MICELLE, the micelle size effect on the LS counting efficiency☆
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 -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].
Section snippets
Monte Carlo simulation of electron-capture and internal conversion transitions
The rearrangement of the atom ensuing electron-capture starts with the capture of one electron from anyone of the four shells K, L1, L2, L3, M. A random number is then generated to simulate the position of this first vacancy. If (being the probability of electron-capture for the K-shell), the vacancy occurs in the K-shell. When the random number falls within the following intervals:
Program structure
The program MICELLE contains a main program and 52 subprograms. All subprograms, with the exception of BETA2 and GAMMA, simulate the rearrangement of the atom ensuing a vacancy in an inner shell. The subprograms CONFIGK, CONFIGL1, …, CONFIGN4 compute the electrons available in the outer shells of the atom, which can be ejected as Auger or Coster–Kronig electrons. The subprogram PV1 generates, according to Eqs. (1), (2), (3), (4), a vacancy within the atom as a consequence of the capture of one
Input–output data files
The input file CTL (Fig. 4) is used to control the different options of the program MICELLE. It contains the following data:
NDECAY number of simulating decay events; R0, H vial internal radius and its height in cm; NSUC number of Monte Carlo simulating X- and γ-ray photons; FIN, FFIN, DINC free parameter interval and increment; NENT integer number between 1 and 5 denoting the type of scintillation cocktail; NQE integer number between 1 and 4 representative of the ionization quench function; IATOMEX the
Test run
As a test run of the program, we propose to compare the effects of the micelle size on the counting efficiency for 125I, when the samples are prepared in the gel phase. The test run output of the first example lists the output on the screen and the data stored in the file X, when the micelle correction option in CTL is enabled (i.e. IMICELL = 1), and the radius of the micelle is set to 4 nm (i.e. RADSPH = 4). Because this simulation corresponds to samples in Insta Gel with a 6.25% of
Acknowledgements
The author would like to acknowledge the financial support of the Science and Technology Ministry of Spain through the Ramón y Cajal Programme.
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