Regular Series


Vol. 52 (2021), No. 2, pp. 81 – 169


Coulomb-nuclear Interference in Elastic Scattering: Eikonal Calculation to All Orders of \(\alpha \)

abstract

The Coulomb-nuclear interference (CNI) has recently been used by the TOTEM Collaboration to analyse proton–proton elastic-scattering data from the LHC and to draw physics conclusions. This paper will present an eikonal calculation of the CNI effects performed to all orders of the fine structure constant, \(\alpha \). This calculation will be used as a reference to benchmark several widely-used CNI formulae and to verify several recent claims by other authors.


Double Electron–Positron Pair Production with Two-electron Capture in Relativistic Heavy-ion Collisions

abstract

We calculated the cross section of double electron–positron pair production with two-electron capture for the collisions of Pb\(+\)Pb ions and we did our calculations at LHC energies. We applied a similar methodology for the calculation of bound-free electron–positron pair production. We used perturbation theory and implemented Monte Carlo integration techniques to calculate the lowest order Feynman diagrams. We also compared our double electron–positron pair production with two-electron capture cross-section results obtained in the literature. These calculations may help us to learn more about strong QED.


all authors

S.Yu. Mezhevych, A.T. Rudchik, A.A. Rudchik, K.W. Kemper, K. Rusek, O.A. Ponkratenko, E.I. Koshchy, S.B. Sakuta

\(^{14}\)C(\(^{11}\)B,\(^{10}\)B)\(^{15}\)C Reaction at \(E_{\mathrm {lab}} =\) 45 MeV and the \(^{10}\)B+\(^{15}\)C Optical Potential

abstract

Complete angular distributions including both forward and backward angles are reported for the \(^{14}\)C(\(^{11}\)B,\(^{10}\)B)\(^{15}\)C reaction at \(E_{\mathrm {lab}}(^{11}{\mathrm {B}})\! =\! 45\) MeV for the ground and excited states of \(^{10}\)B and \(^{15}\)C. The experimental data were analyzed within the coupled reaction channels method that included the \(^{11}\)B+\(^{14}\)C elastic scattering channel as well as channels for one- and two-step transfers of nucleons in the coupling scheme. The necessary \(^{11}\)B+\(^{14}\)C optical potential parameters were obtained from previous work, while those for \(^{10}\)B+\(^{15}\)C were deduced from fitting the CRC reaction calculations to the \(^{14}\)C(\(^{11}\)B,\(^{10}\)B)\(^{15}\)C reaction data. Needed spectroscopic amplitudes of transferred nucleons and clusters were calculated within the translational-invariant shell model. The data are well described by neutron transfers, while contributions from two-step transfers were found to be negligible. Recently published global optical potentials for the elastic scattering of the \(^{8,10,11}\)B isotopes were tested as part of the analysis and found to satisfactorily describe this reaction data if the surface imaginary potentials were omitted for both the entrance and the exit channels, and the parameters for volume real and imaginary potentials were slightly modified.


A Local Reduction of the Dirac Equation Applied to the Study of Quark Interactions

abstract

A general procedure of local reduction for the Dirac equation is introduced to study one- and \(n\)-body interacting systems. In the one-body case, we show that the reduction allows for an approximate solution of the Dirac equation, correlating the upper and the lower components of the wave function. The two-body case is studied in more detail. We show that the method prevents from introducing spurious, unphysical states. The reduction is also applied to another relativistic equation. Finally, the method is used to construct a specific model in order to study the charmonium spectrum.


On a Higher-derivative Spinor Theory

abstract

We study a linear spinorial theory for a field \(\psi \) of rest-mass \(m\) in which the Dirac Lagrangian \(L_{0} = \bar {\psi }{\cal D}{\psi }\) is augmented by a higher-derivative term \(L_{1} = r_{0}\bar {\psi }{\cal D}^{2}\psi \), where \({\cal D} = {i}\gamma ^{k}\partial _{k} - m\) and \(r_0\) is a constant with the dimension of length. Defining operators through \(L = \psi ^{+}\hat {L}{\psi }\) and setting \(p_{\kappa } = -{i}\partial /\partial x^{\kappa }\), the velocity of the charge cloud is \(\alpha ^{\kappa } \equiv \gamma ^{0}\gamma ^{\kappa } = - \partial \hat {L}_{0}/\partial p_{\kappa } \equiv {\mathrm {d}}x^{\kappa }/{\mathrm {d}}t\), which commutes with \(x^{\kappa }\), as pointed out by Schrödinger. Therefore, \(\alpha ^{\kappa }\) can be regarded as a coordinate (independent of position \(x^{\kappa })\), to which there corresponds a canonical momentum \(\pi _{\kappa } = - \partial \hat {L}_{1}/\partial \dot {\alpha }^{\kappa }\) that anti-commutes with \(\alpha ^{\kappa }\). We also discuss the high-energy limit valid at radii \(r \lesssim r_{0} \lesssim 10^{-16}\) cm \(\ll 1/m\), where \(\psi \) is approximately massless, and in the static case obeys the Laplace equation \(\Delta \psi \approx 0\). Expansion of \(\psi \) in spherical harmonics shows that a non-vanishing electric charge density \({\cal J}^0 = e\sqrt {-g}\psi ^{+}\psi \) is only finite at the origin \(r = 0\) if \(\psi \) is spherically symmetric, in agreement with experiment.


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