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In this paper, we present a detailed analytical computation of the triple differential cross sections, in the first Born approximation, for the relativistic electron-impact ionization of hydrogen atom in the metastable 2S-state in the symmetric and asymmetric coplanar geometries. The process is investigated by using the relativistic Dirac-formalism where the effects of spin and relativity are taken into account. It is shown that the nonrelativistic limit is accurately reproduced when applying low incident kinetic energies. At high energies, relativistic and spin effects are found to significantly affect the triple differential cross sections. The numerical results obtained for the triple differential cross section are compared with some other theoretical results in the nonrelativistic regime for asymmetric coplanar geometry. For this particular process and in the absence of any experimental data and theoretical models at high energies for the triple differential cross sections, the results of our calculated relativistic total cross section are compared with available theoretical and experimental results. We hope that the present study will provide significant contribution to future experiments.

In principle, this paper suggests powerful laser technology as a promising instrument that can be experimentally useful to control the lifetime and branching ratio for an unstable particle decay. In a recent paper [ arXiv:2101.00224 ], we calculated theoretically the W − -boson leptonic decay ( W − → l − ν l ) in the presence of a circularly polarized laser and we showed that the laser significantly contributed to the diminution of the leptonic decay rate. In this paper, as a continuation of the previous one, we mainly deal with the theoretical calculation of the W − -boson hadronic decay ( W − → q q ′ ) and we combine the analytical results obtained in both papers to examine the effect of an intense laser, in terms of its field strength and frequency, on the three measurable quantities in W − -boson decay (total decay rate, lifetime and branching ratios). It was found that the laser has notably contributed to the reduction of the total decay rate leading to a longer lifetime. Most importantly, the two branching ratios (one for leptons and the other for hadrons) are affected (increased or decreased) by the presence of a strong external electromagnetic field. Combined together, these two complementary works may provide an in-depth and comprehensive study that would be useful for any experimental investigation in the future.

In the centre of mass frame, we have studied theoretically the Z -boson resonant production in the presence of an intense laser field via the weak process e + e − → μ + μ − . Dressing the incident particles by a Circularly Polarized laser field (CP-laser field), at the first step, shows that for a given laser field’s parameters, the Z - boson cross section decreases by several orders of magnitude. We have compared the Total Cross Section (TCS) obtained by using the scattering matrix method with that given by the Breit-Wigner approach in the presence of a CP-laser field and the results are found to be very consistent. This result indicates that Breit-Wigner formula is valid not only for the laser-free process but also in the presence of a CP-laser field. The dependence of the laser-assisted differential cross section on the Centre of Mass Energy (CME) for different scattering angles proves that it reaches its maximum for small and high scattering angles. At the next step and by dressing both incident and scattered particles, we have shown that the CP-laser field largely affects the TCS, especially when its strength reaches 1 0 9 V . c m − 1 . This result is interpreted by the fact that heavy interacting particles require high laser field intensities to affect the collision’s cross section.

The Lie symmetry method is applied, and exact homotopic solutions of a non-linear double-diffusion problem are obtained. Additionally, we derived Lie point symmetries and corresponding transformations for equations representing heat and mass transfer in a thin liquid film over an unsteady stretching surface, using MAPLE. We used these symmetries to construct new (Lie) similarity transformations that are different from those that are commonly used for flow and mass transfer problems. These new (Lie) similarity transformations map the partial differential equations of a mathematical model under consideration to ordinary differential equations along with boundary conditions. Lie similarity transformations are shown to lead to new solutions for the considered flow problem. These solutions are obtained using the homotopy analysis method to analytically solve the ordinary differential equations that resulted from the reduction of considered flow equations through Lie similarity transformations. With the aid of these solutions, effects of various parameters on the flow and heat transfer are discussed and presented graphically in this study.

In the framework of the first Born approximation, we investigate, in the presence of a circularly polarized electromagnetic laser field, the double effect of Coulomb and anomalous magnetic moment (AMM) on the scattering of electron by a fixed atomic nucleus. In this approximation, the initial and final states of the electron are described by the relativistic Coulomb Dirac–Volkov wave functions with AMM effect. For convenience, we choose the origin of the Laboratory coordinate system at the centre of the fixed nucleus presenting a classical Coulomb potential. Both AMM and Coulomb effects on the incident and scattered electrons have affected the relativistic differential cross section. At high energies of the incident electron, our explored numerical results give the predominance of the AMM effect over that of Coulomb. The behavior of the differential cross section, as a function of the electric field strength as well as the laser frequency, is presented.

Darwin wave functions, as a quasi-relativistic states describing the hydrogen atom, are used to calculate the differential cross section for inelastic excitation of 2p state hydrogen atom by electronic impact in various electron energy regions. The use of these wave functions gives interesting results so long as the condition $$z/c\ll 1$$ is verified. The incident and scattered electrons are described by a free Dirac spinor. Relativistic spin effects are taken into account explicitly via the spinorial part. The computed results, in the first Born approximation, are given and discussed by analogy with the non-relativistic regime and the relativistic $$1s\rightarrow 2s$$ . They are also compared with some other available theoretical models and with the experimental results of Williams (J Phys B At Mol Phys 14:1197, 1981). The general rule of optically allowed and forbidden transitions is also respected.

This work aims to study theoretically the electron-proton scattering for initially spin-polarized electrons in the presence of a circularly polarized electromagnetic field. Using the first Born approximation and the Dirac-Volkov states for dressed electrons, we derive an analytic expression for the differential cross-section with the help of the spin-helicity formalism. Meanwhile, a well-known concept of spin-flip and spin non-flip differential cross sections is applied. The influence of the electromagnetic field on the degree of polarization of the scattered electron is investigated, and the effect of electron spin polarization is examined. We found that the initial spin of the electron can be affected depending on its kinetic energy during the scattering process. This work is a continuation of a recent paper in which we studied the unpolarized electron-proton scattering in the presence of a laser field (Dahiri, et al., Laser Phys. Lett. 18 (2021) 096001).

In the framework of Higgs triplet model (HTM), we study the pair production process of doubly charged Higgs bosons via $e^{+}e^{-}$ annihilation in the presence of a laser field with circular polarization . We begin our work by presenting the theoretical calculation of the differential cross section in the centre of mass frame including both $Z$ and $\gamma$ diagrams. Then, from the numerical analysis of the production cross section's dependence on the laser field parameters, we have shown that the laser-assisted total cross section decreases as far as the electromagnetic field intensity enhances or by decreasing its frequency. Finally, we analyze the variation of the total cross section versus the mass of the doubly charged Higgs boson by fixing the laser field parameters and the centre of mass energy, and we have found that the order of magnitude of the cross section decreases as long as $M_{H^{\pm\pm}}$ increases., Comment: 18 pages, 6 figures

In this study, we have investigated the two-body hadronic decay of the charged kaon, $ K^{+}\rightarrow\pi^{+}+\pi^{0} $, in the presence of a laser field with circular polarization. We have derived, by analytical techniques, the laser-assisted decay width and the branching ratio of the charged kaon decay via the two-body hadronic channel. We have also taken into consideration the impressive results obtained for the laser-assisted charged kaon decay via the leptonic mode in order to understand more clearly the effect of the laser field on the quantities related to the charged kaon decay such as the decay width, the branching ratio and lifetime. A precise comparison of the ratios of hadronic to muonic decay in the presence of the laser field is made to show that the hadronic mode becomes slightly more important by increasing the laser field intensity., Comment: 13 pages, 4 figures

We obtain Lie point symmetries for the system of partial differential equations describing flow and heat transfer in a thin liquid film on an unsteady stretching sheet and use them to construct invariants. We derive similarity transformations using deduced invariants that reduce the independent variables of the considered flow model. Such reductions lead to systems of ordinary differential equations. We solve these systems of ordinary differential equations analytically by applying the Homotopy analysis method.

A theoretical treatment, using the first Born approximation, is presented to analyse the results of relativistic laser-assisted proton – hydrogen atom scattering. Specific calculations are carried out for excitation of hydrogen atoms from 1s1/2 to 2s1/2 states by proton impact. We work in an approximation in which the incoming proton may be described by Dirac–Volkov states in the presence of a laser field. Semi-relativistic Darwin wave functions are used to describe the hydrogen atom in its initial and final states, while relativistic, spin, and laser interaction effects are also accounted for. The results presented in this paper show that the differential cross section for this process depends not only upon the energy of the incident proton, but also upon its interaction with the laser field through intensity and frequency.

Elastic scattering of hydrogen atoms by positron impact is studied at various values of incident positron energy and laser intensities. A discussion of differential cross-sections for positron scattering by hydrogen atoms in presence of laser field is presented along with anomalous magnetic moment of both electrons and positrons fully included. Differential cross sections for electrons and positrons remain almost equal in absence of anomalous magnetic moment effects. A comparison is also made with introduction of anomalous magnetic moment effects of both electrons and positrons. At intensities equal to 0.05 a.u. and above significant discrepancies in differential cross section is found even in first Born approximation.

In framework of first Born approximation, Salamin wave states have been used to calculate the differential cross section for laser assisted semirelativistic 1s–2s excitation of hydrogen atom by electron impact with anomalous magnetic moment effects fully included. The obtained results have been compared with laser assisted relativistic differential cross section without such effects. It is found that the electron’s anomalous magnetic moment effects in laser assisted 1s–2s excitation is very important particularly with increase of intensity. Good agreement with laser assisted differential cross section without anomalous magnetic moment effects is obtained when electron’s anomaly $$\kappa=4a_{e^-}=2(g-2)$$ is taken to be zero.

In the framework of the first Born approximation and using the Dirac–Volkov formalism, we investigate the relativistic model describing the laser assisted elastic differential cross sections (DCSs) for positron scattering by the hydrogen atom. Both the DCSs for electron and positron are notably modified by the circularly polarized laser field, particularly in the regime of high energies and medium intensities. Comparing the two numerical DCSs, we recover the well-known result that the elastic scattering differential cross sections with and without laser field for a hydrogen atom by electron and positron impact are the same (Greiner and Reinhardt. Quantum Electrodynamics, 2nd ed., Springer Verlag, New York, Berlin, Heidelberg. 1994). The numerical results reveal that the differential cross section for positron – hydrogen atom scattering is significantly reduced with the increase of the electric field strength.

In this work, we review and correct the first Born differential cross section for the process of Mott scattering of a Dirac–Volkov electron, namely, expression (26) derived by Szymanowski et al. (Phys. Rev. A, 56, 3846 (1997)). In particular, we disagree with the expression of (dσ/dΩ) that they obtained and we give the exact coefficients multiplying the various Bessel functions appearing in the scattering differential cross section. Comparison of our numerical calculations with those of Szymanowski et al. shows qualitative and quantitative differences when the incoming total electron energy and the electric-field strength are increased particularly in the direction of the laser propagation. Such corrections are very important since the relativistic electronic dressing of any Dirac–Volkov charged particle gives rise to these coefficients that multiply the various Bessel functions, and the relativistic study of other processes (such as excitation, ionization, etc….) depends strongly upon the correctness and reliability of the calculations for this process of Mott scattering in the presence of a laser field. Our work has been accepted, Attaourti and Manaut (Phys. Rev. A, 68, 067401 (2003)) but only as a comment. In this paper, we give full details of the calculations as well as a clear explanation of the large discrepancies that their results could cause when working in the ultra relativistic regime and using a very strong laser field corresponding to an electric field strength ε = 5.89 au.