Quasistochastic semigroup as a generalized group

Two representations of the hyperbolic-tangent semigroup (HTS) are discussed: the group representation (the Lorentz group) and the semigroup representation (the quasistochastic semigroup of relativistic endomorphisms-QSRE). Through a generalization of the condition for regular conjugation, it is established that the QSRE is, in a certain sense, a generalized group, Invertibility of the representation with respect to zero is shown to be an antiautomorphism (for transforms of fixed points of the HTS). The group representation of the HTS is understood from this point of view to be the invertibility with respect to the trivial unit element. Since the class of forms of HTS idempotents is exhausted by simply the unit and zero representations, there can be no other forms of the principle of relativistic invariance.Translated from Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 49–53, June, 1970.The authors thank D. D. Ivanenko for interest in the study and valuable comments.     

Experimental investigation of the dark pseudoresonance on the <Emphasis Type="Italic">D</Emphasis>1 line of the <Superscript>87</Superscript>Rb atom excited by a linearly polarized field

The measurements of the metrological characteristics (amplitude, width, and shift in the magnetic field) of the dark pseudoresonance, which was proposed by Kazakov et al. [quant-ph/0506167] as the reference resonance for an atomic frequency standard, are reported. It has been shown that the characteristics of the pseudoresonance are worse than those of the unsplit electromagnetically induced transparency resonance for the excitation scheme with the lin‖lin polarization on the D1 line of the ⁸⁷Rb atom.     

On the unique possibility of significantly increasing the contrast of dark resonances on the D1 line of <Superscript>87</Superscript>Rb

We propose and study, theoretically and experimentally, a new scheme of excitation of a coherent population trapping resonance for the D1 line of alkali atoms with nuclear spin I = 3/2 by bichromatic linearly polarized light (lin‖lin field) under the conditions of spectral resolution of the excited state. The unique properties of this scheme result in a high contrast of dark resonance for the D1 line of ⁸⁷Rb.     

Laser-induced interference, focusing, and diffraction of rescattering molecular photoelectrons

We solve the time-dependent Schr?dinger equation in three dimensions for H+2 in a one-cycle laser pulse of moderate intensity. We consider fixed nuclear positions and Coulomb electron-nuclear interaction potentials. We analyze the field-induced electron interference and diffraction patterns. To extract the ionization dynamics we subtract the excitations to low-lying bound states explicitly. We follow the time evolution of a well-defined wave packet that is formed near the first peak of the laser field. We observe the fragmentation of the wave packet due to molecular focusing. We show how to retrieve a diffraction molecular image by taking the ratio of the momentum distributions in the two lateral directions. The positions of the diffraction peaks are well described by the classical double slit diffraction rule.     

Breit-Wigner parameters of the <Emphasis Type="Italic">S</Emphasis><Subscript>11</Subscript>(1535) nucleon resonance

The results of a partial-wave analysis of the angular distributions for the process γp → ηp over the energy range up to 2 GeV are presented. Reliable estimates of the Breit-Wigner parameters of the S₁₁(1535) resonance, as well as the energy dependence of the real and imaginary parts of the electric dipole amplitude E₀₊ and its phase, are derived from the energy dependence of the regression coefficient a₀(W).     

Probing the mesonic structure of the nucleon by means of exclusive quasielastic pion knockout in (e, e′π) reactions at high energies

By including the Z diagram in an analysis performed in the laboratory frame (instantaneous form of dynamics), the notion of quasielastic pion knockout by protons and electrons [(p, 2p) and (e, e′p) reactions treated in terms of the relevant pole diagrams] is generalized to the relativistic case where a meson is quasielastically knocked out of a nucleon by an electron having an energy of a few GeV. The concept of the wave function is introduced for the pion (and for other mesons), and its relation to the vertex constant G _πNN and the vertex function g _πNN(k ²) is indicated. The spectroscopic factor S _N ^B? is defined as the normalization of the wave function for the meson ?. It is shown by two methods that, under the kinematical conditions of quasielastic knockout that include the condition E _π?m _π (E _π is the energy of the knock-on pion) and the condition that the square Q ² of the virtual pion mass is large, the competing tree diagram is suppressed in relation to the pole diagram (this is not so in the case of pion photoproduction). From data of a p(e, e′π ⁺)n experiment involving longitudinal virtual photons γ _L ^* , the momentum distribution |Ψ _p ^nπ (k)|² of pions in the nucleon is extracted for the first time over the entire range of significant momenta k, and this result is used to determine the cutoff constant Λ_π and the value of S _p ^nπ ≈0.2. The momentum distribution of positive rho mesons in the soft section of the spectrum is determined from experimental data on the process p(e, e′π ⁺)n proceeding through the mechanism ρ ⁺+γ _T ^* → π ⁺ involving transverse photons. A way to determine the momentum distribution of omega mesons through data on the process p(e, e′π ⁰)p is indicated. Two forms of dynamics—instantaneous form and that of light-front dynamics (the latter does not involve the Z diagram)—are compared for the example where the calculations are performed for the spectroscopic factor S _N ^B? .     

F8BINOL, an electronically perturbed version of BINOL with remarkable configurational stability

[structure: see text] Substitution of hydrogens by fluorines at the 5, 5', 6, 6', 7, 7', 8, and 8' positions of BINOL strongly affects distribution of electron density within the biaryl skeleton but has a very small influence on the torsion angle. The most important consequence of this structural alteration is the dramatic increase in configurational stability of homochiral F8BINOL.     

Numerical simulation of the field distribution produced by the SP-40 magnet of the MARUSYA setup and comparison of simulation results with experimental data

In terms of the magnetostatic problem in the differential statement, a mathematical simulation of the 3D distribution of the magnetic field generated by the SP-40 magnet of the MARUSYA experimental setup (Laboratory of High Energies, Joint Institute for Nuclear Research, Dubna) is carried out. The mathematical statement of the direct magnetostatic problem is given. Computational procedures and field calculation algorithms with one vector and two scalar potentials are described. The simulated magnetic field distribution is compared with experimental data for the field of the modified SP-40 magnet with a pole spacing of 0.207 m. The results of this work are used in experimental data processing and are also helpful in simulation of magnetooptic systems.