Abstract. The Parentage Scheme of Summarization to the N-body symmetrized basis construction [1], necessary for the description of the structural characteristics and decay reactions of the hypernuclear and nuclear systems with arbitrary amount of particles, is applied to the solution of five-body problem in hypernuclear physics. Hypernucleus ݁ܪ ఒ ହ as a system of four nucleons and one hyperon is investigated by the use of the Hyperspherical Function Method in momentum space. The dependence of the structure characteristics and wave functions on the types of nucleon-nucleon and hyperon-nucleon interaction potentials is studied. Mean square ߣ − ܪ ଷ and ߙ − ߣ distances and the binding energies for the ݁ܪ ସ and ݁ܪ ఒ ହ are obtained.
Parentage Scheme of Summarization (PSS) to the N-body symmetrized basis construction necessary for the description of the structural characteristics and decay reactions of the hypernuclear and nuclear systems with arbitrary amount of particles is introduced. Proposed method allows to construct N-particle symmetrized hyperspherical functions on the bases of Nparticle hyperspherical functions symmetrized with respect to N−1-particles by the use of the Kinematic Rotation Coefficients (KRC) related with the (N-1)-th and N-th particle permutations. The main problem that arises when investigating dynamics of few-body systems in physics is the problem of kinematic rotations under particle permutations. When number of particles increases, kinematic rotations include not only particle permutation but also transitions between different possible configurations, and mathematical calculations using complex general formula become impossible. Moreover, no general formula exists for systems with more than four particles. In order to solve kinematic rotation problem for N-particle systems, the recurrence method of determination of the KRC is applied. According to this method, the initial coefficients with the lowest quantum numbers are calculated by solving the overlap integral analytically, wave functions with arbitrary quantum numbers are expanded in terms of the basic hyperspherical functions, and the kinematic rotations of the obtained expansion are performed with the use of already known coefficients with the lowest quantum numbers. Significant advantage of the recurrence method is that no principal difficulties arise when increasing number of particles. Furthermore, recurrence relations contain numerical coefficients that are easy to evaluate by substituting appropriate quantum numbers. The problem of symmetrization of N-Body hyperspherical functions is solved by the use of the PSS. A construction scheme is given for the symmetrized hyperspherical basis in (4+1) and (5+1) configurations. The relations between parentage coefficients and the KRC of the basic hyperspherical functions are obtained. Parentage coefficients for N-Body systems are introduced. It is demonstrated that no principal difficulties arise when increasing number of particles.
The method of object recognition is described by the example of objects of amplitude transparent type. The method is to obtain a photoanisotropic copy of object images on polarization-sensitive material. At consequent illumination of the photoanisotropic copy with a parallel circularly polarized beam of nonactinic light, the transmitted light becomes elliptically polarized. It is shown that the characteristics of the summary polarization ellipse in the Fraunhofer diffraction region uniquely identify the given object. The real-time determination of the characteristics of the summary polarization ellipse is made by means of diffraction gratings of anisotropic profile and by comparison of these characteristics with etalon from the database.
. The binding energy and the structure of superheavy hydrogen-Λ are studied within the method of hyperspherical harmonics. The 6 Λ H hypernucleus is considered as a six body system consisting of particle and five nucleons.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.