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Journal articles on the topic 'Compton formula'

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Published: 5 June 2025

Last updated: 16 July 2025

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Mohammed, Sameen F., Abdulhadi Mirdan Ghaleb, and Esam S. Ali. "Electron Momentum Density of Nanoparticles ZrO2: A Compton Profile Study." International Journal of Nanoscience 20, no. 02 (2021): 2150018. http://dx.doi.org/10.1142/s0219581x21500186.

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This work investigates the electronic momentum density (EMD) distribution in nanosize zirconia (ZrO2) using the technique of Compton scattering. The ZrO2 nanoparticles (11.2[Formula: see text]nm) are synthesized of mechanical milling and characterized by SEM, XRD and TEM probes. The Compton profile [Formula: see text] of nanoZrO2 is measured by Compton spectrometer 59.54[Formula: see text]KeV Gamma rays (Americium-241) source. The study finds out that EMD in nanoZrO2 is narrower comparing in case bulk ZrO2. This study adopts the ionic-model-based free atom [Formula: see text] calculation for many configurations (Zr)[Formula: see text](O[Formula: see text])2 ([Formula: see text]) to measure the charge transfer (CT) on the compound formation. According to this study’s findings, CT values in these materials are ranged from 1.5 to 1.0 electrons from Zr to O atom.

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Zhu, Jiang. "Theory and Application of Compton Scattering Experiment." Highlights in Science, Engineering and Technology 64 (August 21, 2023): 185–90. http://dx.doi.org/10.54097/hset.v64i.11278.

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Compton scattering has been a key concept in atomic and molecular physics, material science, condensed matter physics, and other fields ever since it was originally discovered by Arthur H. Compton in 1923. Additionally, the Compton camera, one of the applications of Compton scattering can gather sufficient data and information about photons with energies above 500 keV, which is important for scientific research into astronomy, medical imaging, and the visualization of radioactive materials. The free electron approximation, the impulse approximation, and the scattering matrix are some of the methods used to arrive at the Compton formula and the underlying principles of the Compton effect. In this article, a full derivation of Compton formula will be included, along with a deduction of the free electron approximation, which shows the relationship between Compton scattering and Thomson scattering, a low-energy limit of the former when the photon energy is much less than the mass energy of the particle. Also, the article will discuss several thoughts of Compton scattering, including the examination of the connection between wavelengths and relative intensities, the defiance of conservation laws, and virtual photon absorption.

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Mohanmurthy, Prajwal, Amrendra Narayan, and Dipangkar Dutta. "A test of local Lorentz invariance with Compton scattering asymmetry." Modern Physics Letters A 31, no. 38 (2016): 1650220. http://dx.doi.org/10.1142/s0217732316502205.

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We report on a measurement of the constancy and anisotropy of the speed of light relative to the electrons in photon–electron scattering. We used the Compton scattering asymmetry measured by the new Compton polarimeter in Hall C at Jefferson Lab (JLab) to test for deviations from unity of the vacuum refractive index (n). For photon energies in the range of 9–46 MeV, we obtain a new limit of 1 − n < 1.4 × 10[Formula: see text]. In addition, the absence of sidereal variation over the six-month period of the measurement constrains any anisotropies in the speed of light. These constitute the first study of Lorentz invariance (LI) using Compton asymmetry. Within the minimal Standard Model extension (MSME) framework, our result yield limits on the photon and electron coefficients [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Although these limits are several orders of magnitude larger than the current best limits, they demonstrate the feasibility of using Compton asymmetry for tests of LI. Future parity-violating electron-scattering experiments at JLab will use higher energy electrons enabling better constraints.

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Moinester, Murray, and Stefan Scherer. "Compton scattering off pions and electromagnetic polarizabilities." International Journal of Modern Physics A 34, no. 16 (2019): 1930008. http://dx.doi.org/10.1142/s0217751x19300084.

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The electric [Formula: see text] and magnetic [Formula: see text] Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the [Formula: see text] Compton scattering angular distribution at back scattering angles and [Formula: see text] absolute cross sections. Theory derivations are given for the [Formula: see text] Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The [Formula: see text] polarizabilities were deduced from DESY Crystal Ball [Formula: see text] data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering [Formula: see text] at CERN COMPASS, (2) two-photon pion pair production [Formula: see text] at SLAC Mark II, and (3) radiative pion photoproduction [Formula: see text] from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value [Formula: see text] agrees well with the two-loop ChPT prediction [Formula: see text], strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.

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Lake, Matthew J., and Bernard Carr. "Does Compton–Schwarzschild duality in higher dimensions exclude TeV quantum gravity?" International Journal of Modern Physics D 27, no. 16 (2018): 1930001. http://dx.doi.org/10.1142/s0218271819300015.

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In three spatial dimensions, the Compton wavelength [Formula: see text]) and Schwarzschild radius [Formula: see text]) are dual under the transformation [Formula: see text], where [Formula: see text] is the Planck mass. This suggests that there could be a fundamental link — termed the Black Hole Uncertainty Principle or Compton–Schwarzschild correspondence — between elementary particles with [Formula: see text] and black holes in the [Formula: see text] regime. In the presence of [Formula: see text] extra dimensions, compactified on some scale [Formula: see text] exceeding the Planck length [Formula: see text], one expects [Formula: see text] for [Formula: see text], which breaks this duality. However, it may be restored in some circumstances because the effective Compton wavelength of a particle depends on the form of the [Formula: see text]-dimensional wave function. If this is spherically symmetric, then one still has [Formula: see text], as in the [Formula: see text]-dimensional case. The effective Planck length is then increased and the Planck mass reduced, allowing the possibility of TeV quantum gravity and black hole production at the LHC. However, if the wave function of a particle is asymmetric and has a scale [Formula: see text] in the extra dimensions, then [Formula: see text], so that the duality between [Formula: see text] and [Formula: see text] is preserved. In this case, the effective Planck length is increased even more but the Planck mass is unchanged, so that TeV quantum gravity is precluded and black holes cannot be generated in collider experiments. Nevertheless, the extra dimensions could still have consequences for the detectability of black hole evaporations and the enhancement of pair-production at accelerators on scales below [Formula: see text]. Though phenomenologically general for higher-dimensional theories, our results are shown to be consistent with string theory via the minimum positional uncertainty derived from [Formula: see text]-particle scattering amplitudes.

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Pardy, Miroslav. "Compton scattering in dielectric medium." Intellectual Archive 12, no. 4 (2023): 1–13. http://dx.doi.org/10.32370/ia_2023_12_1.

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We determine the Compton effect from the Volkov solution of the Dirac equation for a process in medium with the index of refraction n. Volkov solution involves the mass shift, or, the mass renormalization of an electron. We determine the modified Compton formula for the considered physical situation. The index of refraction causes that the wave lengths of the scattered photons are shorter for some angles than the wave lengths of the original photons. This is anomalous Compton effect.

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Basko, R., G. L. Zeng, and G. T. Gullberg. "Analytical reconstruction formula for one-dimensional Compton camera." IEEE Transactions on Nuclear Science 44, no. 3 (1997): 1342–46. http://dx.doi.org/10.1109/23.597011.

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DONG, YU-BING, T. MORII, and T. YAMANISHI. "SEMI-INCLUSIVE HADRON PAIR PRODUCTION AND POLARIZED GLUONS IN THE PROTON." International Journal of Modern Physics A 18, no. 08 (2003): 1273–80. http://dx.doi.org/10.1142/s0217751x03014605.

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To extract the polarized gluon distribution Δg, we study the large–pTlight hadron pair productions in polarized semi-inclusive reaction, which are dominantly produced via 2 mechanisms: photon–gluon fusion(PGF) and QCD Compton. The PGF gives us a direct information on Δg in the nucleon, whereas QCD Compton is background to the signal process for extracting Δg. By using symmetry relation among fragmentation functions and taking an appropriate combination of light hadron pair production processes, we can remove an effect of QCD Compton from those cross sections. Here we propose a new formula for extracting Δg from those processes.

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KAISER, N. "ISOSPIN BREAKING IN PION COMPTON SCATTERING." International Journal of Modern Physics E 21, no. 10 (2012): 1230009. http://dx.doi.org/10.1142/s0218301312300093.

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Using chiral perturbation theory we calculate for pion Compton scattering the isospin-breaking effects induced by the difference between the charged and neutral pion mass. At one-loop order this correction is directly proportional to [Formula: see text] and free of any contributions from short-distance electromagnetic counterterms. The differential cross-section for charged pion Compton scattering π-γ→π-γ gets affected (in backward directions) at the level of a few permille only. At the same time the isospin-breaking correction leads to a small shift of the pion polarizability difference by δ(απ-βπ)≃1.3⋅10-5 fm 3. In the case of the low-energy γγ→π0π0 reaction isospin breaking manifests itself through a cusp effect at the π+π- threshold. We give an improved estimate for this cusp effect using the empirical ππ-scattering length difference [Formula: see text].

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Kim, C., S. Moon, and J. Oh. "INVERSION FORMULA FOR THE WEIGHTED CONICAL RADON TRANSFORM." Eurasian Journal of Mathematical and Computer Applications 12, no. 4 (2024): 67–74. https://doi.org/10.32523/2306-6172-2024-12-4-67-74.

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The conical Radon transform, particularly relevant for Compton camera applications, maps a given function to its surface integral over a set of cones. This study focuses on the weighted conical Radon transform, obtained by incorporating a weight effect into the conical Radon transform detailed in [20]. The n-dimensional weighted conical Radon transform is first defined, following which its inversion formula is derived by expressing its projection as a convolution.

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Gharibyan, Vahagn. "Experimental hint for gravitational CP violation." Modern Physics Letters A 35, no. 11 (2020): 2050079. http://dx.doi.org/10.1142/s0217732320500790.

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An equality of particle and antiparticle gravitational interactions holds in general relativity and is supported by indirect observations. Gravity dependence on rotation or spin direction is experimentally constrained for non-relativistic matter. Here, a method based on high-energy Compton scattering is developed to measure the gravitational interaction of accelerated charged particles. Within that formalism, the Compton spectra measured at HERA rule out the speculated anti-gravity possibility for antimatter at a confidence level close to 100%. The same data, however, imply a gravitational CP violation around 13 GeV energies, by a maximal amount of [Formula: see text] for the charge and [Formula: see text] for the space parity. The detected asymmetry hints for a stronger gravitational coupling to left helicity electrons relative to right helicity positrons.

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A.A., Makhmudov, and Khudayberganov A.M. "METHODS OF THEORETICAL TEACHING THE TOPIC "COMPTON EFFECT" OF THE SECTION "ATOMIC PHYSICS" OF THE COURSE OF GENERAL PHYSICS IN HIGHER EDUCATIONAL INSTITUTIONS." International Journal of Education, Social Science & Humanities. FARS Publishers 11, no. 1 (2023): 123–31. https://doi.org/10.5281/zenodo.7512801.

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This article describes the method of theoretical teaching of the topic "Compton effect" in higher educational institutions, which refers to the section "Atomic physics" of the course of general physics. Improvements to this technique were also considered.

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Marukyan, Hrachya. "DVCS at HERMES." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660050. http://dx.doi.org/10.1142/s2010194516600508.

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Deeply virtual Compton scattering process was studied widely at the HERMES experiment through measurements of various cross-section asymmetries. These measurements exploited the rich data collected at HERMES on scattering a longitudinally polarized lepton (electron/positron) beam off unpolarized, longitudinally and transversely polarized hydrogen targets, unpolarized and longitudinally polarized deuterium targets, as well as unpolarized nuclear targets. The operation of a recoil detector during the last two years of HERMES running enabled for the full kinematic reconstruction of the events of exclusively produced real photons and a clean (with a background well below the 1[Formula: see text]) measurement of the beam-helicity asymmetry. Also, first measurement of the beam-helicity asymmetry related to the associated deeply virtual Compton scattering process, where the proton is excited to a [Formula: see text]-resonance state, was possible using the recoil detector information.

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KROLL, P., M. SCHÜRMANN, and W. SCHWEIGER. "EXCLUSIVE PHOTON-PROTON REACTIONS AT MODERATELY LARGE MOMENTUM TRANSFER." International Journal of Modern Physics A 06, no. 23 (1991): 4107–32. http://dx.doi.org/10.1142/s0217751x91002021.

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The diquark model in which protons are viewed as being built up by quarks and diquarks (the latter are treated as quasi-elementary constituents at moderately large momentum transfer) is applied to Compton scattering off protons and combined with similar studies of the electromagnetic form factors of nucleons and of [Formula: see text]. It is demonstrated that the model is able to describe very well the data for these reactions at moderately large values of the momentum transfer with a common set of parameters. We also investigate the helicity dependence of the amplitudes. Very interesting and characteristic predictions for various observables are given. In particular a sizeable transversal polarization of the proton is obtained for Compton scattering.

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Singh, Tejinder P. "A new length scale, and modified Einstein–Cartan–Dirac equations for a point mass." International Journal of Modern Physics D 27, no. 08 (2018): 1850077. http://dx.doi.org/10.1142/s0218271818500773.

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We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale [Formula: see text], dubbed the Compton–Schwarzschild length, to which the Compton wavelength and Schwarzschild radius are small mass and large mass approximations, respectively. Here, we write down the field equations which follow from this action. We argue that the large mass limit yields Einstein equations, provided we assume the wave function collapse and localization for large masses. The small mass limit yields the Dirac equation. We explain why the Kerr–Newman black hole has the same gyromagnetic ratio as the Dirac electron, both being twice the classical value. The small mass limit also provides compelling reasons for introducing torsion, which is sourced by the spin density of the Dirac field. There is thus a symmetry between torsion and gravity: torsion couples to quantum objects through Planck’s constant [Formula: see text] (but not [Formula: see text]) and is important in the microscopic limit. Whereas gravity couples to classical matter, as usual, through Newton’s gravitational constant [Formula: see text] (but not [Formula: see text]), and is important in the macroscopic limit. We construct the Einstein–Cartan–Dirac equations which include the length [Formula: see text]. We find a potentially significant change in the coupling constant of the torsion driven cubic nonlinear self-interaction term in the Dirac–Hehl–Datta equation. We speculate on the possibility that gravity is not a fundamental interaction, but emerges as a consequence of wave function collapse, and that the gravitational constant maybe expressible in terms of Planck’s constant and the parameters of dynamical collapse models.

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Gasparyan, A. M., M. F. M. Lutz, and B. Pasquini. "Spin Observables in Pion Photoproduction and Nucleon Compton Scattering from the Chiral Lagrangian and Dispersion Relations." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660066. http://dx.doi.org/10.1142/s2010194516600661.

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A scheme based on the chiral Lagrangian, analyticity and unitarity is applied to spin observables in pion photoproduction and nucleon Compton scattering. Subthreshold partial-wave amplitudes are calculated in chiral perturbation theory and extrapolated beyond the threshold region imposing the micro-causality and the unitarity constraint. A reasonable description of various spin observables up to energies [Formula: see text] MeV is obtained in terms of the parameters relevant at order [Formula: see text] in the chiral Lagrangian. Nucleon spin-polarizabilities predicted in our scheme are consistent with recent measurements of double polarization asymmetries at MAMI.

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UI, Takuji, Masanao KATO, and Eiichi ASADA. "An absorption correction formula for X-ray fluorescence analysis using Compton scattering." Analytical Sciences 6, no. 2 (1990): 183–86. http://dx.doi.org/10.2116/analsci.6.183.

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Ishii, Keizo, Atsuki Terakawa, Keitaro Hitomi, and Mitsuhiro Nogami. "Development of a 20MeV proton particle-induced X-ray emission analysis method in a helium atmosphere." International Journal of PIXE 29, no. 03n04 (2019): 113–17. http://dx.doi.org/10.1142/s0129083519500219.

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We developed a 20[Formula: see text]MeV particle-induced X-ray emission (PIXE) analysis method using a medical cyclotron, which is conventionally used for positron emission tomography analysis performed in vacuo, during which the target sample is damaged. For non-destructive analysis and ease of switching between target samples, we developed a technique allowing 20[Formula: see text]MeV proton PIXE analysis to be performed at the atmospheric pressure. We filled the PIXE analysis chamber with helium and checked that the continuous background of the Compton tails of nuclear reaction [Formula: see text]-rays increased only minimally, and that the quasi-free electron bremsstrahlung (QFEB) did not increase at all, in the X-ray energy spectrum.

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Kazantsev, Ivan G., Samuel Matej, Robert M. Lewitt, et al. "Modeling and simulation of Compton scatter image formation in positron emission tomography." Journal of Inverse and Ill-posed Problems 28, no. 6 (2020): 923–32. http://dx.doi.org/10.1515/jiip-2020-0052.

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AbstractWe present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the positron emission tomography. The formula of the forward model has been obtained using the single scatter simulation approximation under simplified assumptions, and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter physics. The numerical comparative study has been performed using a digital cylindrical phantom filled in with water and containing spherical sources of emission activity located at the central and several displaced positions. Good fits of the formula-based and statistically generated profiles of scatter projections are observed in the presented numerical results.

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John, R. W. "Brilliance of X rays and gamma rays produced by Compton backscattering of laser light from high-energy electrons." Laser and Particle Beams 16, no. 1 (1998): 115–27. http://dx.doi.org/10.1017/s0263034600011824.

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In the Compton backscattering of laser light from a high-energy electron beam, the scattered photons are, as is well known, much harder than the incident photons. In connection with the inverse Compton effect, the spectral brightness, the brilliance of the backscattered radiation is theoretically investigated. For the brilliance B [photons/(sec × mm2 × sr × 0.1% bandwidth)] of the scattered radiation a defining relation is given. Then, the intensity I0 and the wavelength λ 0 of the incident laser light are assumed such that the intensity parameter η is sufficiently smaller than 1, so that with regard to the scattering process, multiphoton effects need not be considered, and the backscattered photon energy hν and the differential cross section dσ/dω approximately do not depend on η. In this case, the brilliance B linearly scales with I0. Furthermore, it is assumed that the primary electron and the incident laser photon are counterpropagating along a straight line, the head-on incidence of the laser photon. On these assumptions, for the brilliance B of the backscattered radiation, B depending on the back-scattered photon energy hν, an explicit formula is derived; from it, by approximations, a shorter formula for B is obtained.

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Burinskii, Alexander. "Weakness of gravity as illusion which hides true path to unification of gravity with particle physics." International Journal of Modern Physics D 26, no. 12 (2017): 1743022. http://dx.doi.org/10.1142/s0218271817430222.

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Well known weakness of gravity in particle physics is an illusion caused by underestimation of the role of spin in gravity. Relativistic rotation is inseparable from spin, which for elementary particles is extremely high and exceeds mass on 20–22 orders (in units [Formula: see text]). Such a huge spin generates frame-dragging that distorts space much stronger than mass, and effective scale of gravitational interaction is shifted from Planck to Compton distances. We show that compatibility between gravity and quantum theory can be achieved without modifications of Einstein–Maxwell equations, by coupling to a supersymmetric Higgs model of symmetry breaking and forming a nonperturbative super-bag solution, which generates a gravity-free Compton zone necessary for consistent work of quantum theory. Super-bag is naturally upgraded to Wess–Zumino supersymmetric QED model, forming a bridge to perturbative formalism of conventional QED.

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Moniruzzaman, M., and S. B. Faruque. "A Short Note on Minimal Length." Journal of Scientific Research 11, no. 2 (2019): 151–55. http://dx.doi.org/10.3329/jsr.v11i2.36244.

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After revival of the concept of minimal length, many investigations have been devoted, in literature, to estimate upper bound on minimal length for systems like hydrogen atom, deuteron etc. We report here a possible origin of minimal length for atomic and nuclear systems which is connected with the fundamental interaction strength and the Compton wavelength. The formula we appear at is numerically close to the upperbounds found in literature.

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Piedra, Owen Pavel Fernández. "Renormalized quantum stress–energy tensor for massive spinor fields around global monopoles." Modern Physics Letters A 35, no. 11 (2020): 2050077. http://dx.doi.org/10.1142/s0217732320500777.

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The renormalized quantum stress–energy tensor [Formula: see text] for a massive spinor field around global monopoles is constructed within the framework of Schwinger–DeWitt approximation, valid whenever the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry. The results obtained show that the quantum massive spinor field in the global monopole spacetime violates all the pointwise energy conditions.

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LI, HAU-BIN, and HENRY T. WONG. "NEUTRINO MAGNETIC MOMENT RESULTS AT THE KUO-SHENG NUCLEAR POWER PLANT." Modern Physics Letters A 19, no. 13n16 (2004): 1239–43. http://dx.doi.org/10.1142/s021773230401463x.

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A search of neutrino magnetic moment was carried out at the Kuo-Sheng Nuclear Power Station at a distance of 28 m from the 2.9 GW reactor core. With a high purity germanium detector of mass 1.06 kg surrounded by scintillating NaI(Tl) and CsI(Tl) crystals as anti-Compton detectors, a detection threshold of 5 keV and a background level of 1 kg -1 kev -1 day -1 at 12-60 keV were achieved. Based on 4712 and 1250 hours of Reactor ON and OFF data, respectively, the limits on the neutrino magnetic moment of [Formula: see text] at 90(68)% confidence level were derived. Indirect bounds of the [Formula: see text] radiative lifetime of [Formula: see text] can be inferred. The present status and future plans are discussed.

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MORICCIANI, D., O. BARTALINI, V. BELLINI, et al. "RECENT RESULTS FROM GRAAL." International Journal of Modern Physics A 20, no. 02n03 (2005): 503–13. http://dx.doi.org/10.1142/s0217751x05021671.

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A polarised and tagged [Formula: see text] ray beam is produced at GRAAL by the Compton scattering of laser light on the high energy electron of the ESRF storage ring. We present results on the beam polarisation asymmetries and cross sections in the photoproduction of mesons on hydrogen and deuterium target in the energy region 500-1500 MeV. These very precise results cover the angular range 30°-150°, providing stringent constraints to theoretical models.

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Pardy, Miroslav. "The interaction of electron with the infinitesimally short electromagnetic pulse." Intellectual Archive 12, no. 4 (2023): 14–26. http://dx.doi.org/10.32370/ia_2023_12_2.

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After the classical approach to acceleration of a charged particle by the δ-form impulsive force, we consider the corresponding quantum theory based on the Volkov solution of the Dirac equation. We determine the modified Compton formula for frequency of photons generated by the scattering of the δ-form laser pulse on the electron in a rest. The article follows the physical ideas involved in the author text with the title Electron in an Ultrashort Laser Pulse (Pardy, 2003).

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Protheroe, R. J. "Factors Determining Variability Time in Active Galactic Nucleus Jets." Publications of the Astronomical Society of Australia 19, no. 4 (2002): 486–98. http://dx.doi.org/10.1071/as02008.

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AbstractThe relationship between observed variability time and emission region geometry is explored for the case of emission by relativistic jets.The approximate formula for the jet-frame size of the emission region, R′ = DcΔtobs, is shown to lead to large systematic errors when used together with observed luminosity and assumed or estimated Doppler factor D to estimate the jet-frame photon energy density. These results have implications for AGN models in which low-energy photons are targets for interaction of high energy particles and photons, e.g. synchrotron-self Compton models and hadronic blazar models, as well as models of intraday variable sources in which the photon energy density imposes a brightness temperature limit through Compton scattering.The actual relationship between emission region geometry and observed variability is discussed for a variety of geometries including cylinders, spheroids, bent, helical and conical jet structures, and intrinsic variability models including shock excitation. The effects of time delays due to finite particle acceleration and radiation timescales are also discussed.

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Schildknecht, Dieter. "Color transparency and saturation in QCD." Modern Physics Letters A 29, no. 25 (2014): 1430028. http://dx.doi.org/10.1142/s0217732314300286.

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We review the theoretical interpretation of deep-inelastic electron–proton scattering at low values of the Bjorken variable x ≃Q2/W2 ≲ 0.1. The process proceeds via the interaction of quark–antiquark [Formula: see text] color-dipole fluctuations of the (virtual) photon with the proton. In terms of the forward Compton scattering amplitude, two reaction channels contribute to the interaction of the [Formula: see text] color dipole with the gluon field in the proton. Dependent on the kinematics, there is either color transparency, corresponding to a cancellation of the amplitudes for the two reaction channels, or saturation, occurring when the process is dominated by a single interaction channel. The connection between the color-dipole picture and the pQCD improved parton model is elaborated upon.

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MOAYEDI, S. K., M. R. SETARE, H. MOAYERI, and M. POORAKBAR. "FORMULATION OF THE SPINOR FIELD IN THE PRESENCE OF A MINIMAL LENGTH BASED ON THE QUESNE–TKACHUK ALGEBRA." International Journal of Modern Physics A 26, no. 29 (2011): 4981–90. http://dx.doi.org/10.1142/s0217751x11054802.

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In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen.39, 10909, (2006)) introduced a (D+1)-dimensional (β, β′)-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space–time described by Quesne–Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′ = 2β up to first order over deformation parameter β. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for [Formula: see text]. Applying the condition [Formula: see text] to an electron, the upper bound for the isotropic minimal length becomes about 3 ×10-13 m. This value is near to the reduced Compton wavelength of the electron [Formula: see text] and is not incompatible with the results obtained for the minimal length in previous investigations.

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Baghmanyan, V., та N. Sahakyan. "X-ray and γ-ray emissions from NLSy1 galaxies". International Journal of Modern Physics D 27, № 10 (2018): 1844001. http://dx.doi.org/10.1142/s0218271818440017.

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The recent observations by Fermi large area telescope (Fermi-LAT) showed that in addition to the radio galaxies and blazars, Narrow-Line Seyfert 1 (NLSy1) galaxies are also [Formula: see text]-rays emitters. NLSy1 are AGNs with optical spectral properties similar to those of Seyfert 1 galaxies, except for having narrow Balmer lines and strong optical lines. They also exhibit strong X-ray variability, steep X-ray spectra and relatively high luminosity. The multiwavelength emission properties of 1H 0323+342, SBS 0846+513 and PMN J0948+0022 are discussed, using the [Formula: see text]-ray data from the last 8.8 years Fermi-LAT observations as well as available Swift(UVOT/XRT) data. It is shown that one-zone synchrotron/synchrotron self-Compton (SSC) model can satisfactorily reproduce their observed broadband spectra.

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Kassandrov, Vladimir V., and Nina V. Markova. "Relativistic generalization of the Schrödinger-Newton model for the wavefunction reduction." International Journal of Modern Physics A 35, no. 02n03 (2020): 2040017. http://dx.doi.org/10.1142/s0217751x20400175.

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We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of Schrödinger and Poisson equations. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. Regular solutions to the latter form a discrete spectrum in which all the “active” gravitational masses are always positive, and approximately equal to inertial masses and to the mass [Formula: see text] of the quanta of Dirac field up to the corrections of order [Formula: see text]. Here [Formula: see text] is the gravitational analogue of the fine structure constant negligibly small for nucleons. In the limit [Formula: see text] the model reduces back to the nonrelativistic Schrödinger-Newton one. The equivalence principle is fulfilled with an extremely high precision. The above solutions correspond to various states of the same (free) particle rather than to different particles. These states possess a negligibly small difference in characteristics but essentially differ in the widths of the wavefunctions. For the ground state the latter is [Formula: see text] times larger the Compton length, so that a nucleon cannot be sufficiently localized to model the reduction process.

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Nazari, F., and A. Mirjalili. "Investigating GPDs in the framework of the double distribution model." International Journal of Modern Physics A 31, no. 17 (2016): 1650091. http://dx.doi.org/10.1142/s0217751x16500913.

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In this paper, we construct the generalized parton distribution (GPD) in terms of the kinematical variables [Formula: see text], [Formula: see text], [Formula: see text], using the double distribution model. By employing these functions, we could extract some quantities which makes it possible to gain a three-dimensional insight into the nucleon structure function at the parton level. The main objective of GPDs is to combine and generalize the concepts of ordinary parton distributions and form factors. They also provide an exclusive framework to describe the nucleons in terms of quarks and gluons. Here, we first calculate, in the Double Distribution model, the GPD based on the usual parton distributions arising from the GRV and CTEQ phenomenological models. Obtaining quarks and gluons angular momenta from the GPD, we would be able to calculate the scattering observables which are related to spin asymmetries of the produced quarkonium. These quantities are represented by [Formula: see text] and [Formula: see text]. We also calculate the Pauli and Dirac form factors in deeply virtual Compton scattering. Finally, in order to compare our results with the existing experimental data, we use the difference of the polarized cross-section for an initial longitudinal leptonic beam and unpolarized target particles [Formula: see text]. In all cases, our obtained results are in good agreement with the available experimental data.

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Maqbool, Hunain, Wardah Naim, and Muhammad Maqbool. "X-Ray Interaction Cross-Sections and Scattering Coefficients of 21Sc45, 25Mn55, 31Ga70, 56Ba137, and 78Pt195 for Applications in Radiation Shielding and Radiology." International Journal of Radiology Case Reports 2, no. 1 (2025): 17–27. https://doi.org/10.61797/ijrcr.v2i1.436.

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One of the most successful ways of treating cancer and malignant tumors is radiation. Most of the radiological and diagnostic processes are also possible due to the use of radiation. However, it is important to protect radiation workers using various shielding materials due to the hazards associated with high-energy radiation. In addition, the quality of radiological images is also affected by the energy and intensity of radiation used in the imaging process. The use of shielding material is more productive in shielding as well as good quality radiological imaging only if its basic characteristics properties and interaction with radiation are studied. The purpose of the present work is to use the Klein-Nishina formula to calculate the electronic cross-sections, atomic cross-sections, energy-transfer cross-sections, and Compton scattering coefficients of Scandium (21Sc45), Manganese (25Mn55), Gallium (31Ga70), Barium (56Ba137), and Platinum (78Pt195) when X-rays or γ-radiation interact with these elements. The results show that the Klein-Nishina cross-section per electron and Klein-ishina cross-sections per atom decrease with increasing photon energy and increase when the charge number Z of the elements is increased. The Compton Scattering coefficients also decrease for highly energetic radiation and increase with the ratio of charge number Z and mass number A of an element. Thus, the Compton scattering coefficients should not be studied as a function of Z or A separately but instead as a function of Z/A. The results also conclude that the investigated materials can be used for applications in radiation shielding, dosimetry, and radiological imaging applications.

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Marinković, Predrag, and Radovan Ilić. "Radiography simulation based on point-kernel model and dose buildup factors." Journal of X-Ray Science and Technology: Clinical Applications of Diagnosis and Therapeutics 17, no. 1 (2009): 41–59. http://dx.doi.org/10.3233/xst-2009-021500215.

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Three-dimensional point-kernel multiple scatter model for radiography simulation, based on dose X-ray buildup factors, is proposed and validated to Monte Carlo simulation. This model embraces nonuniform attenuation in object of imaging (patient body tissue). Photon multiple scattering is treated as in the point-kernel integration gamma ray shielding problems via scatter voxels. First order Compton scattering is described by means of Klein-Nishina formula. Photon multiple scattering is accounted by using dose buildup factors. The proposed model is convenient in those situations where more exact techniques, like Monte Carlo, are not time consuming acceptable.

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Lu, Wei. "Remark on the Kinematics of the One-Photon Production in Electron–Proton Scattering." Modern Physics Letters A 12, no. 21 (1997): 1553–59. http://dx.doi.org/10.1142/s0217732397001588.

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We clarify some misleading mistakes in the literature about the phase space for the one-photon production in electron–proton scattering and present the correct overall phase space factor in the cross-section formula. Our conclusion is that the earlier diquark model predictions for the cross-sections of the one-photon production in electron–proton scattering are unreliable. Furthermore, we specify the phase space boundaries. In relation to the recent proposal to measure the off-diagonal quark distribution functions in the deeply virtual Compton scattering off the proton, we point out that the kinematics strongly disfavors such experiments.

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Mikesell, J. L., F. E. Senftle, T. A. Lloyd, A. B. Tanner, C. T. Merritt, and E. R. Force. "Borehole field calibration and measurement of low‐concentration manganese by decay gamma rays." GEOPHYSICS 51, no. 12 (1986): 2219–24. http://dx.doi.org/10.1190/1.1442075.

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The manganese concentration in the Arundel clay formation, Prince Georges County, Maryland, was determined from a borehole by using delayed neutron activation. The neutrons were produced by a [Formula: see text] source. The 847 keV gamma ray of manganese was detected continuously, and its counting rate was measured at intervals of 15 s as the measuring sonde was moved at a rate of 0.5 cm/s. The technique measured the concentration ratio of manganese to aluminum. This ratio, when combined with an estimate of the aluminum concentration of the clay, made it possible to determine the percentage concentration of manganese without using a test‐pit calibration facility. The measurements were made by using an NaI(Tl) scintillation detector and a Ge(HP) solid‐state detector cooled by solid propane. A two‐pass technique had to be used with the scintillation detector because Compton background from the 1 779 keV photopeak of aluminum masked the manganese line. The Compton background did not interfere when the solid‐state detector was used. The borehole measurements compared favorably with a chemical core analysis and were unaffected by water in the borehole.

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Arslanaliev, A., Y. Kostylenko, and O. Shebeko. "A New Family of Interactions between Clothed Particles in QED." Ukrainian Journal of Physics 66, no. 10 (2021): 833. http://dx.doi.org/10.15407/ujpe66.10.833.

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The method of unitary clothing transformations (UCTs) has been applied to the quantum electrodynamics (QED) by using the clothed particle representation (CPR). Within CPR, the Hamiltonian for interacting electromagnetic and electron-positron fields takes the form in which the interaction operators responsible for such two-particle processes as e−e− → e−e−, e+e+ → e+e+, e−e+ → e−e+, e−e+ → yy, yy → e−e+, ye− → ye−, and ye+ → ye+ are obtained on the same physical footing. These novel interactions include the off-energy-shell and recoil effects (the latter without any expansion in (v/c)2-series) and their on-energy shell matrix elements reproduce the well-known results derived within the perturbation theory based on the Dyson expansion for the S-matrix (in particular, the Møller formula for the e−e−-scattering, the Bhabha formula for e−e+-scattering, and the Klein–Nishina one for the Compton scattering).

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POLLOCK, M. D. "MAGNETIC FIELDS AND VACUUM POLARIZATION AT THE PLANCK ERA." International Journal of Modern Physics D 12, no. 07 (2003): 1289–98. http://dx.doi.org/10.1142/s0218271803003396.

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The one-loop effective action describing polarization of the vacuum due to virtual electron-positron pairs in the Maxwell theory of electromagnetism was obtained by Heisenberg and Euler, in the limit of a background field that is constant on the scale of the electron Compton-wavelength. The case of vanishing electric field and constant, ultra-strong magnetic field B≫Bc, where [Formula: see text], yields a configuration whose energy density is less than that of the equivalent radiation field, suggesting why a magnetic field may be present in the early Universe back to the Planck era. For there is a similar but larger effect, allowing a "ferromagnetic" Yang–Mills vacuum state, in the grand-unified theory at temperatures [Formula: see text], analyzed by Skalozub. Some further aspects of ultra-strong magnetic fields are discussed vis-à-vis the origin of the Galactic field B g .

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Singh, Tejinder P. "Dark energy as a large scale quantum gravitational phenomenon." Modern Physics Letters A 35, no. 23 (2020): 2050195. http://dx.doi.org/10.1142/s0217732320501953.

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In our recently proposed quantum theory of gravity, the universe is made of ‘atoms‘” of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localization of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about [Formula: see text], forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about [Formula: see text] such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac’s large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about [Formula: see text].

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SINITSYNA, V. G., T. P. ARSOV, A. Y. ALAVERDIAN, et al. "OBSERVED AND EXPECTED 1–30 TEV GAMMA-RAY EMISSION FROM GEMINGA AND TYCHO'S SUPERNOVA REMNANTS." International Journal of Modern Physics A 20, no. 29 (2005): 7026–28. http://dx.doi.org/10.1142/s0217751x05030752.

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The gamma-quantum emitting objects in our Galaxy are the supernova remnants and binaries. Preliminary analysis of the data for γ-ray sources Tycho Brage and Geminga obtained with the SHALON γ-ray telescope is briefly discussed. The energy spectra of γ's from the Geminga and Tycho's sources, F (E > 0.8 TeV ) ∝ Ek are found to be harder than the spectrum from Crab Nebula. The expected π0-decay γ-ray flux [Formula: see text] extends up to ~ 30 TeV, whereas the inverse Compton γ-ray flux has a cutoff above a few TeV. Hence, the detection of γ rays at energies ~ 10 – 30 TeV provides a hint of their hadronic origin.

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Frontera, Filippo, Lorenzo Amati, Ruben Farinelli, et al. "Possible physical explanation of the intrinsic Ep,i-“intensity” correlation commonly used to “standardize” GRBs." International Journal of Modern Physics D 25, no. 05 (2016): 1630014. http://dx.doi.org/10.1142/s0218271816300147.

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It is recognized that very likely the correlation between peak energy [Formula: see text] and bolometric intensity is intrinsic to GRBs. However, its physical origin is still debated. In this paper, we will discuss a possible interpretation of the correlation in the light of a GRB prompt emission spectral model, grbcomp, proposed in [L. Titarchuk, R. Farinelli, F. Frontera and L. Amati, Astrophys. J. 752 (2012) 116]. grbcomp is essentially a photospheric model for the prompt emission of GRBs. Its main ingredients are a thermal bath of soft seed photons and a subrelativistically expanding outflow plasma, consequence of the star explosion. The emerging spectrum is the result of two phases: first, up to the photospheric radius, Comptonization of a subrelativistic electron outflow with thermal bath of soft photons, then, convolution of the Comptonized photons in the first phase with a Green function. The result of this convolution is consistent with different physical processes, in particular Inverse Compton. grbcomp has been successfully tested using a significant sample of GRB time resolved spectra in the broad energy band from 2[Formula: see text]keV to 2[Formula: see text]MeV [F. Frontera, L. Amati, R. Farinelli, S. Dichiara, C. Guidorzi, R. Landi and L. Titarchuk, Astrophys. J. 779 (2013) 175].

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Cappello, G., O. Adriani, S. Albergo, et al. "Collimation and characterization of ELI-NP gamma beam." International Journal of Modern Physics: Conference Series 48 (January 2018): 1860116. http://dx.doi.org/10.1142/s2010194518601163.

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The ELI-NP facility, currently being built in Bucharest, Romania, will deliver an intense and almost monochromatic gamma beam with tunable energy between 0.2 and 20 MeV. The challenging energy bandwidth of [Formula: see text]0.5% will be adjusted through the collimation system, while the main beam parameters will be measured through a devoted gamma-beam characterization system.[Formula: see text] The gamma-beam characterization system, designed by the EuroGammaS collaboration, consists of four elements: a Compton spectrometer that measures the gamma energy spectrum; a sampling calorimeter for a fast combined measurement of the beam average energy and its intensity, which will be used also as a monitor during machine commissioning and development; a nuclear resonant scattering system for absolute energy inter-calibration of the other detectors; and a gamma beam profile imager to be used for alignment and diagnostics purposes. The collimation and characterization system will be presented in this article. These systems have already been built and tested, while the delivery at ELI-NP facility and the final commissioning is scheduled by Fall 2018.

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Minty, B. R. S. "Airborne gamma‐ray spectrometric background estimation using full spectrum analysis." GEOPHYSICS 57, no. 2 (1992): 279–87. http://dx.doi.org/10.1190/1.1443241.

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We have developed a new technique for estimating airborne gamma‐ray spectrometric backgrounds. The background comes from three sources, namely aircraft, cosmic and atmospheric (radon) radiation. The aircraft and cosmic components are independently estimated by suitable calibration and the monitoring of a 3–6 MeV “cosmic” channel. Multichannel observations of the spectra are used to estimate the atmospheric background directly based on the observation that for gamma‐ray counts above the Compton continuum, the low energy [Formula: see text] photopeak at 0.609 MeV for atmospheric radiation suffers far less attenuation relative to the [Formula: see text] peak at 1.76 MeV than is the case for radiation from uranium in the ground. Since thorium and potassium sources do not contribute appreciably to these peak countrates, they can be used to calculate the contributions of radon and uranium to the observed spectrum. The technique appears to be less susceptible to errors due to the effects of variations in the vertical distribution of airborne radon and its daughters than upward‐looking detector techniques.

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de VEGA, H. J. "REAL TIME NONEQUILIBRIUM DYNAMICS OF QUANTUM PLASMAS: QUANTUM KINETICS AND THE DYNAMICAL RENORMALIZATION GROUP." International Journal of Modern Physics A 16, supp01c (2001): 1260–64. http://dx.doi.org/10.1142/s0217751x01009478.

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We implement the dynamical renormalization group (DRG) using the hard thermal loop (HTL) approximation for the real-time nonequilibrium dynamics in hot plasmas. The focus is on the study of the relaxation of gauge and fermionic mean fields and on the quantum kinetics of the photon and fermion distribution functions. As a concrete physical prediction, we find that for a QGP of temperature T~200 MeV and lifetime 10≤t≤ 50 fm /c there is a new contribution to the hard (k~T) photon production form off-shell bremsstrahlung (q→qγ and [Formula: see text] at just O(α) that grows logarithmically in time and is comparable to the known on-shell Compton scattering and pair annihilation at O(ααs).

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Raghuwanshi, S. S., B. K. Bhaumik, and S. G. Tewari. "A direct method for determining the altitude variation of the uranium stripping ratio in airborne gamma‐ray surveys." GEOPHYSICS 54, no. 10 (1989): 1350–53. http://dx.doi.org/10.1190/1.1442597.

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In airborne gamma‐ray spectrometric surveys, it is essential to calculate the net counts in the thorium, uranium, and potassium channels for quantitative analysis. The net uranium, thorium, and potassium counts are given by [Formula: see text], (1a) [Formula: see text] (1b) and [Formula: see text], (1c) where [Formula: see text], [Formula: see text], and [Formula: see text] are the background corrected counts per second for uranium, thorium, and potassium channels, respectively; α and β are the Compton contributions of thorium gamma rays in the uranium and potassium windows, respectively; and γ is the contribution of uranium gamma rays in the potassium window. In some countries, such as the U.S., Canada, and India, it is common practice to compute the stripping ratios by taking measurements over a set of calibration pads with known and varying amounts of uranium, thorium, and potassium (Grasty and Darnley, 1971; Grasty, 1975; Lovborg, 1984). These factors are determined by keeping the detector system inside the survey aircraft over the calibration pads. The stripping coefficients do not have fixed values but vary with source‐detector distance. Because most airborne surveys are conducted at about 120 m above ground level, the stripping ratios measured over the pads should be corrected for variations with ground clearance. In practice, the ground clearance in airborne gamma‐ray surveys may vary from about 40 m to 200 m depending upon the topography of the area flown. It is, therefore, necessary to know the values of the stripping coefficients as a function of ground clearance at least within the range of investigations. If this is known, it is possible to apply proper corrections while converting all data to a uniform datum of 122 m.

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Moon, Sunghwan, and Kiwoon Kwon. "Inversion formula for the conical Radon transform arising in a single first semicircle second Compton camera with rotation." Japan Journal of Industrial and Applied Mathematics 36, no. 3 (2019): 989–1004. http://dx.doi.org/10.1007/s13160-019-00379-x.

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Morvidone, M., M. K. Nguyen, T. T. Truong, and H. Zaidi. "On the V-Line Radon Transform and Its Imaging Applications." International Journal of Biomedical Imaging 2010 (2010): 1–6. http://dx.doi.org/10.1155/2010/208179.

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Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results.

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Sidharth, B. G., A. Das, C. R. Das, L. V. Laperashvili, and H. B. Nielsen. "Topological structure of the vacuum, cosmological constant and dark energy." International Journal of Modern Physics A 31, no. 34 (2016): 1630051. http://dx.doi.org/10.1142/s0217751x16300519.

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In this review, we present a theory of cosmological constant and dark energy (DE), based on the topological structure of the vacuum. The multiple point principle (MPP) is reviewed. It demonstrates the existence of the two vacua into the SM. The Froggatt–Nielsen’s prediction of the top-quark and Higgs masses is given in the assumption that there exist two degenerate vacua in the SM. This prediction was improved by the next-order calculations. We also considered Sidharth’s theory of cosmological constant based on the noncommutative geometry of the Planck scale space–time, what gives an extremely small DE density providing the accelerating expansion of the Universe. Theory of two degenerate vacua — the Planck scale phase and electroweak (EW) phase — is also reviewed, topological defects in these vacua are investigated, also the Compton wavelength phase suggested by Sidharth is discussed. A general theory of the phase transition and the problem of the vacuum stability in the SM is reviewed. Assuming the existence of a new scalar [Formula: see text] bound state [Formula: see text], earlier predicted by Froggatt, Nielsen and Laperashvili, we try to provide the vacuum stability in the SM and exact accuracy of the MPP.

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MEI, D. C., and L. ZHANG. "THE DOPPLER FACTORS AT X-RAY BAND OF THE BLAZARS." International Journal of Modern Physics D 14, no. 06 (2005): 947–56. http://dx.doi.org/10.1142/s0218271805005888.

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We study the Doppler factors for a group blazars at soft X-ray band. In our estimates, we have made the assumptions that (i) blazars can be divided into high-energy-peaked (HEP) objects whose synchrotron peak frequencies νp > 1014.7 Hz , and the low-energy-peaked (LEP) objects whose synchrotron peak frequencies νp≤1014.7 Hz , and (ii) the intrinsic radiation from a blazar in the energy range from radio to soft X-ray bands is the synchrotron radiation for HEP objects and the soft X-ray emission comes from inverse Compton scattering for LEP objects. Under the above assumptions, we estimate Doppler factors at optical (δO) and X-rays (δx) for 54 blazars by using the known radio Doppler factors and the observed flux densities in radio, optical and X-ray bands, and Doppler factors [Formula: see text] at X-ray band in which X-rays are assumed to be produced only by the synchrotron radiation. We get [Formula: see text] . The Doppler factors are different in various wavebands, and on average, the Doppler factor decreases with frequency from radio to X-ray bands.

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HU, YONGHONG, та YUNYI WU. "CHIRALITY-ASYMMETRY MACROSCOPIC FORCE INDUCED BY AXION BETWEEN THE α-QUARTZ AND COPPER BLOCK". Modern Physics Letters B 26, № 06 (2012): 1150035. http://dx.doi.org/10.1142/s0217984911500357.

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A macroscopic force induced by the effective potential suggested by Moody and Wilczek between α-quartz crystal and copper block is studied in detail. The matrix elements in the force formula are analyzed according to representations of the non-symmorphic space group P 3121 of α-quartz crystal. The asymmetry distribution of valence electrons and the selection rules do not cancel the force. We conclude that there exists a CP-violating macroscopic force. According to the limit of the production of the axion coupling constants gs gp/ℏc ≤ 10-26 at the Compton wavelength λ = 10-3 m, the macroscopic force between a 0.08 × 0.08 × 0.02 m3 block of α-quartz and a 0.08 × 0.08× 0.01 m3 copper block with a separation being 0.5 × 10-3 m in between, is estimated at less than 3.09 × 10-26 N.

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