Abstract
We investigate the 2nd order process of two photons being emitted by a high-energy electron dressed in the strong background electric field found between the planes in a crystal. The strong crystalline field combined with ultra relativistic electrons is one of very few cases where the Schwinger field can be experimentally achieved in the electron's rest frame. The radiation being emitted, the so-called channeling radiation, is a well studied phenomenon. However only the first order diagram corresponding to emission of a single photon has been studied so far. We elaborate on how the 2 photon emission process should be understood in terms of a two-step versus a one-step process, i.e., if one can consider one photon being emitted after the other, or if there is also a contribution where the two photons are emitted 'simultaneously'. From the calculated full probability we see that the two-step contribution is simply the product of probabilities for single photon emission while the additional one-step terms are, mainly, interferences due to several possible intermediate virtual states. These terms can contribute significantly when the crystal is thin. Therefore, in addition, we see how one can, for a thick crystal, calculate multiple photon emissions quickly by neglecting the one-step terms, which represents a solution of the problem of quantum radiation reaction in a crystal beyond the usually applied constant field approximation. We explicitly calculate an example of 180 GeV electrons in a thin Silicon crystal and argue why it is, for experimental reasons, more feasible to see the one-step contribution in a crystal experiment than in a laser experiment.
Highlights
Strong field QED is the study of physical processes that take place in a strong background field, and nonlinear effects of quantum nature arise when the size of the Lorentz invariant parameter qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi χ 1⁄4 e ðFμνpνÞ2=m3
We show that the two-photon emission probability contains the cascade along with one-step terms that scale linearly with the crystal thickness
Electrons were chosen for this reason as it is not as numerically heavy when the quantum numbers are relatively small, as opposed to the positron case, which would require large quantum numbers to obtain an appreciable value of the quantum nonlinearity parameter χ, which means that quantum effects such as spin and recoil are important in the emission process
Summary
Strong field QED is the study of physical processes that take place in a strong background field, and nonlinear effects of quantum nature arise when the size of the Lorentz invariant parameter qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi χ 1⁄4 e ðFμνpνÞ2=m3. For the theory of channeling radiation, in particular, the development of the semiclassical operator method by Baier et al [24] stands out and has been extensively applied to the phenomenon of channeling [25] This method allowed the inclusion of quantum effects such as the electron spin and the photon recoil, which are important when χ is no longer small, while needing only the classical trajectory of the electron/positron in the external field. The authors of this method, seeking analytical results, in most applications to channeling, applied the approximation of the local constant field, which greatly simplifies calculations. We adopt the metric tensor ημν 1⁄4 diagðþ1; −1; −1; −1Þ
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
