Nonlinear single Compton scattering of an electron wave packet

Abstract

Nonlinear single Compton scattering has been thoroughly investigated in the literature under the assumption that initially the electron has a definite momentum.Here, we study a more general initial state, and consider the electron as a wavepacket. In particular, we investigate the energy spectrum of the emitted radiation and show that in typical experimental situations some features of the spectra shown in previous works are almost completely washed out. Moreover, we show that at comparable relative uncertainties, the one in the momentum of the incoming electron has a larger impact on the photon spectra at a fixed observation direction than the one on the laser frequency. I. INTRODUCTIONAccording to classical electrodynamics a charged particle (an electron, for definiteness) accelerated by a background electromagnetic field emits radiation [1]. In the underlying quantum theory, QED, the radiation process is rather described as the emission of photons by the electron [2,3]. Due to energy-momentum conservation a free electron is stable and cannot emit photons. The scattering of an electron with a single photon is known as (linear) Compton scattering. In general, the simultaneous interaction of an electron with many photons is suppressed by the appearance in the interaction probabilities of a corresponding power of the fine-structure constant α QED ≈ 1/137 1. However, if the electron interacts with a coherent collection of photons, like those in a laser beam, the effective coupling strength appearing in perturbative expansions is not just α QED , but it also depends on the typical amplitude and angular frequency of the laser field [4]. Qualitatively it is clear that a laser field characterized by an amplitude E and by an angular frequency ω is able to transfer

Single and double nonlinear Compton scattering

“…We also find that the (leading order) exchange term P 22 ex is on the same order of magnitude as the (leading order) direct terms P 22→1 and P 22→2 . Here, though, P 22 ex is not only on the same order of magnitude, but it in fact cancels P 22→1 to leading order in χ; this generalizes the a 0 1 results in the previous section to a 0 1. Note also that the dependence on the momenta remains the same as in the a 0 1 limit.…”

“…In this paper we do not consider effects of finite-sized wave packets. See[22] for such effects in photon emission by a single electron, and[23] for two-electron wave packets and the difference in coherence compared to the classical prediction[24].…”

Numerical approach to the semiclassical method of radiation emission for arbitrary electron spin and photon polarization

“…We use the obtained formulas in the case of a background plane wave, as the Dirac equation then can be solved analytically [4], to do a direct comparison with the spectrum obtained using the exact solution of the Dirac equation (Volkov states) [4][5][6]. This is the usual approach for such processes [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. We consider the case of a short circularly polarized laser pulse, and find agreement, as expected.…”

“…By replacing these expressions in Eq. (22), and carrying out the integration over d 4 x, we can write the amplitude in the form…”

“…Now, in order to find the probability using Eq. (18) we take the norm-square of the above amplitude and, having in mind the case of a narrow wave packet [22], replace |c(p i )| 2 = δ 3 (p i − p i,0 )/(2π) 3 . Analogously as above, we now have a delta-function which we can evaluate by integration over d 3 p f and the transformation of the deltafunction yields a factor of ω0ε f k0p f .…”