Robin P. Gardner

Prediction of the pulse-height spectral distortion caused by the peak pile-up effect

Abstract A method is developed for calculating the distortion in pulse-height spectra obtained from spectrometry systems caused by the peak pulse pile-up effect. A general expression for double pulse coincidences is derived from the interval distribution for calculating the observed spectrum in terms of the true (undistorted) spectrum, the allowable pulse width, and the pulse shape. A specific model with explicit solution is obtained by assuming that the pulse shape is parabolic. Good agreement is obtained between this model and experimental data on a specific system which has a pulse shape that is approximately parabolic. An iterative procedure can be employed with the present model to obtain true spectra from observed spectra that contain considerable pulse pile-up.

On the solid angle subtended by a circular disc

Abstract The solid angle subtended by a circular disc from a point is approximated by the analytical expression for the solid angle for n-sided, regular polygon of area equal to that of the disc. When the point is farther from the plane of the disc than 0.1 the disc radius, polygons of 20 and 36 sides are required for approximating the solid angle subtended by the disc to within 1 and 0.1% respectively. In addition, the average solid angles subtended by circular discs from circular discs are calculated and given in tabular form for a range of disc sizes.

An investigation of the possible interaction mechanisms for Si(Li) and Ge detector response functions by Monte Carlo simulation

Abstract Simple physical mechanisms implemented by either analog Monte Carlo simulations or analytical models have been used to investigate the Si(Li) and Ge detector response functions for X- and gamma rays, respectively. The mechanisms investigated include the various possible combinations of partial losses of photoelectric and Auger electrons from the detector surfaces and complete losses of the various photons involved such as the Si K X-ray, the 0.511 MeV annihilation photons, and single or multiple Compton scattered photons. The most probable interaction mechanisms for each detector response function feature are identified and the simple analytical functions that have been used in the past are justified.

A generalized method for correcting pulse-height spectra for the peak pile-up effect due to double sum pulses: Part I. Predicting spectral distortion for arbitrary pulse shapes☆

Abstract In a previous paper a method for calculating the distorted or observed high counting rate pulse-height spectra from spectrometry systems when the undistorted or true spectra are known from low counting-rate spectra was developed based on double sum pulses and approximation of the pulse shape by a parabola. The present Part I paper extends this to double sum pulses of any arbitrary shape by methods that are suitable for use on any spectrometry system. In Part II of this paper a method for performing the inverse calculation for obtaining true from observed spectra is developed that is based on the model predicting spectral distortion developed here and in the previous paper.

A new Monte Carlo assisted approach to detector response functions

The physical mechanisms that describe the components of NaI, Ge and Si(Li) detector responses have been investigated using Monte Carlo simulation. The mechanisms described focus on the shape of the Compton edge, the magnitude of the flat continuum, and the shape of the exponential tails features. These features are not accurately predicted by previous Monte Carlo simulations. Probable interaction mechanisms for each detector response component are given based on this Monte Carlo simulation.

An improved Si(Li) detector response function

Abstract An improved Si(Li) detector response function model over the range from 5 to 60 keV has been developed. The values of the model parameters are obtained by least-squares fitting of the pulse-height spectra from a number of pure-element samples excited by 109 Cd or 241 Am sources. Simple functional forms of the separable parts of the detected X-ray pulse-height spectrum as functions of incident energy are summed to produce the generalized response function. Compared to previous work [Nucl. Instr. and Meth. A243 (1986) 121, ref. [1]] the following changes and improvements have been made: (1) the entire useful energy range of the Si(Li) detector from 5 to 60 keV is treated rather than the previous upper limit of about 20 keV, (2) a Compton-scattering continuum function from both the detector and the surrounding material has been added to account for the additional features observed with high-energy X-rays, (3) consideration of radiative Auger satellite X-ray lines has been found to account for the previously observed discrepancy in the model parameters for K α and K β X-rays, (4) the resulting generalized detector response function has a much simpler and more consistent form than the previous one, ref. [1] and (5) the new model parameters expressed as functions of energy are more consistent with physical phenomena than before and are not just fitted polynomials. Applications of the new Si(Li) detector response function are discussed.

A semi-empirical model for the gamma-ray response function of germanium detectors based on fundamental interaction mechanisms

Abstract A model for describing the response function of large volume gamma-ray detectors over the range of incident gamma ray energies between 1.0 and 6.5 MeV has been developed and applied to a 39% high purity germanium detector. Functional forms for describing the various features of the response function are based either on empirical functions or on the shape of exact analytical expressions for the interaction mechanisms as in the case of multiple Compton scattering of the primary and the annihilation photons. These functions are combined and fit by an appropriate linear-nonlinear least squares method to measured single energy photon spectra. The model parameters so obtained are then fit to simple functions of the incident gamma-ray energies to form the complete response function of the detector. Validity of the model is demonstrated by synthesizing a 49Ca spectrum using the response function and comparing it to the equivalent measured spectrum.

Solid angle subtended by a circular cylinder

Abstract The solid angle subtended at a point by the lateral surface of a right circular cylinder is approximated by replacing the cylinder surface area seen from the point by a regular polygonal cylindrical surface. This approximation combined with a similar approximation for the solid angle subtended by a circular disc, enables the calculation of the total solid angle from a right circular cylinder to any desired degree of accuracy.

A new G–M counter dead time model

A hybrid G-M counter dead time model was derived by combining the idealized paralyzable and non-paralyzable models. The new model involves two parameters, which are the paralyzable and non-paralyzable dead times. The dead times used in the model are very closely related to the physical dead time of the G-M tube and its resolving time. To check the validity of the model, the decaying source method with 56Mn was used. The corrected counting rates by the new G-M dead time model were compared with the observed counting rates obtained from the measurement and gave very good agreement within 5% up to 7 x 10(4) counts/s for a G-M tube with a dead time of about 300 micros.

Monte Carlo calculation of efficiencies of right-circular cylindrical NaI detectors for arbitrarily located point sources

Abstract An efficient Monte Carlo program for calculation of total intrinsic efficiency, peak-to-total ratio and source intrinsic efficiency of bare right-circular cylindrical NaI(Tl) detectors from an arbitrarily located isotropic point source emitting photons of energy 1 MeV or below is outlined. Total variance reduction based on physical principles is used throughout to insure that each proton history is successful in order to minimize computer time. Results show close agreement with other Monte Carlo calculations for sources located along the detector axis and with experiments for sources located off-axis.