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For an accurate calculation of target x-ray production or of projectile energy loss in low-Z materials, it is necessary to know the projectile charge state at each point in the material. If the projectile is fast enough so that charge transfer can be neglected with respect to electron stripping, it is possible to deduce a simple expression for the charge fractions as a function of the penetration distance into the target. The expression depends essentially only on the stripping cross section per electron of the particular shell being stripped, on the initial number of electrons on the projectile, and on the charge state. A small correction has to be applied for the effect of shells lying inside of the shell being stripped. The expression has been tested with Xe⁴⁵⁺ projectiles between 82 and 300 MeV/u and with U⁸³⁺ projectiles between 105 and 960 MeV/u with targets of Be, C, mylar, and Al. Model calculations are made of the effect of charge distributions on PIXE x-ray production and on projectile energy loss.

We investigate the minimum energy configuration of N equal point charges interacting via the Coulomb potential 1/r, and placed on an infinitely thin conducting disk. By minimizing total interaction energy, we obtain numerically the minimum energy configurations from which the rules for the distribution of charges on the disk are obtained.

We have investigated the minimum-energy distribution of N, 3 ≤ N ≤ 97, equal point charges confined to the surface of a sphere. Charges interact with each other via the Coulomb potential of the form 1/r. Minimum-energy distributions have been determined by minimizing the tangential forces on each charge. Further numerical evidence shows that in the minimum-energy state of N charges on the sphere, it is not possible to place a charge at the geometrical center. Besides, it has been found that the most and reliable information about the relative stability properties of the distributions can be obtained with the help of second difference energy consideration.

The minimum-energy configurations of $N(2\le N\le 160)$ identical classical point charges confined within a square under the effect of a Coulombic $1∕r$ potential have been determined by performing steepest-descent simulations. The energies of the final optimized configurations are given, along with their corresponding structural charge distributions. When all systems evolve in time to reach a minimum-energy configuration, local or global, they are all seen to be in quest of symmetry.

We have studied nuclear structure and reaction properties of Ne, Mg and Si isotopes, using relativistic mean field (RMF) densities, in the framework of Glauber model. Total reaction cross-section σ_R for Ne isotopes on ¹²C target have been calculated at incident energy 240 MeV. The results are compared with the experimental data and with the recent theoretical study [W. Horiuchi et al., Phys. Rev. C 86, 024614 (2012)]. Study of σ_R using deformed densities have shown a good agreement with the data. We have also predicted total reaction cross-section σ_R for Ne, Mg and Si isotopes as projectiles and ¹²C as target at different incident energies.

The electronic structure and its derived valence and conduction charge distributions along with the optical properties of zinc-blende GaAs${}_{1-x}$P${}_x$ ternary alloys have been studied. The calculations are performed using a pseudopotential approach under the virtual crystal approximation (VCA) which takes into account the compositional disorder effect. Our findings are found to be generally in good accord with experiment. The composition dependence of direct and indirect bandgaps showed a clear bandgap bowing. The nature of the gap is found to depend on phosphorous content. The bonding and ionicity of the material of interest have been examined in terms of the anti-symmetric gap and charge densities. The variation in the optical constants versus phosphorous concentration has been discussed. The present investigation may give a useful applications in infrared and visible spectrum light emitters.

Using density function theory calculation method, we investigated the charge distribution in nano- or low-dimension materials and some high pressure three-dimensional solids in many simple substances. It is found that if an atom in simple substances has different atomic environment from the other(s) nearby, they always have spontaneous charge inhomogeneity within local area. Charge inhomogeneity introduced by inequivalent atomic positions is a general phenomenon in simple substances, especially in their nano-materials. Such self-ionization significantly changes elemental matter’s physical and chemical properties. These results can advance the understanding on condensed matters, especially the internal structures and physical or chemical properties of elemental nano-materials, and could be a starting point for experimental investigation of self-ionization in them. The charge inhomogeneity of simple substances means their nonzero oxidation state or nonzero valence.

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors each of capacitance C is calculated. The method is generalized to infinite Simple Cubic (SC) lattice of identical capacitors each of capacitance C. We make use of the superposition principle and the symmetry of the infinite grid.

Some ground states features of ³²S, ³⁹K, ⁴⁰Ca and ⁴⁸Ca nuclei are investigated using the Hartree–Fock method with the Skyrme SKM^* and SLy4 forces calculated in two different code implementations. The calculated total binding energies per particle and root mean square (rms) nuclear charge radii using the Skyrme–Hartree–Fock (SHF) + BCS method are compared with relativistic mean-field (RMF) theory and experimental values. The obtained charge density distributions from these code implementations are compared with the experimental data. Pairing effects are also included in calculations for the same nuclei. Variations of the total binding energies per particle and rms nuclear charge radii were investigated as the last shell nucleons were carried to the upper shell.

The dynamics involved in the decay of light mass nuclei formed in asymmetric channels ¹²C + ²⁸Si, ¹¹B + ²⁸Si and ¹²C + ²⁷Al have been investigated using the dynamical cluster-decay model (DCM). In reference to the experimentally measured charge particle cross-sections, the fragment masses contributing towards the decay of ⁴⁰Ca* and ³⁹K* nuclei have been identified using spherical choice of fragmentation. Also, the role of entrance channel has been investigated by studying the decay of ³⁹K* nuclear system formed in two different reactions at same excitation energy. The behavior of fragmentation potential, preformation probability, penetrability and emission time, is analyzed to figure out the favorable mass fragments, their relative emergence and the entrance channel effects observed in the decay of light mass nuclei. In addition to this, the cross-sections for the light particles (LPs) and heavier charge fragments have been estimated for the compound nucleus (CN) decay. Besides this, one of the noncompound nucleus (nCN) process, deep inelastic collision (DIC) has been addressed in context of DCM approach for the first time. The cross-sections obtained in framework of DCM for both CN and nCN processes are found to have nice agreement with the available experimental data.

In this work, we designed a composite intrinsic chiral structure through introducing an anisotropic environment around the extrinsic chiral structure. The designed structure is made up of an extrinsic chiral nanocrescent based on an anisotropic substrate. The simulation results of the extinction show that intrinsic chirality can be obtained and tuned by changing the angle between the optical axis of the anisotropic substrate and the mirror axis of the nanocrescent ($\varphi$). The maximum value of circular dichroism (CD) is up to about 0.035. Additionally, according to the charge distributions, the obtainment of our intrinsic chirality is originated from a new symmetry breaking introduced by the anisotropic substrate to the extrinsic chiral structure. This study could provide a new perspective for understanding chirality generation and could promote the application of chirality in imaging, sensing, etc.

The atom-bond electronegativity equalization method (ABEEM) and its applications for predicting intrinsic properties of large molecules, such as the charge distribution, the molecular energy, the local softness and the Fukui function, the regio- and stereo-selectivity of Diels–Alder reactions, the linear response function, and the charge polarization normal modes have been formulated. The examples show that there is a very good agreement of the ABEEM results with those of the corresponding ab initio quantum chemical calculations, demonstrating the reasonable and possible ABEEM's applications to the large molecular systems.

Tetramer of lactose repressor (LacR) protein plays an essential role in controlling the transcription of DNA. The previous experimental studies elucidated that the carboxyl-terminal domain of LacR is important for the tetramerization of LacR. In the present study, we investigated stable structures of monomers, dimers and tetramer of LacR by molecular mechanics and molecular dynamics simulations, based on AMBER force field to elucidate the effect of the tetramerization domain on LacR structure. The obtained stable structures for both the LacR tetramers, with and without the tetramerization domain, indicate that this domain is essential for constructing a compact structure of LacR tetramer. On the other hand, this domain does not affect the structure of LacR dimer. Furthermore, we investigated the charge distributions and binding energies for these stable structures by the charge equilibration and semiempirical molecular orbital methods. The results elucidate how the removal of the tetramerization domain causes the change in the electrostatic interaction between LacR dimers in the LacR tetramer, resulting in the separation of LacR dimers without the domain.