Collinear acousto-optical filtration of polychromatic Bessel light beams in lithium niobate crystals

The features of collinear acousto - optical filtration of quasi - diffractive Bessel light beams of o- and e-type in uniaxial crystals are investigated. Using the method of overlap integrals, an expression is found for the diffraction efficiency depending on the parameters of the acousto-optical interaction, as well as on the values of the overlap integrals. It is shown that for the zero-order mode of a Bessel light beam for a lithium niobate crystal under conditions of transverse phase synchronism and in the optical spectrum range of 0.4-0.7 μm, the filter bandwidth of ∼0.2 nm is achievable; with an increase in the order of the mode m≥1, the increase in the bandwidth is insignificant and is ∼0.23 -0.24 nm.

Recoupling mechanism for exotic mesons and baryons

The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel — the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating mesons (baryons). The explicit calculation with the known wave functions yields the peak at E = 4.12 GeV for the transitions $$ J/\psi +\phi \leftrightarrow {D}_s^{\ast }+{\overline{D}}_s^{\ast } $$ J / ψ + ϕ ↔ D s ∗ + D ¯ s ∗ , which can be associated with χc1 (4140), and a narrow peak at 3.98 GeV with the width 10 MeV for the transitions $$ {D}_s^{-}+{D}_0^{\ast}\leftrightarrow J/\psi +{K}^{\ast -} $$ D s − + D 0 ∗ ↔ J / ψ + K ∗ − , which can be associated with th recently discovered Zcs (3985).

Cyclopentadienyl System: Solving the Secular Determinant, π Energy, Delocalization Energy, Wave Functions, Electron Density and Charge Density

In this study, characteristics of Hückel strategy, were abused so as to acquire some significant outcomes, through a theoretical technique with which it is conceivable to get secular equations, π energy, wave functions, electron density and charge density, as an account of cyclopentadienyl system i.e. C5H5+ (cation), C5H5- (anion), and C5H5. (radical) and permitting the expression of delocalization energy of conjugated cyclopentadienyl ring framework. Here, it was presented the secular determinant of the Hückel technique and applied to cyclopentadienyl system framework so as to communicate their orbital energies of cyclopentadienyl system, also to communicate its electron and charge density in terms of stable configuration of a system. It is settled by the Hückel strategy and applied by the assumptions for nearby comparability such as coulomb integrals, exchange integrals and overlap integrals. This simple way hypothetical strategy will allow to graduate and post graduate understudies to understanding the investigation of stable configuration, electron and charge density and also other parameters.

The weak decay $$B_c$$ to Z(3930) and X(4160) by Bethe–Salpeter method

Considering Z(3930) and X(4160) as $$\chi _{c2}(2P)$$χc2(2P) and $$\chi _{c2}(3P)$$χc2(3P) states, the semileptonic and nonleptonic of $$B_c$$Bc decays to Z(3930) and X(4160) are studied by the improved Bethe–Salpeter (B–S) Method. The form factors of decay are calculated through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The influence of relativistic corrections are considered in the exclusive decays. Branching ratios of $$B_c$$Bc weak decays to Z(3930) and X(4160) are predicted. Some of the branching ratios are: $$Br(B_c^+\rightarrow Z(3930)e^+\nu _e)=(3.03^{+0.09}_{-0.16})\times 10^{-4}$$Br(Bc+→Z(3930)e+νe)=(3.03-0.16+0.09)×10-4 and $$Br(B_c^+\rightarrow X(4160)e^+\nu _e)=(3.55^{+0.83}_{-0.35})\times 10^{-6}$$Br(Bc+→X(4160)e+νe)=(3.55-0.35+0.83)×10-6. These results may provide useful information to discover Z(3930) and X(4160) and the necessary information for the phenomenological study of $$B_c$$Bc physics.

Relative probability of recoilless Λ-production in nuclei in the plane-wave impulse approximation

The problem of estimating the relative probability Ρ of recoilless Λ production in nuclei by means of the (K-,π-) reaction is investigated in the plane-wave impulse approximation, which leads to approximate expressions of the "Debye-Waller type". The values of the relevant average overlap integrals between Λ and neutron normalized harmonic oscillator wave func­ tions are close to 1.

Systematic study of the muon-nucleus overlap integrals for various processes in muonic atoms

As it is known, the bound muon of a muonic atom can participate in many electroweak processes as the allowed channels of the ordinary ^""-capture by the atomic nucleus, μ~ •+- (A, Z) -» (A,Z — l) + νβ, and the muon decay in orbit, μ~ -» e~ + υμ ·+- ve, as well as the exotic channels of the muon-to-electron, μ~ + (A, Z) —> (.A, Z)* + e~, and muon-to-positron, μ~ + (A, Ζ) -» (A, Ζ — 2) + e+, conversions. The latter reactions have not been seen by experiments up to now, but they are predicted by various extensions of the standard model (they violate the flavor and/or lepton quantum numbers). For all the above muonic processes, the muon-nucleus overlap integrals are necessary in order to calculate the relevant rates. These integrals can be evaluated if, in addition to the nuclear states, the wave function of the bound muon (also that of the outgoinglepton) are known. In the present work, we perform precise calculations of the muon (and electron/positron) wave functions for both the Schrödinger and Dirac equations. We use modern neural network techniques to overcome the difficulties arising from the finite size of the nucléon and nuclear Coulomb potential. As some applications, the obtained muonnucleus integrals for various muonic atoms are going to be used for evaluating exclusive muon-capture rates and muon to electron/positron conversion branching ratios.