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.

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.

Considered are examples when the Dirac equation is reduced to a Schrödinger-like one with constraints, including only the upper component of the Dirac wave function. Such a transformation is often defined as the “Schrödinger-equivalent potential”, although some researchers prefer to term it the Dirac-equation-based (DEB) optical potential.

Such a potential can be deformed to obtain a transition operator ΔU_DEB to use it in 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 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 (U_s) and a vector potential (U_v). 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.

The lecture courses are intended for students studying experimental nuclear physics and engineering.