Models for the Simulation of X-Ray Fluorescence and PIXE

1. Models for the Simulation of X-Ray Fluorescence and PIXE A. Mantero, S. Saliceti, B. Mascialino, Maria Grazia Pia INFN Genova, Italy NSS, Rome, 21 October 2004 http://www.ge.infn.it/geant4/lowE/index.html

2. Fluorescence Emission Original motivation from astrophysics requirements Cosmic rays, jovian electrons X-Ray Surveys ofAsteroids and Moons Solar X-rays, e, p Geant3.21 ITS3.0, EGS4 Courtesy SOHO EIT Geant4 Induced X-ray line emission: indicator of target composition (~100 mm surface layer) C, N, O line emissions included Wide field of applications beyond astrophysics Courtesy ESA Space Environment & Effects Analysis Section

3. X-ray fluorescence and Auger effect • Calculation of shell cross sections • Based on Livermore (EPDL) Library for photoelectric effect • Based on Livermore (EEDL) Library for electron ionisation • Based on Penelope model for Compton scattering • Detailed atom description and calculation of the energy of generated photons/electrons • Based on Livermore EADL Library • Production threshold as in all other Geant4 processes, no photon/electrons generated and local energy deposit if the transition predicts a particle below threshold

4. Test process • Unit, integration and system tests • Verification of direct physics results against established references • Comparison of simulation results to experimental data from test beams • Pure materials • Complex composite materials • Quantitative comparison of simulation/experimental distributions with rigorous statistical methods • Parametric and non-parametric analysis

5. K transition K transition Verification: X-ray fluorescence Comparison of monocromatic photon lines generated by Geant4 Atomic Relaxation w.r.t. reference tables (NIST) Transitions (Fe) Transition Probability Energy (eV) K L2 1.01391 -1 6349.85 K L3 1.98621 -1 6362.71 K M2 1.22111 -2 7015.36 K M3 2.40042 -2 7016.95 L2 M1 4.03768 -3 632.540 L2 M4 1.40199 -3 720.640 L3 M1 3.75953 -3 619.680 L3 M5 1.28521 -3 707.950

6. 428.75, 429.75 eV (430 unresolved) 366.25 eV (367) 436.75, 437.75 eV (437 unresolved) Verification: Auger effect Auger electron lines from various materials w.r.t. published experimental results Precision: 0.74 % ± 0.07 Cu Auger spectrum

7. Si FCM beamline Si reference XRF chamber GaAs Test beam at Bessy Advanced Concepts and Science Payloads A. Owens, A. Peacock Complex geological materials Hawaiian basalt Icelandic basalt Anorthosite Dolerite Gabbro Hematite

8. Anderson Darling test A2 0.04 0.01 0.21 0.41 Beam Energy 4.9 6.5 8.2 9.5 Ac (95%) = 0.752 Comparison with experimental data Pearson correlation analysis: r>0.93 p<0.0001 Effects of detector response function + presence of trace elements Experimental and simulated X-ray spectra are statistically compatibleat 95% C.L.

9. PIXE • Calculation of cross sections for shell ionization induced by protons or ions • Two models available in Geant4: • Theoretical model by Grizsinsky – intrinsically inadequate • Data-driven model, based on evaluated data library by Paul & Sacher (compilation of experimental data complemented by calculations from EPCSSR model by Brandt & Lapicki) • Generation of X-ray spectrum based on EADL • Uses the common de-excitation package

10. Fit to Paul & Sacher data library; results of the fit are used to predict the value of a cross section at a given proton energy allow extrapolations to lower/higher E than data compilation First iteration, Geant4 6.2 (June 2004) The best fit is with three parametric functions for different groups of elements 6 ≤ Z ≤ 25 26 ≤ Z ≤ 65 66 ≤ Z ≤ 99 Second iteration, Geant4 7.0 (December 2004) Refined grouping of elements and parametric functions, to improve the model at low energies PIXE – Cross section model Next: protons, L shell ions, K shell

11. Regression deviation Residual deviation Total deviation Quality of the PIXE model • How good is the regression model adopted w.r.t. the data library? • Goodness of model verified with analysis of residuals and of regression deviation • Multiple regression index R2 • ANOVA • Fisher’s test • Results (from a set of elements covering the periodic table) • 1st version (Geant4 6.2): average R2 99.8 • 2nd version (Geant4 7.0): average R2 improved to 99.9 at low energies • p-value from test on the F statistics < 0.001 in all cases Test statistics Fisher distribution

12. Bepi Colombo Mission to Mercury Study of the elemental composition of Mercury by means of X-ray fluorescence and PIXE Insight into the formation of the Solar System (discrimination among various models)

13. A Library For Simulated X-Ray Emission form Planetry Surfaces A. Mantero, S. Saliceti, B. Mascialino, Maria Grazia Pia INFN Genova, Italy A.Owens, ESA NSS, Rome, 21 October 2004

14. The BepiColombo Mission to Mercury HERMES Is an X-Ray spectrometer to measure the composition of the upper layers of planetary surface Composed of 2 orbiters carrying a total of 25 scientific experiments: • Magnetic Field Study • Planet Surface Mapping • Planet Surface Composition study • 4 spectrometer (IR, X, , n) • 1 laser altimeter

15. Solid State Detectors Gas Detectors • Better Resolution • -140 eV @ 5.89 KeV” • Greater Efficiency at low Energies • Faster count speed • Poor resolution • - “< 1KeV @ 5.95 KeV” • Poor efficiency at low energies Basalt fluorescence spectrum Beam Energy 9.5 KeV Only for some elements Ka lines can be detected (Mg, Al, Si, S, Ca, Ti, and Fe) Counts Energy (KeV) X-Ray Detectors

16. We need to study possible responses of the instruments before they are in flight with a very good precision for all the possible situations they can find Rocks X-Ray Emission Library • Space missions are risky, so solid strategies for risk mitigation are to be undertaken • HERMES is an X-Ray spectrometer studying Mercury's surface composition • Solid state detector have a better definition than “normal” gas-filled proportional counters • We will measure detailed X-Ray spectra leading to detailed elemental composition of the crust of the planet

17. Si FCM beamline Si reference XRF chamber GaAs • A total of 8 rocks have been irradiated and by now 5 of them have been simulated. • Basalt (Hawaii, Madagascar and Iceland) • Anorthosite • Ematite • Gabbro • Dolerite (Whin Sill, Java) • Obsidian Rocks X-Ray Emission Library Test beams at BESSY labs have been undertaken in order to provide a set of X-Ray spectra from PSSL rocks that could be found rocky planets (Mars, Venus, Mercury)

18. Geant4 provides advanced instruments for the description of geometry and materials Thanks to a Geant4 simulation we can simulate any rock of known composition with a high degree of confidence Rocks Spectra Simulation

19. Rocks Spectra Simulation

20. Summary • Geant4 provides precise models for detailed processes at the level of atomic substructure (shells) • X-ray fluorescence, Auger electron emission and PIXE are accurately simulated • Rigorous test process and quantitative statistical analysis for software and physics validation have been performed • A new generation of X-Ray detectors will be used shortly for planetary investigations, giving precise results • A library of rocks X-Rayspectra is needed for accurate physic reach and risk mitigation studies • Geant4 is capable of generating X-Ray spectra for any rock of known composition and a library is under production.