In general, since X-rays are very penetrating they probe the depth of the target, sampling the information in a large volume. This makes it very probable that secondary radiation may suffer further interactions before leaving the medium where it started to interact, giving place to a multiple scattering process where the photons change energy and angle distribution according to the number and type of the collisions undergone. Therefore, a multiple scattering scheme within photon transport theory seems to be the simplest approach to study the diffusion of X-rays in a dense material.

This approach has been used successfully by this research group to analyse the build-up of X-ray spectra emitted after photon excitation (fluorescence), improving the knowledge and interpretation of experimental X-ray spectra in materials of high complexity (multi-component mono- and multi-layers). The reached high degree of detail in the description of the spectra has been due, essentially, to two factors: an accurate knowledge of the interaction cross sections for the prevailing processes in the X-ray regime: photoelectric effect, Rayleigh and Compton scattering; and a detailed description of the evolution of the polarisation state across interactions by using an exact solution of the vector transport equation. The approach has been extended to photons in other energy regimes (i.e. to the LIDAR in the visible range, by using appropriate cross-sections in that range), and to photons produced by excitation with other kind of particles (i.e. by electrons in the microprobe, or by protons in particle accelerators). In this last case, a more complex problem arises because the transport description requires to find the solution to a coupled system of transport equations, one for the charged particles, and one for the photons. Some computer codes were developed during these studies for both, a numerical evaluation of the deterministic solutions and a Monte Carlo simulation of polarised photons, which constitute a good basis for supporting any further serious software development involving photon transport.

Polarisation is the most important and promising property of the radiation in view of the interests of industry in X-ray imaging and chemical quantitation. The multiple scattering description of polarised photon diffusion represents a unified approach to describe attenuation of photon beams maintaining all the optical properties which are related to the polarisation state. In fact, a correct description of the angular distribution of the radiation is essential for a correct interpretation of X-ray images, and for the moment, such a description is only possible with recourse to the vector transport model for polarised radiation. It is worth mentioning that such a description covers photons having all the possible states of polarisation, in particular those that born unpolarised but become polarised as a consequence of scattering. This represents one of the interest cases for application of X-ray imaging in computed tomography, archaeometry, air-pollution/environment and element mapping with micro-beam techniques.

Several codes for photon transport with different degrees of refinement on the description of the interactions photon-atom, the composition of the sample, the polarisation, etc. have been developed along the years by our group. All these codes use a simple geometry since they have been mainly designed for testing the deterministic models, and symmetrically, the more valid variance reduction techniques to apply in Monte Carlo simulations.

• 1987-1992. XRFPC: Deterministic Code to compute the corrections to the characteristic intensity produced by multiple scattering of pure photoelectric interactions.
• 1990- SHAPE: Deterministic Code to compute X- or gamma-ray spectra identifying all the components of multiple scattering due to scattering Rayleigh, Compton and photoelectric effect. The spectrum can be corrected by the responses of different detectors. The program is very useful since allows the understanding of the influence of the contribution from different types of atoms on the irradiated spectrum, as a function of the geometry, the energy of the source and the polarisation state of the source. The interactions photon-atom are described with maximum detail and state of art knowledge of the cross-sections. Uses a data base containing all the elements of the periodic table (Z=1-92). The code is used for research in several laboratories in the world.
• 1995- MSXRF: Deterministic Code to compute the multiple scattering contributions to the characteristic intensity, identifying all the multiple scattering components due to Rayleigh and Compton scattering and photoelectric effect. The intensity can be corrected with the response of several detectors. The program allows the understanding of the influence of the different types of interactions on the characteristic lines, as a function of the geometry of the set-up, and the energy and polarisation state of the source. The interactions photon-atom are described with maximum detail and state of art knowledge of the cross-sections. Uses a data base containing all the elements of the periodic table (Z=1-92). The code is used for material analysis with XRF techniques.
• 1996- MCSHAPE. Vector Monte Carlo for multiple scattering computation involving sources with arbitrary conditions of polarisation. The complete description of the polarisation effects makes this code the only existing tool able to describe the full polarisation state in radiation diffusion experiments with x- and gamma-rays. (in collaboration with M. Bastiano).
• 1998- 3D deterministic code for coupled electron-photon transport.
• 2005- 3DMCSHAPE. It brings the MCSHAPE Vector Monte Carlo code towards 3-D using voxels (under development).

In this site it is possible to find also some useful utility codes.

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ALMA MATER STUDIORUM - Università  di Bologna
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