- Multiple scattering Special transport algorithm [1], based on Moli??re's theory of multiple Coulomb scattering improved by Bethe [19,20,21], with account of several correlations: * between lateral and longitudinal displacement and the deflection angle * between projected angles * between projected step length and total deflection Accurate treatment of boundaries and curved trajectories in magnetic fields Automatic control of the step length Path length correction Spin-relativistic effects at the level of the second Born approximation Nuclear size effects (scattering suppression) on option (simple nuclear charge form factors are implemented, more sophisticated ones can be supplied by the user). Fano correction for heavy charged particle multiple scattering - Single scattering: The algorithm is based on the Rutherford formula with a screening factor in the form used by Moliere (for consistency with the multiple scattering model used by FLUKA), integrated analytically without any approximation. Nuclear form factors and spin-relativistic corrections at the first or second Born approximation level are accounted for by a rejection technique. - Photoelectric effect and fluorescence: Interactions are sampled separately for each component element and for each edge. The edge fine structure is taken into account. The angular distribution of photoelectrons is obtained according to the fully relativistic theory of Sauter [6]. Parametrizations/tabulations for photoelectric cross sections including all known edges up to Z=100 and down to a few eV Fluorescence and approximate Auger electron emission are simulated for all K and most L lines - Stopping power: dE/dx Bethe-Bloch theory [13,14,15,16,17]. - Improved ionization potential, handling of porous substances, ranging out particles below energy cutoff [2]. Charged particle energy loss fluctuations below an (arbitrary) explicit ray production threshold are obtained from a sophisticated statistical approach which includes "close" collisions, plus a two-oscillators model for "distant" collisions [3]. Ionization fluctuations including corrections for particle spin and electrons/positrons and "distant collision" straggling corrections (similar to Blunck-Leisegang ones). Original approach making use of very general statistical properties of the problem. Within this framework "practical" solutions have been implemented into the code with very satisfactory results. This approach exploits the properties of the cumulants of distributions, and in particular of the cumulants of the distribution of Poisson distributed variables [3]. Ionization potentials and density effect parameters by Sternheimer, Berger and Seltzer: [4,5] Radiative energy losses for e+, e- made to be consistent with Berger & Seltzer bremsstrahlung data [8]. Shell corrections derived from Ziegler [18] Differences between positrons and electrons are taken into account concerning both stopping power and bremsstrahlung [9]. - Barkas effect - Bloch term - Heavy ion dE/dx: energy loss straggling according to * "normal" first Born approximation * charge exchange effects (dominant at low energies, ad hoc model developed for FLUKA) * Effective charge parameterization * Nuclear form factors at high energies * Direct e+/e-production - Delta ray production and transport with account for spin effects. The variations with energy of the discrete event cross sections and of the continuous energy loss in each transport step are taken into account exactly. Bhabha and Moller scattering for e+ and e- : [7] - Bremsstrahlung Very accurate electron-nucleus and electron-electron bremsstrahlung cross-sections, differential in photon energy, were published by Seltzer and Berger for all elements up to 10 GeV [8]. Those data were obtained at low energy by numerical phase-shift calculations, and above 50 MeV using the DBMO formulae with screening based on Hartree-Fock form factors and several corrections. In FLUKA the full set of Seltzer and Berger cross-sections has been tabulated, with extra points computed close to the finite value at "tip" energy. The energy mesh has been concentrated, especially near the photon spectrum tip, and the maximum energy has been extended to 1000 PeV taking into account the Landau-Pomeranchuk-Migdal (LPM) suppression effect [22,23,24,25] and the Ter-Mikaelyan polarization effect [26] in the soft part of the bremsstrahlung spectrum . Positron bremsstrahlung is treated separately with ad hoc spectra at low energies, using below 50 MeV the scaling function for the radiation integral given by Kim et al. [9] and differential cross-sections have been obtained by fitting proper analytical formulae to numerical results of Feng et al. [10]. The photon angular distribution, fully correlated with the photon energy sampled from the Seltzer-Berger distributions. is obtained sampling the emission angle from the double differential formula reported by Koch and Motz [11]. - Positron annihilation: at rest and & in flight, according to Heitler. - at rest: account for mutual polarization of the two photons - Compton scattering inclusion of binding effects through use of inelastic Hartree-Fock form factors or full Compton profile treatment, using detailed momentum distributions for each atomic shell [27] (Doppler shift comes out automatically) - Photon cross sections: The photon cross-sections used in FLUKA are taken from the EPDL97 evaluated library [12], with the exception of Compton, which is computed from the free electron one according to the corrections explained above. - Pair production angular and energy distributions are described in full detail and correlated. Much care has been devoted to the low photon energy range. LPM effect. - Coherent (Rayleigh) scattering: algorithm using EPDL97 elastic atomic form factors. - Photon polarization in Compton, Rayleigh and photoelectric effects. - Photonuclear cross sections: total cross sections as follow. * Giant Resonance: tabulation from fits to experimental data when possible, otherwise parameterization * Quasi-deuteron: analytical formula (Levinger's model [28], with the value of the Levinger constant as recommended by Tavares et al. [29] and a Pauli-blocking function according to Chadwick et al. [30]. * Delta resonance: fit to available experimental data * High-energy region: weighted sum of (gamma,n) and (gamma,p) cross sections, plus a shadowing factor. The interaction dynamics in all cases is handled via the FLUKA hadronic models (evaporation, PEANUT, Vector Meson Dominance). - Electromagnetic dissociation of ions - Heavy charged particle bremsstrahlung: treated as a continuous energy loss and deposition or as discrete processes depending on user choice - Heavy charged particle pair production: continuous or explicit treatment on user request - Heavy ion direct particle pair production - Leading particle biasing improved and extended to all EMF particles - Negative muon capture: mu- at rest + atom --> excited muonic atom --> X-rays + g.s. muonic atom -> muon capture by nuclei Competition between mu decay and mu capture (Goulard-Primakoff formula) - Muon photonuclear interactions, with or without transport of the produced secondaries. The cross section is factorized (following Bezrukov-Bugaev) in virtual photon production and photon-nucleus reaction. Nuclear screening is taken into account. Only Virtual Meson Interactions are modeled, following the FLUKA meson-nucleon interaction models. - Actual muon decay distribution - pion/muon polarized decays - Deexcitation gamma generation - Cerenkov photon production and full transport of optical photons, including reflection/refraction and absorption (with user provided optical properties) - Scintillation photon production (with user provided production properties) - Explicit capture photon generation for Xenon isotopes, for 113-Cd, 10-B and for 40-Ar and 36-Ar - Ability to define different materials for dE/dx and nuclear interactions. Region-by-region (and voxel-by-voxel) density correction factors for dE/dx and other processes - Photomuon production (Bethe-Heitler) - Individual primary ionization events for both close and distant collisions implemented on request (with user provided infos) - Complete databases for gamma and beta radiations generated out of the data collected from NNDC. - Online evolution of radioactive isotopes and remnant doses calculations for arbitrary irradiation profiles and cooling times - Beta +/- spectra including Coulomb and screening corrections. - Gamma and beta radioactive decays References [1] A. Ferrari, P. R. Sala, R. Guaraldi and F. Padoani, "An improved multiple scattering model for charged particle transport", Nucl. Instr. Meth. B71 (1992) 412. [2] A. Fasso`, A. Ferrari, J. Ranft, P.R. Sala, "An update about FLUKA", Proc. 2nd Workshop on Simulating Accelerator Radiation Environments (SARE 2), CERN, Geneva, Switzerland 9-11 Oct. 1995.Ed. G.R. Stevenson, CERN Report TIS-RP/97-05 (1997), p. 158 [3] A. Fasso`, A. Ferrari, J. Ranft, P.R. Sala, "New developments in FLUKA modelling of hadronic and EM interactions", Proc. 3rd Workshop on Simulating Accelerator Radiation Environments (SARE 3), KEK, Tsukuba, Japan, 7-9 May 1997, Ed. H. Hirayama, KEK Proceedings 97-5, 1997, p. 32: [4] P. Aarnio, A. Fasso`, A. Ferrari, H.-J. M??hring, J. Ranft, P.R. Sala, G.R. Stevenson, J.M. Zazula , "Electron-photon transport: always so good as we think? Experience with FLUKA", Proc. Int. Conference on Monte Carlo Simulation in High Energy and Nuclear Physics (MC93), Tallahassee (Florida) 22-26 February 1993, Ed. P. Dragovitsch, S.L. Linn, M. Burbank (1994), p. 100 [5] R.M. Sternheimer, M.J. Berger, S.M. Seltzer, "Density effect for the ionization loss of charged particles in various substances", At. Data Nucl. Data Tab. 30, 261-271 (1984) [4] [6] F. Sauter, "Ueber den atomaren Photoeffekt bei grosser Haerte der anregenden Strahlung", Ann. der Phys. 9, 217-247 (1931), and "Ueber den atomaren Photoeffekt in der K-Schale nach der relativistischen Wellenmechanik Diracs", Ann. der Phys. 9, 454-488 (1931) [7] E.A. Uehling, Ann. Rev. Nucl. Sci. 4, 315 (1954) [8] S.M. Seltzer and M.J. Berger, "Bremsstrahlung spectra from electrons with kinetic energy 1 keV-10 GeV incident on screened nuclei and orbital electrons of neutral atoms with Z = 1-100, At. Data Nucl. Data Tab. (1986) 345 [9] L. Kim, R.H. Pratt, S.M. Seltzer, M.J. Berger, "Ratio of positron to electron bremsstrahlung energy loss: an approximate scaling law Phys. Rev. A33, 3002-3009 (1986) [10] I.J. Feng, R.H. Pratt and H.K. Tseng, "Positron bremsstrahlung", Phys. Rev. A24, 1358-1363 (1981) [11] H.W. Koch and J.W. Motz, "Bremsstrahlung Cross-Section Formulas and Related Data", Rev. Mod. Phys. 314, 920-955 (1959) [12] D.E. Cullen, J.H. Hubbell, L. Kissel, UCRL-LR-50400. [13] H.A. Bethe, "Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie", Ann. Physik 5, 325-400 (1930); Selected Works of Hans A. Bethe, World Scientific, Singapore 1996, p. 77-154 [14] H.A. Bethe, "Bremsformel fuer Elektronen relativistischer Geschwindigkeit", Z. Phys. 76, 293-299 (1932) [15] H.A. Bethe and W. Heitler, "On the stopping of fast particles and on the creation of positive electrons", Proc. Roy. Soc. A146, 83-112 (1934); Selected Works of Hans A. Bethe, World Scientific, Singapore 1996, p. 187-218 [16] F. Bloch, "Zur Bremsung rasch bewegter Teilchen beim Durchgang durch die Materie", Ann. Phys. 16, 287 (1933) [17] F. Bloch, "Bremsvermoegen von Atomen mit mehreren Elektronen", Z. Phys. 81, 363-376 (1933) [18] J.F. Ziegler, H.H. Andersen, "The stopping and ranges of ions in matter", Vol. 1-4, Pergamon Press, New York 1977 [19] G.Z. Moliere, "Theorie der Streuung schneller geladener Teilchen II - Mehrfach und Vielfachstreuung", Z. Naturforsch. 3a, 78-97 (1948) [20] G.Z. Moliere, "Theorie der Streuung schneller geladener Teilchen IIIc - Die Vielfachstreuung von Bahnspuren unter Beruecksichtigung der statistischen Kopplung", Z. Naturforsch. 10a, 177-211 (1955) [21] H.A. Bethe, "Moliere's theory of multiple scattering", Phys. Rev. 89, 1256-1266 (1953) [22] L.D. Landau, I.Ya. Pomeranchuk, "The limits of applicability of the theory of bremsstrahlung by electrons and of creation of pairs at large energies" (In Russian), Dokl. Akad. Nauk SSSR 92, 535-536 (1953); Collected papers of L.D. Landau, Pergamon Press, Oxford 1965, p. 586-588 [23] L.D. Landau, I.Ya. Pomeranchuk, "Electron-cascade processes at ultra-high energies" (In Russian), Dokl. Akad. Nauk SSSR 92, 735-738 (1953); Collected papers of L.D. Landau, Pergamon Press, Oxford 1965, p. 589-593 [24] A.B. Migdal, "Bremsstrahlung and pair production in condensed media at high energies", Phys. Rev. 103, 1811 (1956) [25] A.B. Migdal, "Bremsstrahlung and pair production at high energies in condensed media", Zh. Exp. Teor. Fiz. SSSR 32, 633-646 (1957); Sov. Phys. JETP 5, 527-536 (1957) [26] M.L. Ter-Mikaelyan, "Bremsstrahlung radiation spectrum in a medium", Dokl. Akad. Nauk SSSR 94, 1033 (1954) [27] F.Biggs, L.B. Mendelsohn, J.B. Mann, "Hartree-Fock Compton profiles for the elements", At. Data Nucl. Data Tab. 16, 201 (1975) [28] J.S. Levinger, "Modified quasi-deuteron model", Phys. Lett. 82B, 181 (1979) [29] O.A.P. Tavares and M.L. Terranova, "Nuclear photoabsorption by quasi-deuterons and an updated evaluation of Levinger's constant", J. Phys. G18, 521 (1992) [30] M.B. Chadwick, P. Oblozinsky, P.E. Hodgson and G. Reffo, "Pauli-blocking in the quasideuteron model of photoabsorption", Phys. Rev. C44, 814 (1991)