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The interaction of X-ray with matter
Published in Rolf Behling, Modern Diagnostic X-Ray Sources, 2021
where Δλ denotes the wavelength shift between the incoming and the outgoing photons, λc is the Compton wavelength of the electron, θ describes the angle of scattering between the directions of the incoming and the outgoing photons, h is Planck’s number, m is the electron rest mass, and c is the speed of light.
Quantum Basics for Nanotechnology
Published in Paolo Di Sia, Mathematics and Physics for Nanotechnology, 2019
where λC is said Compton wavelength (λC = 2.43 × 10–12m) (Fig. 11.5). The shift λ of the wavelength depends on the observation angle θ, not on the initial length λ of the incident beam.
Molecular Electronics: Device-Level and System-Level Considerations
Published in Sergey Edward Lyshevski, Molecular Electronics, Circuits, and Processing Platforms, 2018
From ΔE = hc/λ, one finds the Compton wavelength to be λ = 218 nm. Performing the experiments, it is found that the maximum of the first electronic absorption band occurs at 210 nm. Hence, the use of quantum theory provides one with accurate results.
Towards highly accurate calculations of parity violation in chiral molecules: relativistic coupled-cluster theory including QED-effects
Published in Molecular Physics, 2021
Our calculations are based on the Dirac–Coulomb Hamiltonian Here, the first and third terms represent the nucleus-nucleus and electron–electron repulsion, respectively. The one-electron part is given by the Dirac Hamiltonian in the scalar potential of fixed nuclei and will be extended by effective QED-potentials where and refer to the contributions from the vacuum polarisation and the electron self-energy, respectively, associated with nucleus A. We employ the Uehling potential [76] for the vacuum polarisation term . The Uehling potential for a spherically symmetric extended nucleus can be expressed as follows [94] where α the fine structure constant, the reduced Compton wavelength and is the normalised charge density of nucleus A.
Inexplicability of Beth’s experiment within the framework of Maxwell’s electrodynamics
Published in Journal of Modern Optics, 2021
Hehl writes that spin is not associated with a motion of matter [15]. ‘The current density in Dirac’s theory can be split into a convective part and a polarization part. The polarization part is determined by the spin distribution of the electron field. It should lead to no energy flux in the rest system of the electron because the genuine spin ‘motion’ takes place only within a region of the order of the Compton wavelength of the electron’. This is especially important for us because there is no movement in Beth’s experiment.
Effects of the long-range neutrino-mediated force in atomic phenomena
Published in Molecular Physics, 2022
Phillip Munro-Laylim, Vladimir Dzuba, Victor Flambaum
The wave function of deuteron may be found using the short range nature of the strong interaction and relatively small binding energy of the deuteron. Outside the interaction range, we use solution to the Schrodinger equation for zero potential. Within the interaction range fm, the wave function has a constant value for s orbital. Therefore, the wave function is given by where the normalisation constant B is given by for eV (reduced mass and binding energy MeV). The Jastrow factor, [29], is included to account for the nucleon repulsion at short distance. For a contact potential , perturbation theory is used to find Substituting g for the neutrino-mediated potential in Equation (6), we obtain the energy shift for the deuteron binding energy which evaluates to Following Ref. [11], we take difference between experimental [30] and theoretical [31] results as eV. This gives This constraint is 4 orders of magnitude stronger than previously calculated in Ref. [11]. This is mainly due to the Z boson propagator cut-off (Z boson Compton wavelength) instead of the nuclear radius cut-off in Ref. [11]. Formally, this looks like the second strongest constraint among two-body systems (the strongest constraint comes from muonium HFS). However, deuteron is a system with the strong interaction and this constraint is probably less reliable than the constraints from the lepton systems.