Teaching Documents by Anatoli Plavko
ATLAS of Data 2: Polarization Phenomena in Inelastic Scattering of 20 MeV Protons from Nuclei near N = 50, 2025
The materials presented below in the form of an atlas of data (called Atlas of Data 2) are devote... more The materials presented below in the form of an atlas of data (called Atlas of Data 2) are devoted to the manifestation of the spin of particles in their inelastic scattering from atomic nuclei. A number of analytical studies of physical phenomena observed in experiments are also discussed. Atlas of Data 2 can be considered as an additional supplement to the author’s Lecture Course “Spin Observables in Proton-Nucleus Scattering” published in parts online. The Atlas is the first part (⸹ 1) of the Survey of experimental data that the author previously submitted to the Department of Physics, Bryn Mawr College, USA. In the future, the author intends to present other atlases with the inclusion of subsequent paragraphs of the Survey. To this will be added separate appendices, where attention will be focused on the main issues, or on the presentation of new important results that have appeared since the publication of the Survey.
Spin Observables in Proton-Nucleus Scattering. ATLAS of Data., Apr 8, 2025
The author’s lecture courses available online seem to be overloaded with demonstration materials.... more The author’s lecture courses available online seem to be overloaded with demonstration materials. Therefore, some of these materials, especially those relating to various experiments, are presented here separately in the form of an ATLAS that can be considered as a supplement to the lectures.
Lecture Courses. Spin observables in proton-nucleus scattering. Chapter Four. Part 1: Nuclear forces in double inelastic scattering of polarized protons, 2024
The values of the normal-component spin observables, Ay, P and, DNN supplemented here with the do... more The values of the normal-component spin observables, Ay, P and, DNN supplemented here with the double-scattering spin (polarization) transfer coefficients Dij in the (p,p’) reactions. Measurements with the polarized beam, normal to the scattering plane, usually provide the cross-section dϭ/dΩ (θ), the analyzing power Ay(θ), and the DNN (θ) polarization transfer (PT) at certain angles. The (p,p’) measurements with in-plane polarization have yielded the transfer coefficients DSS, DSL, and DLL, DLS. Accordingly, the subscripts L and S refer to polarization along or perpendicular to the proton momentum, with the first subscript indicating the incoming momentum, and the second – the outgoing momentum. The coefficient Dij appears to be quite sensitive to the effective interaction and its modification in the nuclear medium. Within the framework of the plane-wave approximation, the observables are divided into the so-called polarized cross-sections. To construct them, we used combinations of the polarized transfer coefficients Dij within the model of Bleszynski et al. Under certain conditions, some particular combinations of the scattering observables can be attributed to specific (spin-dependent) amplitudes of the effective interaction. The lectures demonstrate how the polarization observables, acquired in the (p,p’) reactions, can be determined by the spin dependence of the nucleon-nucleon (NN) interaction. Thus, the spin-transfer parameters can be conveyed by simple expressions in the plane-wave impulse approximation (PWIA). As a result, the diagonal Dij can be presented through the C, B, E, and F amplitudes in the NN interaction (as Moss has shown). The studies of Bleszynski et al. are of great importance as they have established certain combinations (Dk) in terms of the Dij. When these conditions are met, the values Dk may appear sensitive primarily to an individual component in the NN interaction. Some of our works published in English and Russian are presented in Supplement 1.
Spin Observables in Proton-Nucleus Scattering. Chapter Three: Formalism for Polarization Transfer Experiments in Nuclear Physics. , 2024
The lectures demonstrate that the density matrix is a compact method of specifying polarization. ... more The lectures demonstrate that the density matrix is a compact method of specifying polarization. Accordingly, we consider the density formalism of the beam, and show that the density matrix of the beam is a very convenient tool for describing proton scattering and polarization in nuclei. Based on this formalism, we obtain expressions practically for all observed quantities that we managed to extract in the experiment. We briefly describe methodology of obtaining triple scattering parameters, introduced by Wolfenstein for the description of nucleon-nucleon and nucleon-nucleus scattering. In this description, we are based primarily on the formalism developed, summarized and modeled by Ohlsen after that of Wolfenstein. Some of the represented theoretical aspects are illustrated in three accompanying supplements.
Polarization Transfer Coefficients for (p,p’) reactions. Tutorial. Коэффициенты передачи поляризации для реакций (p,p’). Учебное пособие., 2023
We report systematized measurements and the corresponding analysis of polarization transfer for t... more We report systematized measurements and the corresponding analysis of polarization transfer for the 12C 12C reaction to strong isoscalar and isovector states in 12C, induced by 150–500 polarized protons. The spin observables and their combinations , proposed in the model of Blezynski et al., are used. The comparison of the measured with the corresponding calculated , using zero-range treatment (code LEA) and exact finite-range calculations (DWBA program), made it possible to identify the presence of a contribution associated with exchange amplitudes. It is an important circumstance since, according to Love and Comfort, a qualitative theoretical understanding of the sources of nonlocality is currently unavailable. However, it is the presence of such a contribution that can, in principle, significantly change the exchange part of proton-induced reaction calculations. Therefore, the main task we set here is to find out whether the data can establish the presence of nonlocal or exchange features of the interaction. Hence, it is important to understand whether the could prove helpful in discriminating between different details of the effective NN interaction having different nonlocal behaviors. Ultimately, if this aspect of the spin-dependent part of the effective NN interaction were somehow evaluated, or at least calibrated, then the reaction could be used as a more quantitative probe of the other interesting modes of nuclear excitation. Chapter II (the Supplement to Lecture Course III, issue 2) considers approaches to qualitative assessment of the impact of the local and nonlocal content of the effective proton-nucleus interaction on polarization transfer in the reactions with various types of excitation in the nucleus.
Analyzing powers vary in their oscillation characteristics. In the case of normal-parity excitati... more Analyzing powers vary in their oscillation characteristics. In the case of normal-parity excitations, this characteristic can additionally confirm calculated amplitudes. We can also assume that small analyzing powers generally suggest abnormal-parity amplitudes. Indeed, there is an excitation showing that small analyzing powers confirm the abnormal-parity character of these transitions.
А.В. Плавко. Спин-орбитальные взаимодействия при рассеянии протонов в нерелятивистских и релятивистских моделях. Курс лекций I. Spin-Orbit Interactions at Proton Scattering in Nonrelativistic and Relativistic Models. Online Lecture Course I., 2019
The lectures consider nonrelativistic and relativistic formalism in inelastic proton scattering; ... more The lectures consider nonrelativistic and relativistic formalism in inelastic proton scattering; interaction of nucleons in free space; application of nucleon interaction formalism to the process of their scattering from nuclei; the method of coupled channels; relations between the formalism of the Schrödinger and Dirac equations; transformation of the relativistic equation into the “Schrödinger equivalent”; comparison of analytical approaches in the relativistic conception of inelastic proton scattering; the deformation model in the distorted-wave method based on relativistic and nonrelativistic formalisms; the optical model of the nucleus; application of various elements of the above discussed formalism to the analysis of experimental data on inelastic proton scattering.
With all the approaches, special attention is paid to the spin-orbit interaction and its origin,
А.В. Плавко. Курс лекций II. Спин частицы в процессах движения. Часть А: Переход от классической физики к квантовой, 2019
Part A of Lecture Course II considers the following topics: stationary and nonstationary formalis... more Part A of Lecture Course II considers the following topics: stationary and nonstationary formalism of the Schrödinger equation; the Klein–Gordon–Fock equation; transition from classical physics to the Lorenz transformations in the Dirac theory.
The present lecture course is a continuation of Lecture Course I (also available on this site).
Плавко А.В. Нерелятивистский и релятивистский формализм в рассеянии протонов на ядрах. Часть В.
Part B of the online Course “Nonrelativistic and Relativistic Formalism in Proton Scattering from... more Part B of the online Course “Nonrelativistic and Relativistic Formalism in Proton Scattering from Nuclei” (lectures 8-10) is the continuation and development of the previously published lectures of Parts A and B. It considers the specifics of equations studied, analytical approaches in relativistic formalism in elastic proton scattering, matrixes in relativistic formalism, and deformation models in the distorted waves method based on relativistic and nonrelativistic formalism
Fundamentals of Non-Relativistic and Relativistic Formalism in Proton Scattering from Nuclei. Lectures, part B (1-7).
The present publication (in Russian) continues a series of lectures for students of Physics Depar... more The present publication (in Russian) continues a series of lectures for students of Physics Departments of universitues on non-relativictic and relativictic formalism at proton scattering from nuclei, thus covering the gap in the available textbooks.
On Nonrelativistic and Relativistic Formalism in Proton Scattering from Nuclei. Part A. / О нерелятивистском и релятивистском формализме в рассеянии протонов на ядрах. Курс лекций (онлайн). Часть А., 2018
The present course of lectures is aimed at senior students. specializing in nuclear physics and e... more The present course of lectures is aimed at senior students. specializing in nuclear physics and engineering. The lectures may serve as a tool to learn about quantum mechanics, nonrelativistic and relativistic, and thus cover the gap in the available textbooks.
Papers by Anatoli Plavko
Physics of Atomic Nuclei, 2006
The experimental energy dependence of the differential analyzing power for 5 − 1 , T = 0 and 6 − ... more The experimental energy dependence of the differential analyzing power for 5 − 1 , T = 0 and 6 − 1 , T = 1 levels in the 28 Si nucleus is compared with the results of the calculations based on the DWBA-91 code. Information obtained for the nuclear structure from an analysis of inelastic scattering is discussed.
Study of the (p,p') and (p,d) reactions with polarized protons on isotopes of sulfur and some other light and intermediate nuclei
Experimental data obtained previously on (p,p') and (p,d) reactions with polarized protons on... more Experimental data obtained previously on (p,p') and (p,d) reactions with polarized protons on /sup 32/S, /sup 34/S, /sup 92/Mo, /sup 92/Zr, /sup 40/Ca, / sup 64/Ni, /sup 28/Si, /sup 16/O, /sup 12/C, /sup 31/S, and /sup 33/S were anal yzed and differential cross sections and angular distribution of the asymmetry of the proton inelastic scattering were determined. (JSR)
ELASTIC AND INELASTIC SCATTERING OF 6-MeV PROTONS ON $ sup 59$ Co AND THE EXCITED-CORE MODEL
ELASTIC AND INELASTIC SCATTERING OF 6-MeV PROTONS ON $ sup 59$ Co AND THE EXCITED-CORE MODEL
ELASTIC AND INELASTIC SCATTERING OF 6-MeV PROTONS ON $ sup 59$ Co AND THE EXCITED-CORE MODEL
Some nonconforming finite elements for the plate bending problem Revue française d'automatique, i... more Some nonconforming finite elements for the plate bending problem Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, tome 9, n o 1 (1975), p. 9-53. <http://www.numdam.org/item?id=M2AN_1975__9_1_9_0> © AFCET, 1975, tous droits réservés. L'accès aux archives de la revue « Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/
ELASTIC AND INELASTIC PROTON SCATTERING ON $sup 24$Mg, $sup 25$Mg, AND $sup 26$Mg
ELASTIC AND INELASTIC SCATTERING OF 24.5-MeV POLARIZED PROTONS BY $sup 32$S AND $sup 34$S
Bulletin of the Russian Academy of Sciences: Physics, 2012
The diagonal coefficients of spin transfer D ii in the small angle inelastic scattering of polari... more The diagonal coefficients of spin transfer D ii in the small angle inelastic scattering of polarized protons with the excitation of the two lowest 1 + levels in 12 C are analyzed. The isoscalar (T = 0, E* = 12.71 MeV) and isovector (T = 1, E* = 15.11 MeV) transitions are considered. The coefficients D ii are cal culated within DWBA using different effective nucleon-nucleon (NN) interactions between an incident pro ton and the nucleons of the nucleus. We consider the Franey-Love interaction and the Geramb effective interactions based on the Paris NN potential, and also the effective NN potential based on the chiral pertur bation theory, etc. The impact of the wave function antisymmetrization is studied from the coefficients D ii in a system that includes a projectile and nucleons of the nucleus, along with the impact of other effects.
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Teaching Documents by Anatoli Plavko
With all the approaches, special attention is paid to the spin-orbit interaction and its origin,
The present lecture course is a continuation of Lecture Course I (also available on this site).
Papers by Anatoli Plavko