scholarly journals Massless Composite Bosons Formed by the Coupled Electron-Positron Pairs and Two-Photon Angular Correlations in the Colliding Beam Reaction e-e+→Bγγ with Emission of the Massless Boson

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
A. I. Agafonov
Keyword(s):  
Wave Function ◽  
Free Particle ◽  
Plane Waves ◽  
Wave Functions ◽  
Two Photon ◽  
Electron Positron ◽  
Correlation Spectrum ◽  
Composite Bosons ◽  
Massless Boson ◽  
Colliding Beams

The approach in which the electron and positron are treated as ordinary, different particles, each being characterized by the complete set of the Dirac plane waves, is examined. This completely symmetric representation that is beyond the standard QED makes it necessary to choose another solution of the Dirac equation for the free particle propagator as compared to that used currently. The Bethe-Salpeter equation with these particle propagators is solved in the ladder approximation. A new solution has been found represented by the massless composite bosons formed by the coupled electron-positron pairs with the coupling equal to the fine structure constant. It has been demonstrated that (1) the massless boson states have normalizable complex wave functions which are transversely compressed plane waves; (2) the transverse radius of the wave functions diverges as the boson energy goes to zero; that is, the composite bosons cannot be at rest; (3) increasing the boson energy results in an extension of the transverse wave function in the momentum space and a corresponding contraction of the real space coordinate wave function. The new reaction e-e+→Bγγ is investigated with the products composed of the massless composite boson and two photons. The cross-section of this reaction is derived for nonrelativistic colliding beams of spin-polarized electrons and positrons. In this case the 2γ angular correlation spectrum is characterized by a narrow peak with the full-width-at-half-maximum not exceeding 0.2 mrad. It is shown that in order to distinguish between the conventional annihilation of the singlet electron-positron pair with the two-photon emission and the new examined reaction yielding the three particles, experiments are proposed with the extremely nonrelativistic colliding beams.

scholarly journals HIGHER TWIST EFFECTS IN PHOTON–PHOTON COLLISIONS

2008 ◽  
Vol 17 (06) ◽  
pp. 1041-1059 ◽  
Author(s):  
A. I. AHMADOV ◽  
I. BOZTOSUN ◽  
A. SOYLU ◽  
E. A. DADASHOV
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Cross Sections ◽  
Production Cross ◽  
Wave Functions ◽  
Feynman Diagrams ◽  
High Twist ◽  
Higher Twist Effects ◽  
Two Photon ◽  
Pion Wave Function

In this article, we investigate the contribution of the high twist Feynman diagrams to the large-pT single pseudoscalar and vector mesons inclusive production cross section in two-photon collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients a2 and a4 have been extracted from the CLEO data, Braun–Filyanov pion wave function, the asymptotic and the Chernyak–Zhitnitsky wave functions are all used in the calculations. For ρ-meson we used the Ball–Braun wave function. The results of the calculations reveal that the high twist cross sections, the ratio R, the dependence transverse momentum pT and the rapidity y of meson in the Φ CLEO (x, Q2) wave function case is very close to the Φ asy (x) asymptotic wave function case. It is shown that the high twist contribution to the cross section depends on the choice of the meson wave functions.

Positron Annihilation and the Band Structure in Molybdenum

1972 ◽  
Vol 50 (15) ◽  
pp. 1777-1781 ◽  
Author(s):  
S. M. Kim ◽  
W. J. L. Buyers
Keyword(s):  
Wave Function ◽  
Band Structure ◽  
Angular Correlation ◽  
Room Temperature ◽  
Theoretical Calculations ◽  
Plane Waves ◽  
Interpolation Scheme ◽  
Accurate Representation ◽  
Two Photon ◽  
Positron Wave Function

Measurements have been made of the two-photon angular correlation from positrons annihilating in single-crystal molybdenum at room temperature. By means of a combination of conventional slits and Soller slits the number of annihilations for which the momentum lies along a line in the momentum distribution is obtained, and results are presented for the [ζ,ζ,0], [0,0,ζ, and [ζ,ζ,0.71] directions. Theoretical calculations of the angular correlation have been made based on the interpolation or pseudopotential scheme with s–d interaction included. The parameters of the interpolation scheme have been chosen so that an accurate representation is obtained of the APW band structure of Mattheiss. The positron wave function has been obtained in terms of 141 plane waves. The width of the calculated two-photon angular correlation is found to be much broader than the experimental width unless the relative s and d enhancement is considered.

The Theoretical Solutions of Several Integrations in Relation with the Plane Wave Functions

2012 ◽  
Vol 166-169 ◽  
pp. 2009-2015
Author(s):  
Wen Pu Shi ◽  
Cui Hua Li
Keyword(s):  
Wave Function ◽  
Plane Wave ◽  
Analytical Solutions ◽  
Elastic Waves ◽  
Plane Waves ◽  
Stationary Wave ◽  
Wave Functions ◽  
Analysis Method ◽  
Principle Of Superposition ◽  
Scattering Problems

Several integrations of the plane wave functions frequently appearing in the scattering problems of elastic waves are considered in this study. In conjunction with the principle of superposition and the stationary wave function expansion, the exact solutions are obtained. As in the scattering problems of elastic waves and plane waves, the theoretical solutions can improve the convergence speed of the arithmetic and the computation precision. The analysis method and the analytical solutions can also be very helpful to solving other complex integrations in relation with the cylinder functions and plane functions.

scholarly journals Quantum Implications of Non-Extensive Statistics

2021 ◽  
Vol 9 ◽  
Author(s):  
Nana Cabo Bizet ◽  
César Damián ◽  
Octavio Obregón ◽  
Roberto Santos-Silva
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Series Solution ◽  
Semiclassical Approximation ◽  
Free Particle ◽  
Wave Functions ◽  
Power Series Solution ◽  
Nonlinear Quantum ◽  
Nonadditive Statistics ◽  
Q Wave

Exploring the analogy between quantum mechanics and statistical mechanics, we formulate an integrated version of the Quantropy functional. With this prescription, we compute the propagator associated to Boltzmann–Gibbs statistics in the semiclassical approximation as K=F(T)exp(iScl/ℏ). We determine also propagators associated to different nonadditive statistics; those are the entropies depending only on the probability S± and Tsallis entropy Sq. For S±, we obtain a power series solution for the probability vs. the energy, which can be analytically continued to the complex plane and employed to obtain the propagators. Our work is motivated by the work of Nobre et al. where a modified q-Schrödinger equation is obtained that provides the wave function for the free particle as a q-exponential. The modified q-propagator obtained with our method leads to the same q-wave function for that case. The procedure presented in this work allows to calculate q-wave functions in problems with interactions determining nonlinear quantum implications of nonadditive statistics. In a similar manner, the corresponding generalized wave functions associated to S± can also be constructed. The corrections to the original propagator are explicitly determined in the case of a free particle and the harmonic oscillator for which the semiclassical approximation is exact, and also the case of a particle with an infinite potential barrier is discussed.

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

scholarly journals Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 53
Author(s):  
Jack C. Straton
Keyword(s):  
Quantum Theory ◽  
Arbitrary Function ◽  
Plane Waves ◽  
Wave Functions ◽  
One Dimension ◽  
Two Dimensional ◽  
Transition Amplitudes ◽  
Multidimensional Integrals ◽  
Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

Baryon resonances from electron-positron colliding beams

1969 ◽  
Vol 60 (4) ◽  
pp. 599-614 ◽  
Author(s):  
E. Celeghini ◽  
R. Gatto
Keyword(s):  
Electron Positron ◽  
Baryon Resonances ◽  
Colliding Beams
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