Jorge E. Fernández Laboratory of Montecuccolino (DIENCA), Alma Mater Studiorum University of Bologna, via dei Colli, 16, Bologna, Italy

Transcription

1 Information technology (IT) for teaching X- and gamma-ray transport: the computer codes MUPLOT and SHAPE, and the web site dedicated to photon transport Jorge E. Fernández Laboratory of Montecuccolino (DIENCA), Alma Mater Studiorum University of Bologna, via dei Colli, 16, Bologna, Italy Transport theory can be successfully used for describing the diffusion of X- and gamma-rays in matter. In the framework of the cooperation between the Polytechnic University of Valencia and the University of Bologna, a short PhD course is being offered to tech the foundations of photon transport with application to some paradigmatic X-ray spectrometry problems. The course gives also an introduction to an advanced aspect of photon transport: the description of the photon polarization and its influence on the diffusion. The course makes recourse to some IT tools developed at Bologna: (1) the graphic application MUPLOT which is used as a dedicated calculator for computing photon mass attenuation coefficients (total, photoelectric, Rayleigh scattering and Compton scattering) for mixtures and compounds using 92 elements of the periodic table; (2) the deterministic code SHAPE which is used for building up X- and gamma-ray fluorescence spectra and for showing the influence of the single interactions (or chains of interactions) on different parts of the spectrum; and (3) the web site which describes these and other downloadable codes, and contains explanations on the transport theory and useful data bases for photon transport in the x-ray regime. A course on photon transport focused on x-ray spectrometry applications Title: Problems of multiple scattering and polarization effects in x-ray spectrometry Level: Ph.D. Duration: 2 weeks Hours/week: 8 (thoeretical lessons), 2 (computer exercises) To be offered preferably during the 1 st semester. Description of the course: it comprises 16 hours of theoretical lessons plus 4 hours of practical lessons on the use of the codes SHAPE y MCSHAPE, plus the development of small programs on photon transport by the students. Contents: Description of the diffusion of photons using the integro-diferential Boltzmann transport equation. Analytical solution in number of collisions for plane geometry. Description of the diffusion of photons using the integral equation Application to the study of multiple scattering of x- and gamma-rays. Application in x-ray fluorescence (XRF) and in non-destructive analysis (NDT). Stokes representation of the polarization state. Modification of the transport equation to include the effects of polarization. Description of the main interactions in the x-ray regime (photoelectric effect, Rayleigh scattering and Compton scattering) as a function of the polarization of the incident photons. Applications of polarization in x- and gamma-ray spectrometry. Applications to the reconstruction of tomographic images. Monte Carlo simulation of polarized photons transport. 1

2 MUPLOT : software tool for the computation of x-ray attenuation coefficients. It allows the computation of attenuation coefficients (total, photoelectric, Rayleigh and Compton) for materials defined as: (a) single element, entering atomic number Z or chemical symbol (allowed elements are Z=1..92), compound (entering chemical formula), mixture of elements (entering elements and weight concentrations), mixture of compounds (entering chemical formulas and weight fractions). It follows an example for a compound (water). It is given a name to the substance ( water in this case) and is selected to define it using a chemical formula. The chemical formula for water is entered: elements are named with their chemical symbols. In this case the formula for water is H 2 O. Once completed the definition, the initial dialog activates two buttons: Plot and Table as in the following figure. 2

3 By pressing the Plot button, we obtain the plot of the attenuation coeffcient for the selected substance. With different colours are indicated the single components: photoelectric, Rayleigh (coherent) and Compton (incoherent). By pressing Table instead, is possible to obtain a table at fixed energy values (plus photoelectric edges) as the following: 3

4 Both, plot and table can be printed or saved to a file. The table can be saved also in ASCII format to use successively the calculated values. SHAPE: a deterministic code for building-up x-ray fluorescence spectra. X-ray fluorescence (XRF) is a well known spectroscopical technique, which is normally applied using reflection geometry, and that can be well described by a 1D transport model. In addition, the participating interactions between photons and matter (photoelectric effect, Rayleigh and Compton scattering) are all well known, and it is possible to demonstrate that a Neumann series expansion in number-of-collisions is rapidly convergent after two or three collisions of these. Therefore, the problem adapts very well to be described using a few collision chains using a deterministic code. SHAPE is a code to build-up x-ray fluorescence (XRF) intensity spectra by computing the intensity contributions from multiple-collision chains with recourse to the computation of analytical solutions deduced in the frame of photon transport theory. The used theoretical model describes the diffusion of photons in an homogeneous target of infinite thickness comprising different kinds of isolated atoms. It is assumed that the excitation is produced either with an unpolarized or with a linearly polarized, monochromatic and collimated source, and that the emitted spectrum is collected into a sharply collimated solid angle using a Si or Ge solid state detector. Recently, SHAPE has been modified to include the effects of the photon polarization, as much as the scattering interactions Rayleigh and Compton change the state of polarization of the radiation undergoing these kinds of collisions. Thus, the multiple scattering intensity results modified by these polarization changes. This happens even if the source emits unpolarized photons, and much more when it is linearly polarized as can be done with this version of SHAPE. The physical variables defining the problem are the source energy, the directions of incidence (two angles) and take-off (two angles), and the sample composition (up to 10 different especies of atoms). In addition, SHAPE allows us to keep only the interactions of interest, making possible the study of selected groups of interactions that modify isolated portions of the spectrum. 4

5 The interactions are classified by the number and the type of the collisions. With SHAPE you can calculate all the contributions due to 1 and 2 collisions of any combination of the photoelectric, Compton and Rayleigh effects, and those due to 3 collisions of pure photolectric type. Both directions -incidence and take-off- define the scattering angle. Due to the symmetry of the problem, we only need only three of the four angles: the two polar angles (about the normal to the sample) and the take-off azimuthal angle (assuming the incidence azimuthal angle is 0). So, the take-off azimuthal angle is always measured from the projection of the incidence direction on the sample surface. With this information SHAPE computes first the discrete and continuous parts of the backscattered spectrum (in wavelength). For the interactions photoelectric, Rayleigh and Compton, it uses the kernels described in the bibliography below. These kernels are sufficiently precise as to give an energy detailed spectrum. SHAPE converts the wavelength spectra to the energy domain and simulates the response of either an intrinsic Ge or a Si solid state detectors to render the output closer to that of an experimental spectrum. It also simulates the spectrum modification as a consequence of the attenuation in the air paths between the SOURCE and the TARGET, and between the TARGET and the DETECTOR, which are denoted as d1 and d2, respectively. To convert the discrete components of the spectrum, the line width of the monochromatic excitation source must be introduced interactively. The natural widths of the characteristic lines (much narrower than the breadth due to the detection process) are included in the data base. The line width of Compton peak, the so called Compton profile -dependent of the momentum distribution of the electrons in the atoms of the target- is usually greater to the detection width, and is also included in the data base. The Rayleigh width should be defined accurately to fit well the experimental height in the region of the Rayleigh and Compton peaks. The interactive input of this width can be skipped by calling SHAPE in batch mode. The figure below shows an interactive session using SHAPE: 5

6 The interface allows the user to settle intuitively the set-up by chossing the excitation detection geometry, the detector used, the calibration of the detector/mca, the source energy and polarization state, and the composition of the target which defines the interacting atoms. Using SHAPE (declaring set-up) geometry source energy target detector & MCA source polarization state current set-up window An important feature is the possibility to switch on/off single interactions chains, giving the possibility to identify the influence in the total spectrum: Using SHAPE (switching interactions on/off) changed interaction 6

7 The results of the computations are presented graphically and as a file. Using SHAPE (plotting) 123 means one + two +three collisions postfix d means with detector influcence Web site devoted to photon transport ( It has been created a web site devoted to disseminate state-of-art knowledge on x- and gamma-ray photon transport, and to share a number of codes developed at Bologna. The web site furnishes a multiple scattering description of an special subject like polarised photon diffusion, and explains how it represents a unified approach to describe attenuation of photon beams maintaining the optical properties which are related to the polarisation state. The site contains the descriptions of several codes of photon transport developed along the years at Bologna. In particular, it describes codes for photon transport having different degrees of refinement on the description of the interactions photon-atom, the composition of the sample, the polarisation, etc. Up to now, these codes used always a simple geometry (1D) since they were initially designed for testing deterministic models, and symmetrically, to validate variance reduction techniques in Monte Carlo simulations. More recently it has become necessary to design 3D codes able to describe realistic physical situations. 7

8 The following codes are discussed (and can be freely downloaded) in the web site: 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. 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). D3DSHAPE deterministic code for coupled electron-photon transport (under development). MC3DSHAPE. It extends the MCSHAPE Vector Monte Carlo code towards 3-D using cubic voxels to represent volumes (under development). 8

9 The features of some of these codes are compared below: Features Details SHAPE v2.20 D3DSHAPE v1.0 MCSHAPE v2.04 Physics Miscellaneous Transport model Code Applications photoelectric effect ~1000 characteristic lines line width atomic Rayleigh scattering atomic Compton scattering Compton profile first collision only electron bremsstrahlung foreseen in v3 foreseen in v3 open data bases user defined elements foreseen in v3 infinite thickness targets finite thickness targets multilayer targets polarization representation Stokes Stokes source polarization state linear/ unpolarised unpolarised arbitrary calculated spectrum intensity component only full polarization state monochromatic source polychromatic source postprocessor external detector solid state Si/Ge foreseen in v3 reflection geometry transmission geometry selective computation of single interaction chains partial foreseen in v3 particle photons photonselectrons photons scalar equation vector equation solution deterministic deterministic Monte Carlo collisions D spatial geometry 3-D spatial geometry foreseen in v3 language DELPHI FORTRAN 77 FORTRAN 90 additional libraries graphics WINTERACTER platform DOSWINDOWS LINUX WINDOWSLINUX distribution web site alpha testing web site parallelization MPICH v1.0 (only Linux) spectroscopy analytical chemistry radiation metrology radiation shielding dosimetry foreseen in v2 foreseen in v3 radiation transport teaching 9

10 Conclusions X-ray photon transport is a good benchmark for transport theory because: the transport equation for photons is linear (is analogous to the neutron transport equation) the interactions involved are both, isotropic (photoelectric characteristic emission) and anisotropic (Rayleigh and Compton scattering). the spectroscopic application obliges to maintain the full energy and angle distributions all interactions are necessary at all energies it is shown how the introduction of the polarization state changes the transport equation and it reflects in a change of the angular distribution at each energy the computations, even if complex, can be well understood with the help of the developed tools Two remarkable advantages of this course are that it can be taught in a short period and that the acquired knowledge can be used for professional or research follow-up. 10