Variation of radiation length due to LPM effect

Abstract

The photon emission intensity spectrum is calculated taking into account influence of multiple scattering (the LPM effect) under conditions of recent CERN SPS experiment. It is shown that the theory quite satisfactory describes data. The integral characteristics: the radiation length and total probability of photon emission are analyzed under influence of the LPM effect, and the asymptotic expansions of these characteristics are derived.

Transverse spectrum of bremsstrahlung in finite condensed media

“…In a typical run we computed 10 4 paths for 50 frequencies and 100 photon angles, spanning from ∼ 10 3 steps for the shortest medium to ∼ 10 5 steps for the largest. In order to check that our results are correct we implemented also the Fokker-Planck approximation (23) for (17) in this discretized approach and compared with the δz → 0 limit of (14), which within this approximation produces six integrable Gaussian path integrals extending the Boltzmann transport approach [4] to finite mediums. We present our result for the Debye and Fokker-Planck cases for targets of lengths l = 0.0038, 0.023 and 0.2 mm, corresponding to an average of n c = 142, 862 and 7502 collisions, respectively, for electrons of p 0 = 8 and 25 GeV, in order to compare to the SLAC data presented in [22,32,33].…”

“…Since in the entire medium l there are l/δl(ω) coherence lengths, then we write the incoherent sum δl(ω)). (26) By integrating in the photon solid angle Ω k and using (17) we find (27) where the electron momentum change is |δp| = 2p 0 β sin(θ/2) and…”

“…This calculation has shown that except for the spin corrections for hard photons, the LPM suppression for an averaged target still agrees with the expected classical behavior of the infrared divergence. Further and more recent developments in various approaches have been introduced since then by Blankenbecler and Drell [5][6][7], Zakharov [8][9][10][11][12][13][14], the Baier-Dokshitzer-Mueller-Schiff-Peigné group (BDMPS) [15], Baier and Katkov [16][17][18] and Wiedemann and Gyulassy [19], and extensive reviews were presented in [20,21]. We note, however, that all the existing calculations were done in the Fokker-Planck approximation, which both in the Boltzmann transport approach [4,15] and in the path integral formulation [8,19] lead to a Gaussian distribution of momenta.…”

<title>Coherent and incoherent processes and the LPM effect in oriented single crystals at high-energy</title>

“…(17) has a good accuracy only for energy much smaller (at least on one order of magnitude) than ε 0 (see discussion after Eq. (15) in 15 ).…”

“…In this notations the contribution of multiple scattering into the local intensity for small values of χ m and ε/ε 0 has a form (see Eq. (15) in 15 and Eq. (50) below)…”