The effect of the electron's anomalous magnetic moment on the relativistic electronic dressing for the process of electron-hydrogen atom elastic collisions is investigated. We consider a laser field with circular polarization and various electric field strengths. The Dirac-Volkov states taking into account this anomaly are used to describe the process in the first order of perturbation theory. The correlation between the terms coming from this anomaly and the electric field strength gives rise to new results, namely the strong dependence of the spinor part of the differential cross section (DCS) with respect to these terms. A detailed study has been devoted to the non relativistic regime as well as the moderate relativistic regime. Some aspects of this dependence as well as the dynamical behavior of the DCS in the relativistic regime have been addressed.
The value of the electron's magnetic moment is a fundamental quantity in Physics. Its deviation from the value expected from Dirac theory has given enormous impetus to the field of quantum theory and especially to Quantum Electrodynamics (QED). It is usually expressed in term of the g-factor, ( e.g for the electron g = 2). This result differs from the observed value by a small fraction of a percent. The difference is the well known anomalous magnetic moment, denoted a and defined as : a = (g -2)/2. The one-loop contribution to the anomalous magnetic moment of the electron is found by calculating the vertex function. The calculation is relatively straightforward [1] and the one-loop result is :
where α is the fine structure constant. This result was first found by Schwinger [2] in 1948. A recent experimental value for a was obtained by Gabrielse [3] :
The state of the art status of QED predictions of the electron anomaly has been remarkably reviewed by E. Remiddi [4]. As for laser-assisted processes in Relativistic Atomic Physics, the expectation of major * Electronic address: attaourti@ucam.ac.ma advances in laser capabilities has placed a new focus on the fundamentals of QED which occupies a place of paramount importance among the theories used in the formalism needed to obtain theoretical predictions for the intricate understanding of various fundamental processes. QED has proven itself to be capable of remarkable quantitative agreement between theoretical predictions and precise laboratory measurements. When presently achievable intensities are around 10 22 W/cm 2 , electrons are so shaken that their velocity approaches the speed of light. Therefore, the interactions between laser and matter become relativistic. Recently, relativistic laser-atom physics emerged as a new fertile reseach area. This is due to the newly opened possibility to submit atoms to ultra-intense pulses of infrared coherent radiation from lasers of various types. The dynamics of a free electron embedded within a constant amplitude classical field has been addressed since the early years of quantum mechanics. In 1935, an exact expression for the wave function had been derived within the framework of the Dirac theory [5]; see also [6] for an overview of the case of an electron submitted to a short laser pulse.
In the 1960s, the advent of laser devices has motivated theoretical studies related to QED in strong fields. These formal results were considered as being only of academic interest for many years. The state of affairs has significantly changed in the mid-1990s when it has been possible to make to collide a relativistic electron beam from a LINAC with a focused laser (Nd: Yag) radiation. Under such extreme conditions, it has been possible to evidence highly non-linear essentially relativistic QED processes such as a non linear Thomson and Compton scattering and also pair production [7,8,9,10,11]. A first focus issue in 1998 devoted to relativistic effects in strong fields appeared in Optics Express [12] and in 2008, Strong Field Laser Physics [13] gave the main advances in this field as well as the references to the works of all major contributors. A seminal thesis [14] for the first time addressed the study of laser-assisted second-order relativistic QED processes. This, we think will pave the way for a more accurate description of laser-assisted fundamental processes [15], [16]. Our aim in this paper is to shed some light on a difficult and recently addressed description of laser-assisted processes that incorporate the electron anomaly. The process we study is the laser-assisted elastic collision of a Dirac-Volkov electron with a hydrogen atom. We focus on the relativistic electronic dressing with the addition of the electron anomaly. Some results are rather surprising bearing in mind the small value of a. In section 2, we present the formalism as well as the coefficients that intervene in the expression of the DCS. In section 3, we discuss the results we have obtained in the non relativistic, moderate relativistic and relativistic regimes. Atomic units are used throughout ( = e = m = 1) where m denotes the electron mass and work with the metric tensor g µν = diag(1, -1, -1, -1).
The second-order Dirac equation for an electron with anomalous magnetic moment (AMM) in the presence of an external electromagnetic field is [17] :
where
A µ is the four-vector potential, while a = κ/4, κ is the electron’s anomaly. The Feynman slash notation is used throughout p / = p 0 γ 0p.γ and A / = A 0 γ 0 -A.γ. The term F µν σ µν stems from the fact that the electron has a spin one half, the term multiplying a is due to its anomalous magnetic moment. It is possible to rewrite the exact solution found by Y. I. Salamin [18] as :
In the above equation the four-vector q µ is given by :
The four-vector k µ = ( ω c , k) is the four-vector of the circularly polarized laser field A µ = a µ 1 cos φ + a µ 2 sin φ, φ = k.x. Note that k µ is such that
This content is AI-processed based on open access ArXiv data.
