EMILIA, the LS counting efficiency for electron-capture and capture-gamma emitters

Abstract

This version includes new aspects that improve the computation of the counting efficiency for each one of the three available atomic rearrangement detection models (i.e., KLM, KL₁L₂L₃M and KLMN). The first modification involves a correction algorithm that simulates the non-linear response of the detector to photoionization for low-energy X-ray photons. Although this correction has the inconvenience of substantially increasing the number of atomic rearrangement detection pathways, the computed counting efficiency for low-Z nuclides is reduced by 2% for moderate quenching in agreement with experiment. The program also simulates how the addition of extra components, such as a quencher or aqueous solutions, affects the counting efficiency. Since the CIEMAT/NIST method requires identical ionization quench functions for the electron-capture nuclide and the tracer, the computation of the counting efficiency for ³H, the low-energy beta-ray emitter commonly used as tracer, is included in the program as an option.

Program summary

Title of program:EMILIA

Catalogue identifier:ADWK

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWK

Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland

Licensing previsions: none

Computers: revisions: any IBM PC compatible with 80386 or higher Intel processors

Operating systems under which the program has been tested:MS-DOS and higher systems

Programming language used:FORTRAN 77

Memory required to execute with typical data: 253 kword

No. of bits in a word: 32

No. of lines in distributed program, including test data, etc.:7147

No. of bytes in distributed program, including test data, etc.:74 776

Distribution format:tar.gz

Nature of the physical problem: The determination of radioactivity in liquid samples of electron-capture nuclides is demanded in radiation physics, radiation protection, dosimetry, radiobiology and nuclear medicine. The CIEMAT/NIST method has proved to be suitable for radionuclide standardizations when the counting efficiency of the liquid-scintillation spectrometer is sufficiently high. Although the method has widely been applied to beta-ray nuclides, its applicability to electron-capture nuclides nowadays has not the required degree of accuracy. The inaccuracies of the method are mainly induced by the huge number of low-energy electrons and X-ray photons emitted by the atomic rearrangement cascade after the electron-capture process, which are efficiently detected by liquid-scintillation counting, but are of difficult modeling due to the inherent complexity of the atomic rearrangement process and the non-linear response of the spectrometer in the low-energy range.

Solution method: A detailed simulation of the non-linear response of the spectrometer to photoionization must include the radiation emitted by the atomic rearrangement cascade. However, a model considering all possible scintillator de-excitations at atomic level increases exponentially the number of atomic rearrangement detection pathways subsequent to capture. Since the contribution of the non-linear effects to the counting efficiency are only corrective, we can approximate the reduced energy involved in the photoionization process to a sum of only three terms: the photoelectron energy, the mean energy of the KXY Auger electrons and the global energy contribution of the remaining radiation (electrons and X-rays) emitted by the atomic rearrangement cascade. The value of each term depends on the nature of the atom in which photoabsorption is produced and on the atom shell from where the photoelectron is ejected. The non-linear correction required to simulate low-energy X-ray photoabsorption is basically important when the scintillator cocktail contains elements of high atomic numbers. For heavy atoms, the K- and L-shell binding energies can be slightly less than the energy of the colliding photon. For such cases, the non-linear effects can play an important role.

Restrictions on the complexity of the problem: The simulation of all possible detection pathways of atomic rearrangement that follow to photoionization complicates the problem unnecessary. To correct the non-linear effects we consider only significative photoelectric interactions with the K- and L-shells. Also we assume that K-shell photoionizations only generate three types of entities: the photoelectron itself, KXY Auger electrons and a radiation group that includes the remaining emitted particles. For L-shell photoelectrons the radiation emission subsequent to photoionization is considered as a whole.

Introduction

The electron-capture nuclides have extensively been applied in fields that apparently have not very much to do such as radiobiology [1], [2], medicine diagnostics [3], [4], radiotherapy [5], [6] or astrophysics [7], [8]. However, the applicability of the radioisotopes to these disciplines frequently makes necessary to get standardized samples with uncertainties of less than 2%. The CIEMAT/NIST method [9], [10] is a tracing activity measurement method suitable for pure β [11], [12], [13], β-γ [14], [15], [16], pure EC [17], [18], [19] and EC-γ [20], [21], [22] radionuclides. The standardizations are carried out in a commercial liquid-scintillation spectrometer with two photomultipliers in coincidence. The spectrometer is calibrated for a set of samples of the tracer nuclide (usually ³H), and the relationship between the efficiencies of the tracer and the nuclide is computed from the energy distributions of the emitted particles. Also we assume that the generation of photoelectrons at the output of the photocathode follows the Poisson law. Although many laboratories apply the CIEMAT/NIST method to standardize β-ray emitters, a widespread use of the method has not been reached for EC nuclides, due to the uncertainties observed for certain nuclides.

Three different atomic rearrangement models have been proposed to simulate the spectrometer response to EC nuclides. The usual KLM model considers atoms with only three shells, where the energies of the three L_i subshells and the five M_i subshells are averaged to L- and M-shells, respectively. Some examples of codes that apply the three-shell model are: VIASKL [23] and EMI [24]. Since the KLM model does not include Coster–Kronig or Auger transitions from M-shell, its application is only recommended for EC-emitters of low atomic numbers. The second available atomic model, more suitable for heavy nuclides, includes the four shells KLMN. The addition of the N-shell to the atom structure may look apparently trivial, but the KLMN model generates 262 different pathways of atomic rearrangement [25]. The third available atomic model includes the three L-subshells, which increase considerably the number of possible pathways of atomic rearrangement, but have the advantage of making unnecessary averaged values for the L-fluorescence yields or for the KL_iL_j Auger electron energies. Also this model contemplates the Coster–Kronig emissions in a natural way [26]. However, the accuracy of the model has shown to be inadequate for nuclides with atomic numbers within the interval $45<Z<80$ [21]. The program EMILIA makes possible to select any of the three atomic rearrangement models.

As we mentioned above, the basic improvement of this version consists of modeling the non-linear response of the detector to the photoionization process. For typical scintillators such as toluene or Hisafe, the lack of the photoelectric correction generates an overestimation of 1% in the counting efficiency for ⁵⁵Fe. However, that is not the case for the commercial scintillator cocktails: Ultima-Gold and Insta-Gel, for which the non-linear effects in the detection of photoionization generate discrepancies greater than 3% with experiment [27].

One relevant aspect of this version is the computation of the ionization quench function. The structure of the function Q(E) of earlier versions [23], [24] is maintained, but two new options for the numerical integration of the Birks function [28] are added. The first option interpolates the mass collision stopping power in a table. The second applies the Bethe theory to compute the mass collision stopping power from the stoichiometric formula and the mean excitation energies of the component elements [29].

One special feature now included in EMILIA consists of the computation of the counting efficiency for the tracer (i.e., ³H) for the ionization quench function utilized for the nuclide. The successive versions of the programs EFFY [30], EMI [24] and EMI2 [26] apply different Q(E) functions, forcing the current users of the programs to modify this function, and maintain the requirement of identical ionization quench function for the nuclide and the tracer. This inconvenience has conveniently been corrected in this version.

Since the use of quenchers, e.g., carbon tetrachloride, or large volumes of aqueous solutions can modify the measured values of the counting efficiency [31], the program includes one option for allowing the addition of extra components. Two or more additional compounds can be simulated, making this option specially suitable for liquid-scintillation gel samples in which water, chloridric acid and carbon tetrachloride are incorporated to the cocktail in different concentrations.

The detailed analysis of the reliability of the atomic rearrangement models makes necessary to evaluate the influence of the atomic an nuclear parameters on the computed counting efficiency. This version allows the user to find how a 5% uncertainty in the input data is transmitted to the counting efficiency, and determine which parameters mainly contribute to efficiency as the atomic number Z increases [21].