Pion photoproduction on nucleus with two-nucleon emission
Introduction
In nuclear physics, one of the important problems is the study of the nuclear structure at short and medium inter-nucleon distances, where the effects of the non-nucleon degrees of freedom in nuclei appear. The short- and middle-range structure of nuclei is defined by the short- and middle-range components of the nucleon–nucleon potential, which lead to the high-momentum components of the nuclear wave function. These wave function components have a low probability. However, there are nuclear processes which in the selected kinematic regions are almost completely caused by these components of the wave function, which allows the various manifestations of the non-nucleon degrees of freedom in nuclei to be studied.
As is known, the two-nucleon knockout electromagnetic processes are a powerful tool for studying the short- and middle-range dynamics of the interaction between nucleons in nuclei.
In the framework of the independent particle model, the knocking-out from the nucleus of two nucleons can occur by means of the two-body operators corresponding to the meson exchange and isobar currents.
Another two-nucleon knockout mechanism is based on the nucleus model, in which the correlated pairs of nucleons in the nucleus are taken into account. This model is beyond the framework of the independent particle model. The correlation of nucleons in the nucleus is described by the correlation function, which reflects the structure of the nucleon–nucleon potential. The process of knocking out nucleons in this model is due to the action of the single-particle operator. As a result of knocking out either nucleon, the second nucleon of the correlated pair can move to a free state.
Today these two approaches are widely used in the analysis of the knockout reactions, which is oriented mainly to the study of short-range correlations induced by the repulsive part of the nucleon–nucleon potential at small distances [1].
Another type of two-particle correlation in the nucleus is associated with the virtual transitions in the ground state of the nucleus. The interaction of the incident particle with the correlated ΔN system may also lead to the knockout of two nucleons. These ΔN correlations correspond to the middle-range components of the nucleon–nucleon potential.
The role and relevance of these three competing processes can be different in different reactions and kinematics. The peculiarity of manifestations of the ΔN correlations in nuclear reactions consists in the fact that the knocking-out of the Δ-isobar causes production of a pion as a result of decay. Therefore, because of the particle type in the final state, the reactions are more sensitive to the manifestations of the correlation of this type.
This article presents the analysis of the process, taking into account the ΔN correlations in the ground state of the nucleus. The method of analysis is an extension of the approach, developed in [2], [3] for the process at large momentum transfer, to pion photoproduction with the two-nucleon knockout. The direct and exchange reaction mechanisms are considered. The proposed reaction model was first tested in the analysis of the 16O reaction data [4].
Section snippets
Cross-section of the reaction
The differential cross-section reaction can be written in the laboratory system of coordinates as where (, ), (, ), (, ), (, ), and (, ) are the four-momenta of the photon, pion, two nucleons, and the residual nucleus B; is the mass of the nucleus A; is the transition matrix element from the initial state, which includes the photon and the nucleus A, to the final, including the pion, two
The basic assumptions of the model
We analyse the reaction in the framework of the formalism developed in [5] for the description of the ground state of nuclei, which previously we used in [2], [3] for considering the reaction – pion photoproduction with the emission of a single nucleon. According to [5], baryons bound in the nucleus, in addition to the space r, spin s, and isospin t coordinates , are also characterized by the intrinsic coordinate . An eigenfunction of the
Density matrices
In this approach, according to (3) and (5), all information about the structure of the nucleus and the mechanism of the reaction is contained in the two- and three-body density matrices.
The two-particle density matrix (4) contained in the expression for the square of the modulus of the direct amplitude (3) of the reaction was also used to describe the exchange mechanisms of the pion production in the reaction [2]. We are interested in the isobar
Analysis of experimental data
At present, the experimental data of the reaction are practically absent. Therefore, to compare the predictions of our model with experimental data, we will use the reaction measured in the kinematic region where, according to [8], the pion production occurs in the reaction with the emission of two nucleons. This kinematic region is characterized primarily by the large momentum transfers to the NB system, consisting of the free nucleon and the residual nucleus.
We
Signatures of ΔN correlations
The experimental data considered in the previous section are averaged over a large number of the kinematic variables and include the contribution of numerous reaction mechanisms. Such data provide an empirical estimate of the probability of transition in the ground state of the nuclei. For example, this was done in the work [4]. However, such data are not sensitive to the individual components of the used reaction model. Here we will consider the manifestations of the ΔN correlations in
Conclusion
We have presented a model of the pion photoproduction on the nucleus with the emission of two nucleons in the reaction. In this model we have moved beyond the standard shell-model considering ΔN correlations in the nuclear wave functions, which are caused by the virtual transitions in the ground state of the nucleus. The main ingredients of the model are the two- and three-particle density matrices and the transition operators and . The direct and exchange reaction
Acknowledgements
This work was partially supported by the Program of Russian Ministry for Science and Education “Nauka” and A.N.T. was supported in part by the RFBR Grant under number 12-02-00560.
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