Fundamental and Applied Aspects of X-Ray Spectrometry: Detector Influence and Photoelectric Effect Cross-Sections

The first part of this work reports the elementary theory of the atomic photoeffect presented in a form that is suited for practical numerical calculation. A detailed derivation of subshell cross sections for both excitation and ionization, comprising the angular distributions of emitted photoelectrons, is presented taking into account the effect of the polarization of the photons. The theoretical formulas have been implemented in a computer program PHOTACS that calculates tables of excitation and ionization cross sections for any element and subshell. Numerical calculations are practicable for excitations to final states with the principal quantum number up to about 20 and for ionization by photons with energy up to about 2 MeV. The effect of the finite width of atomic energy levels is accounted for by convolving the calculated subshell cross section with a Lorentzian profile. The second part of this work reports unfolding strategies for correcting a radiation measurement from the effects of the detector-pulse handling circuitry system. These strategies comprise the correction from the effects of pulse pile-up (PPU) and the detector response function (DRF). A first principles balance equation for second order PPU is derived and solved for the particular case of rectangular pulse shape. A Monte Carlo (MC) strategy is then implemented in the code MCPPU (Multi-shape pulse pile-up correction) allowing handling more general cases. Regarding the DRF, computed with deterministic or MC codes, it is presented the new tool RESOLUTION which introduces in the computed DRF the effects of energy resolution and incomplete charge collection. In the end the computer program UMESTRAT (Unfolding Maximum Entropy STRATegy) is presented in an updated version which include a new constrain to the total number of photons of the spectrum, which can be easily determined by inverting the diagonal efficiency matrix.