RESUMO
Variational Monte Carlo method is a powerful tool to determine approximate wave functions of atoms, molecules, and solids up to relatively large systems. In the present work, we extend the variational Monte Carlo approach to study confined systems. Important properties of the atoms, such as the spatial distribution of the electronic charge, the energy levels, or the filling of electronic shells, are modified under confinement. An expression of the energy very similar to the estimator used for free systems is derived. This opens the possibility to study confined systems with little changes in the solution of the corresponding free systems. This is illustrated by the study of helium atom in its ground state (1)S and the first (3)S excited state confined by spherical, cylindrical, and plane impenetrable surfaces. The average interelectronic distances are also calculated. They decrease in general when the confinement is stronger; however, it is seen that they present a minimum for excited states under confinement by open surfaces (cylindrical, planes) around the radii values corresponding to ionization. The ground (2)S and the first (2)P and (2)D excited states of the lithium atom are calculated under spherical constraints for different confinement radii. A crossing between the (2)S and (2)P states is observed around rc = 3 atomic units, illustrating the modification of the atomic energy level under confinement. Finally the carbon atom is studied in the spherical symmetry by using both variational and diffusion Monte Carlo methods. It is shown that the hybridized state sp(3) becomes lower in energy than the ground state (3)P due to a modification and a mixing of the atomic orbitals s, p under strong confinement. This result suggests a model, at least of pedagogical interest, to interpret the basic properties of carbon atom in chemistry.
RESUMO
PURPOSE: Halogenated pyrimidines (iododeoxyuridine [IUdR] and bromodeoxyuridine [BUdR]), platinum salts, and gadolinium porphyrins are heavy atom compounds used as radiosensitizers. For IUdR, it has been hypothesized that iodine inner shell ionizations (ISI) and Auger cascades could be one of the primary radiosensitization mechanisms. The purpose of this paper is to estimate the number of ISI produced per tumor cell and per 2 Gy irradiation in clinically relevant modelings. MATERIALS AND METHODS: ISI were evaluated using a two-step method. Photon-induced ISI were calculated using the MCNP-4C Monte Carlo code, heavy atom concentrations from clinical data published in the literature, and at various depths in a water phantom irradiated with 6-MV, (60)Co, (137)Cs, or (192)Ir sources. Electron knock-on induced ISI on K, L, and M atomic shells were evaluated with an hybrid method, using simulated electron spectra and cross-sections derived from the Møller formalism. Using a biological dose equivalence of 0.05 Gy per cell ISI, relative biological effectiveness (RBE) values were calculated for each situation. RESULTS: For platinum and gadolinium, ISI occurs in far less than 0.1% of the cell, whichever is the configuration. For IUdR and BUdR, ISI occurs in between 45% to 483% of the cell. Due to spectrum degradation, about 3 times more photoelectric ISI are generated at greater than shallower depths, and 10 times more for (192)Ir compared with (60)Co or 6-MV X-rays. Photoelectric ISI are about 3 times more frequent for iodine than bromine, but electron knock-on ISI are more frequent on bromine, and at the end about the same number of ISI are generated for both elements. RBEs were found to be between 1.01 and 1.12 for clinically relevant irradiation settings. CONCLUSIONS: The mechanisms of radiosensitization for platinum and gadolinium are clearly not related to an Auger cascade. For halogenated pyrimidines, however, clinically relevant numbers of ISI are generated within each cell. For IUdR, ISI appears to be strongly tied to the photon spectra. Halogenated pyrimidines should be evaluated again clinically, but using lower energy photons like a (192)Ir implant.