We discuss elastic ed scattering beyond the Born approximation. The reaction amplitude contains six generalized form factors, but only three linearly independent combinations of them (generalized charge, quadrupole and magnetic form factors) contribute to the reaction cross section in second order perturbation theory. We examine the two-photon exchange and find that it includes two types of diagrams, where two virtual photons are interacting with the same nucleon and where the photons are interacting with different nucleons. It is shown that the two-photon exchange amplitude is strongly connected with the deuteron wave function at short distances.PACS numbers: 13.40. Gp,21.45.Bc,25.30.Bf I. INTRODUCTIONThe study of electron scattering on the nucleon and the light nuclei provides a convenient tool to study the structure of strongly interacting systems. Due to the smallness of the fine structure constant α ≈ 1 137 , one may expect that the Born approximation (one-photon exchange, OPE) should describe such processes with an accuracy of a few percent. Nevertheless, JLab polarization measurements of G p, together with their theoretical analysis [4-7], show that higher order perturbative effects, such as two-photon exchange (TPE), can strongly affect some observables of the elastic electron-nucleon scattering.Also for more complicated hadronic systems, like the deuteron, 3 He, 4 He, etc., TPE should contribute. Thus for precise studies of these nuclei a quantitative theoretical investigation of TPE effects is important; until now only a few estimates have been done of the contribution of TPE [8][9][10][11][12][13].The aim of this paper is to estimate the TPE amplitude for ed-scattering in the framework of semi-relativistic calculations, with deuteron wave functions from "realistic" NN potentials.The paper is organized as follows. In Sect. II we study the general structure of the reaction amplitude beyond OPE and define six independent generalized form factors which determine the amplitude. We show that only three linearly independent combinations of these generalized form factors contribute to the cross section in second order perturbation theory. We call the corresponding combinations of the form factors generalized charge, quadrupole and magnetic form factors. These generalized form factors are computed in Sect. III. Sect. IV contains numerical results and a brief discussion. II. KINEMATICS AND DEFINITIONSThe electron and deuteron momenta in the initial and final states of elastic ed scattering are denoted by k, k ′ and d, d ′ , respectively; q = k − k ′ is the transferred momentum; M and m are deuteron and nucleon masses; actual calculations will be done with m ≈ 1 2 M . All calculations are done in the Breit frame, where the deuteron has the same energy E d in the initial and final * Electronic address: kobushkin@bitp.kiev.ua

We have derived an analytical trace formula for the level density of the Hénon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has the correct limit to the standard Gutzwiller trace formula for the isolated periodic orbits far from all (critical) symmetry-breaking points. It continuously joins all critical points at which an enhancement of the semiclassical amplitudes occurs. We found a good agreement between the semiclassical and the quantum oscillating level densities for the gross shell structures and for the energy shell corrections, solving the symmetry breaking problem at small energies.

Structure functions and polarization observables in elastic scattering of longitudinally polarized electrons on polarized deuterons are considered within the approximation of one-photon plus two-photon exchange. It is shown that the contribution of two-photon exchange to the generalized deuteron structure function A is of the order of few percent, while the contribution to the generalized structure function B is of the order of 10%-20%. We have found that the components T 20 and T 21 of the tensor analyzing power are mainly determined by one-photon exchange but that T 22 is mainly determined by interference between one-photon exchange and two-photon exchange. We have also considered the polarization observables T 11 , C 21 , and C 22 , which are proportional to the imaginary part of the reaction amplitude and vanish in the framework of one-photon exchange.

The saddle point method is applied to the statistical integral of the Grand Canonical Ensemble for the cases of one-component and two-component van der Waals gas. This made it possible to obtain the state equation and corrections to the pressure and density of the final statistical system. These contributions, taking into account the realistic effective potential, make it possible to take into account the finite dimensions of the system and, as expected, can be used, in particular, in the case of a nuclear fireball that occurs in high-energy nucleus-nucleus collisions. The corrections depending on the size of the system were compared with the corresponding fluctuations. These corrections become insignificant at the thermodynamic boundary, where, according to statistical physics, the difference between the observed thermodynamic quantities obtained in different statistical ensembles disappears. Taking into account modern estimates of the sizes of mesons and nucleons, as well as realistic estimates for the potentials of their effective interactions, formulas for pressure with a transparent nonrelativistic constraint are obtained. It is expected that they can be used to analyze experimental data on the quantitative characteristics of the yield of particles of various types in the final state from the final stages of the freezeout and to determine the critical parameters of the system in high-energy nucleus-nucleus collisions.