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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.

The detector response function of X-ray and gamma-ray detectors is obtained from the convolution of the energy deposition spectrum with the detector resolution function. The energy deposition spectrum can be computed by using deterministic or Monte Carlo codes, while the energy resolution depends specifically on the detection mechanism, which is characteristic of the single detector. In a first approximation, the energy resolution can be modeled using a normalized Gaussian distribution having its full width at half maximum expressed in terms of specific semiempirical formulas for solid-state detectors, scintillators, and gas proportional counters. However, this approach is not sufficient with some solid-state detectors. It is frequent to find that the peaks show a deviation from the Gaussian shape: a long flat shelf structure from the peak centroid to the lower energies and an asymmetry that can be described with an exponential decay on the left side of the peak. These two effects have been introduced in the new tool RESOLUTION by adapting empirical models found in literature. RESOLUTION can be tailored to the specific detector by analyzing measured monochromatic peaks by means of the following strategies: (1) in a first approximation, a Gaussian shape is assumed in order to determine the full width at half maximum parameters, (2) if it is noted a flat background on the left side of the peak, then a shelf function is added, and (3) if a departure of the Gaussian is observed, then an exponential tail function is added. RESOLUTION gives a very precise description of the line shape.