Quantum-field aspects of pion interaction with lightest nuclei

Abstract

Recent development in the quantum field theory approach to the pion-deuteron and pion-aHe (3 H)-interaction processes is reviewed. Some general features of the Bethe-Salpeter and Low-type equations for the processes under study derived in the last few years in the literature are discussed. At present the fundamental importance of studying the pion-deuteron or more generally the pion -- two-nucleon interaction is well understood. The nNN system is often considered as a "theoretical laboratory" for investigating different aspects of the pion-nucleus interaction. In the first stage of investigation of pion-deuteron scattering, carried out predominantly in the energy range 0--300 MeV, the multiple scattering theory has been used, where the many-channel character of the problem is neglected, particularly, the deuteron disintegration channel and the channel of pion absorption by a deuteron are neglected. The necessity of the account of such channels and relativity of pions in the energy region under consideration leads to the use of Faddeev integral equations or their generalization in the case where the relativistic kinematics of pions and pion absorption or emission by a two-nucleon system are taken into account. This type of the theory [1, 2] for the coupled nNN and NN-systems formulated in the framework of the general coupled channel theory for the pion-nucleous interaction [3] by using the projection operator method [4] is expounded (with some generalization) in [5], where other references to the subject can be found. As regards the problem of pion interaction with the simplest (after deuteron) nuclei SHe and 3H from the theoretical point of view it is primarily interesting as a tool for verifying an understanding of the dynamics of the pion-nucleus interaction resulting from an investigation of the pion two-nucleon interaction. But it is clear that study of the zc 3He(3H)-interaction per se is also interesting not only for understanding the dynamics of these processes but to get additional information on the three-nucleon forces. In [6] a successful attempt was made to generalize the multichannel theory of nNN and NN systems [1, 2] to the case of pion interaction with the 3Henucleus. It is worth-while to note that in spite of a sufficient generality of these considerations the antiparticle degree of freedom is neglected and the crossing symmetry of the problem is not taken into account. The importance of allowing for this symmetry was demonstrated in [7] taking ~-12C-scattering at low energies as an example. As to the nN-scattering, the importance of allowing for crossing-symmetry is well known from the Chew-Low theory [8]. The two aforementioned effects are of quantum-field origin and therefore can be taken into account in the framework of the quantum field theory approach to the problem. Some general results obtained using this approach are discussed below. A consistent quantum-field theoretical approach was used in [2] to derive a set of equations for the reactions