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.

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 has been 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.

This Supplement considers approaches to qualitative assessment of the impact of the local and nonlocal content of the effective proton-nucleus interaction on polarization transfer in  reactions with various types of excitation in the nucleus.

In this Supplement, we concentrate on excitations having densities of a similar shape and analyze normal states with various spins and parities. This approach allows us to focus more on the reaction mechanism and the components of nuclear interaction.

For the study, we have selected a series of excitations characterized by a collective state, i.e. those having a symmetric single-lobed density peaked at the nuclear surface. Such a radial shape also applies to the proton transition density, unfolded from a model-independent analysis of the (e, e’) data. The neutron transition density, deduced in one way or another, in general, should also be similar in surface geometry.

 In order to test the shapes of transition densities, we primarily focused on differential cross sections. Indeed, it is known that the differential cross section is proportional to the square of the form factor and, consequently, is especially vulnerable to uncertainties in nuclear structure. On the other hand, however, in the case of significant proton energies (e.g., 800 MeV), we observe a strong diffractive nature of the scattering, which persists over five orders of magnitude in the inelastic excitation. This requires particularly high accuracy in experiments, when identifying scattering angles, for example. In this regard, the author is especially grateful to the coordinator of experimental works at LAMPF, J. B. McClelland, for detailed consultations on the subject of the experiments under consideration, directly at the spectrometer.

The Chapter consists of two sections. The first section (in Russian) is devoted to theoretical studies of proton spin observables in reactions. The second section (in English) deals with experimental measurements and potential combinations of polarization transfer coefficients. Different types of DWIA calculations reported here help to identify the role of nucleon-nucleus kinematics, important for understanding reaction mechanisms.

In polarized proton scattering, it is important to understand how the direction and/or magnitude of proton polarization change during this process. Wolfenstein posed a similar question and then consistently formulated the necessary theory, or at least, gave a masterful review of the corresponding formalism pertaining mainly to the NN problem. According to Ohlsen, Wolfenstein developed for these purposes the general density matrix formalism in elegant and readable form.

In the Chapter presented below, we are mainly based on the Wolfenstein approach modernized by Ohlsen. The latter, according to his review, partially summarized this formalism and, in fact, modeled it after that of Wolfenstein.

Further development of the understanding of this physical process came with the introduction of the model of Bleszynski et al. that represented a particular convenient set of observables expressed in terms of linear combinations of the Wolfenstein parameters. These combinations, in principle, can directly relate to individual terms in the effective NN interaction, but only, of course, when they meet clearly formulated model conditions.

Supplement No. 1, attached to the first (theoretical) section, demonstrates specific applications of the model of Bleszinski et al. to experimental and calculated data in the process of scattering.

Supplement No. 2 provides examples demonstrating the influence of density nuclear characteristics on a series of spin observables.

In Supplement No. 3, we consider processes of proton scattering from nuclei, whose structure is usually represented as formations near or at the N = 50 shell closure. We continue difficult research in an area where numerous experimental and theoretical techniques have already been applied. Here we consider possibilities and uncertainties brought by different scattering models.

Such a joint representation should more clearly represent the physical picture of the observed polarization phenomena.

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