MICELLE, the micelle size effect on the LS counting efficiency

Abstract

This version extends the computation of the liquid-scintillation counting efficiency to electron-capture radionuclides of $30⩽Z⩽54$. The simplified deterministic models of previous versions are replaced by a complete stochastic model, which considers all possible subshells involved in the atomic rearrangement of the atom. The program can simulate samples in the gel phase, including the effects of the micelles on the counting efficiency. These effects have been found to be useful for building nanodosimeters based on gel scintillators.

Program summary

Title of program: MICELLE

Catalogue identifier:ACPU_v3_0

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ACPU_v3_0

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: 235 kword

No. of bits in a word: 16

No. of lines in distributed program, including test data, etc.: 16 653

No. of bytes in distributed program, including test data, etc.: 358 166

Distribution format: tar.gz

Nature of the physical problem: Both β and electron-capture are decay processes characterized by a large variability in energy. In the first case, one single β-particle is emitted per decay following the Fermi distribution. In the second, several electrons (Auger and/or Coster–Kronig) of very different energies can be ejected simultaneously. The detailed simulation of these two electron release processes has practical interest in two situations: (1) to standardize radionuclides with a liquid-scintillation counter, (2) to compute the absorbed dose in the surroundings of a radiolabeled molecule.

Method of solution: Although the application of simplified deterministic models is sufficiently accurate for pure β-ray emitters, the large stochastic variability of both electron-capture and internal conversion processes restricts the accuracy of the deterministic models KLM, KLMN and KL₁L₂L₃M to nuclides of low atomic numbers. To extend the applicability of the method to larger nuclei, both $M_i$- and $N_j$-subshells must be included into the model. However, the addition of these outer atom subshells to the deterministic model involves a huge number of atomic rearrangement pathways, requiring from simplifications which are frequently limited to certain nuclides. A more feasible method considers using random numbers to simulate step by step the rearrangement of the atom.

Restrictions on the complexity of the problem: The program is restricted to radionuclides of atomic numbers within the interval $30⩽Z⩽54$. This version ignores the photoionization quench correction, which can be obviated for $Z⩾30$. On the other hand, the simulation of the mechanisms of multiple ionization require from more elaborated models for $Z>54$. Experiments with gases are only available for nuclides with atomic numbers larger than that of ¹³¹I, for which the emission of Auger electrons, and consequently the ionization of xenon ($Z=54$), stops for transitions outer than N₄O₂O₂.

Introduction

Recent experiments [1], [2] have confirmed the necessity of a more realistic atomic rearrangement model for large-Z electron-capture nuclides. In particular, the three models describing the rearrangement of the atom, KLM [3], KL₁L₂L₃M [4] and KLMN [5], fail to obtain discrepancies with experiment better than 2% [6]. The reason is the increase of the detection probability of the outer atom Auger electrons with the size of the atom.

Although a deterministic model based on atomic rearrangement pathways avoids the use of random number generators for the achievement of the counting efficiency, the total number of pathways is closely related to the atomic number Z of the nuclide. This number can result in many thousands for the model KL₁L₂L₃M₁M₂M₃M₄M₅N, which does not include the $N_j$-subshells [7]. Since some pathway probabilities are negligible compared to others, simplifications are feasible, but with the drawback of depending on the Z-value. In other words, certain pathways with negligible probabilities for a given value of Z may become appreciable for a different Z-value [6].

The idea of simulating the Auger cascade ensuing the electron-capture or internal conversion processes was first proposed by Charlton and Booz [8] and Humm [9]. More recent publications give details on how random number generators can be used to simulate ¹²⁵I [10], [11], [12], but a general code applicable to other radionuclides is not available in the literature.

A feasible atomic rearrangement method is required to compute the counting efficiency for samples in the gel phase. It has been proved that the size of the micelle has a negligible effect on the counting efficiency for pure β-ray nuclides [13]. However, that is not the case for electron-capture nuclides, for which the abundant generation of low-energy electrons in the rearrangement of the atom modifies the counting efficiency in a few percent [13].

Because the medium surrounding the radioactive atom is liquid water in the nanoscale, we can make extensive the New Oak Ridge Electron Code (NOREC) [14] to any micelle size and geometry, and evaluate the micelle effects on the counting efficiency. The computation of the absorbed dose in the surroundings of the emission point facilitates, in another context, the simulation of the damaging efficiency for certain biomolecules [15], and makes feasible to measure doses with gel scintillators [16].