electron momentum spectrometer is used to clarify the ambiguities regarding the orbital ordering.

Assessment of delocalized and localized molecular orbitals through electron momentum spectroscopy

Recently, there was a hot controversy about the concept of localized orbitals, which was triggered by Grushow＇s work titled ＂Is it time to retire the hybrid atomic orbital？＂ [J. Chem. Educ. 88, 860 （2011）]. To clarify the issue, we assess the delocalized and localized molecular orbitals from an experimental view using electron momentum spectroscopy. The delocalized and localized molecular orbitals based on various theoretical models for CH4, NH3, and H20 are compared with the experimental momentum distributions. Our results show that the delocalized molecular orbitals rather than the localized ones can give a direct interpretation of the experimental （e, 2e） results.

Valence orbitals of W(CO)_6 using electron momentum spectroscopy

The binding energy spectra and the momentum distributions of the outer valence orbitals of W（CO）6 have been studied by using electron momentum spectroscopy as well as non-relativistic, scalar relativistic and spin-orbital relativistic DFT-B3LYP calculations. The experimental momentum profiles of the outer valence orbitals obtained with the impact energies of 1200 eV and 2400 eV were compared with various theoretical calculation results. The relativistic calculations could provide better descriptions for the experimental momentum distributions than the non-relativistic ones. Moreover, a new ordering of orbitals 10tlu, 3t2g, and 7eg, i.e., 10t_lu 〈 3t_2g 〈7e_g 〈10a_lg, is established in this work.

Relativistic and distorted wave effects on Xe 4d electron momentum distributions

The relativistic and distorted wave effects are investigated for the electron momentum distributions of Xe 4d electrons.The theoretical results show good agreements with the experimental data measured previously with electron momentum spectroscopy. The distorted wave effect and the relativistic effect are found to play important roles in the low and high momentum regions, respectively.

Time Intervals of the Energy Emission in Quantum Systems Obtained from the Conservation Rule of the Electron Momentum

The paper presents a non-probabilistic approach to the time interval associated with the energy emission produced by the electron transition in a quantum system. The calculations were performed for the hydrogen atom and the electron particle in a one-dimensional potential box. In both cases, the rule of conservation of the electron momentum has been applied. The results, limited to the time intervals of transitions between two neighbouring quantum energy levels, occur to be much similar to those obtained earlier with the aid of the Joule-Lenz energy emission theory.

A New Theory on Electron Wave-Particle Duality

A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.