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Spin Observables in Proton-Nucleus Scattering. Lecture Courses. Chapter One: Spin-Orbit Interactions at Proton Scattering in Nonrelativistic and Relativistic Models



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Spin Observables in Proton-Nucleus Scattering. Lecture Courses. Chapter One: Spin-Orbit Interactions at Proton Scattering in Nonrelativistic and Relativistic Models // New-York: Libmonster (LIBMONSTER.COM). Updated: 08.10.2023 . URL: https://libmonster.com/m/book/download/80/3204 (date of access: 25.02.2024 )

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Reasons for Reading

The lecture courses are intended for students studying experimental nuclear physics and engineering. These lectures could be used as a guide to understanding a number of elements of quantum mechanics, primarily the relation between nonrelativistic and relativistic mechanics. Such a guide, in the author’s opinion, can eliminate the existing gap in the available scientific literature.

 

Opening Paragraph

The proposed lecture courses will consist of five chapters followed by supplements. The list contents will be given at the beginning of each chapter. Part of the lecture material is presented in Russian, and the other part in English. Some short publications with the participation of the author will be added in the supplements.

The lectures are intended as additional material for senior students studying nuclear physics and physical and technical specialties at universities and technical higher educational institutions.

Here, in the preface, we briefly formulate only some approaches for solving a number of physical tasks and focus on particular physical aspects to be discussed in the lectures.

Thus, nucleons, including protons, are known to have both spatial and spin degrees of freedom. It appears that the spin-dependent part of the effective nuclear interaction plays an important role in the determinations of the properties of nuclear excitations.

In a simple representation, in accordance with Dirac’s achievement and the generally accepted convention, the spin of a particle can be set by the ordinary Pauli matrixes.

In a simple interpretation, a picture of the scattering process is that in which one of the two interacting nucleons contained in the initial state belongs to the incident beam (in particular consisting of polarized protons) and strikes the other nucleon in the target nucleus with a certain incident energy Ep. With sufficient Epvalues, to analyze such a process in a simple procedure, a method can be used in which the effective interaction is derived from the free nucleon-nucleus (NN) t matrix based on a phase–shift analysis (proton-nucleus interaction of Love and Franey, also Franey and Love).

In terms of these potentials related to the free NN amplitudes, great achievements have been accomplished in the distorted-wave impulse approximation (DWIA) treatment. In particular, the polarization (spin) observables are essentially determined by the spin dependence of the effective interaction. Therefore, these observables provide an excellent way to check the spin-dependent NN amplitudes.

In the observed experiments, determining incident and scattered polarizations, very important information can be obtained by measuring all the Wolfenstein parameters or, in other words, the polarization transfer coefficients.

Provided that the necessary conditions linked to the physical processes such as distortion of the projectile waves and knock-on exchange are met, certain combinations of the spin-transfer observables can be obtained within the model of Bleszynski et al., thus giving control directly related to individual terms of the effective NN interaction.

Summary

The proposed lecture courses will consist of five chapters followed by supplements. Part of the lecture material will be presented in Russian, and the other part in English. Short publications with the participation of the author will be added to the supplements. The list contents will be given at the beginning of each chapter.

            Chapter One is based on Lecture Course I, Issue 2. It is dedicated to the study of the nonrelativistic Schrödinger equation and its application in the distorted-wave Born approximation (DWBA) and coupled-channels (CC) calculations. The chapter also presents the relativistic model, consisting of a Lorentz scalar potential (Us) and a vector potential (Uv). These potentials are treated in the same fashion as the central potential in the Schrödinger equation.

The standard collective model is obtained by deforming the optical-model potential, using the Schrödinger equation. Similarly, the analysis of proton-nucleus scattering in a purely relativistic way may be based on a phenomenological approach, employing the Dirac equation. Unlike the nonrelativistic approach, in the Dirac formalism, the deformation of the spin-orbit potential appears naturally. In the Schrödinger equation, the spin-orbit potential is introduced as a separate term, which results in the well-known “full Thomas” form for the deformed spin-orbit potential.

Similar results of calculations, using an effective interaction based on the DBHF (Dirac-Brueckner Hatree-Fock) method, are also given. This method characterizes the nuclear mean field by strong, competing vector and scalar fields that together account for both the binding of the nucleons and the large size of the spin-orbit splitting in nuclear states. Medium effects are incorporated through a G-matrix obtained within a Dirac-Brueckner approach to nuclear matter.

The DBHF calculations were run using the DWBA code, as this program allows for finite-range DWIA. Therefore, in the DBHF approach, the mean nuclear potential is expressed in terms of a relativistic scalar and vector fields, and then this potential is used in conventional nonrelativistic analysis based on the DWIA.  Such formalism provides a simple method for incorporating relativistic effects.

The density-dependent effective interaction, derived from a complete set of Lorentz-invariant NN amplitudes, is also discussed. It can be used in a nonrelativistic DWBA formalism. Specific examples of nonrelativistic calculations with the use of density-dependent interaction, such as the Paris-Hamburg (PH) G-matrix, are given to illustrate the role of proton transition densities. They are available from the transition charge densities, measured using electron scattering.

The author provides numerous references to publications, both in Russian and in English, in order to provoke students’ interest to the material and involve them in active reading. Practically the same approach he tested in supervising students’ course works and dissertations / projects while working at the Physics Department of St. Petersburg State University and the Department of Physics and Mathematics of Peter the Great St. Petersburg Polytechnic University.

The lecture courses are intended for students studying experimental nuclear physics and engineering. These lectures could be used as a guide to understanding a number of elements of quantum mechanics, primarily the relation between nonrelativistic and relativistic mechanics. Such a guide, in the author’s opinion, can eliminate the existing gap in the available scientific literature.

Recommended to

The lecture courses may provide some help to students studying nuclear physics.

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The present lectures are aimed at providing a clear explanation of modern experiments related to the spin of the particle. The lectures consider the Dirac approach to the transformation of the existing wave equation (nonstandard Schrödinger equation). This approach consists in the requirement that t…
Published: 09.01.2024
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Anatoli Plavko
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Author(s)A.V. Plavko
Cover Type (if the book was published)Soft Copy
Number of Pages121
Date Published08.10.2023
 
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