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A formalism is presented in which the radiation of photons off high energy electrons during a multiple scattering process with finite condensed media can be evaluated for a general interaction. We show that the arising Landau-Pomeranchuk-Migdal suppression for finite size targets saturates at some characteristic photon energy. Medium coherence effects in the photon dispersion relation can be also considered leading to a dielectric suppression or transition radiation effects in the soft part of the spectrum. The main results of our formulation are presented for a Debye screened interaction and its well-known Fokker-Planck approximation, showing that for finite size targets or for the angular distributions of the final particles the differences between both scenarios cannot be reconciled into a single redefinition of the medium transport parameter (

The Landau-Pomeranchuk-Migdal (LPM) suppression is a well-known effect that has been extensively studied. Interference phenomena in a multiple scattering scenario was initially considered by Ter-Mikaelian as the mechanism regulating the amount of scattering centers which can coherently emit as a single bremsstrahlung source

In this paper, we have developed a formalism and a Monte Carlo code which allows for the computation of the bremsstrahlung spectrum of finite targets, arbitrary interactions and with a full control of the kinematics of the process, so that specific cuts on momenta of the final electron and photon can be applied. In Sec.

In this section we will introduce the general formalism applicable to finite targets and general interactions.

It has been predicted by Ter-Mikaelian

The above classical arguments can be made quantitative and hold also for a quantum evaluation of the amplitude. By Fourier transforming electron states

Diagrammatic representation of the single emission elements appearing in a discretization in the variable

The general behavior of these results can be summarized in Fig.

Schematic representation of the bremsstrahlung regimes for several scenarios. Totally incoherent Bethe-Heitler superposition (BH), Landau-Pomeranchuk-Migdal suppression (LPM), totally coherent Bethe-Heitler superposition (

In Migdal’s calculation of the intensity

We assume from here onwards a constant density

An estimation of the value of

Expression

Differential spectrum of photons emitted by an electron of

Intensity of photons emitted by an electron of

In Fig.

Intensity of photons emitted by an electron of

In Fig.

Intensity of photons emitted by an electron of

In Fig.

Intensity of photons emitted by an electron of

A formalism implemented with a Monte Carlo method has been presented which is able to evaluate the bremsstrahlung intensity in a multiple scattering scenario under a general interaction. We have also found an heuristic formula which describes the LPM effect for finite size targets. Dielectric and transition radiation effects related to effective photon masses in the medium dispersion relation are included in this formalism if needed. Our results reproduce the experimental data of SLAC.

We have shown that the Fokker-Planck approximation does not fit well the differential angular spectrum, especially if kinematical cuts are applied in the final particles. In the integrated spectrum, the Fokker-Planck approximation fails to reproduce the spectrum. If the

We thank J. Alvarez-Muñiz, N. Armesto, C. Salgado, and J. Sanchez-Guillen for reading the manuscript and for discussions. We thank the grant María de Maeztu Unit of Excellence of Spain and the support of Xunta de Galicia under the Project No. ED431C2017. This paper has been partially done under the Project No. FPA2017-83814-P of Ministerio de Ciencia, Innovación y Universidades (Spain).