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In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge $Z_{cr}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, $Z_{cr,2e}=0.91085$ and $Z_{cr,3e}=2.009$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z-Z_{cr})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at $Z_{cr}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of 1/Z-expansion is briefly discussed., 10 pages, LaTeX, typos corrected, Fig.1 added, a Note Added with calculated critical charge for $2^1S$ state for $(Z,e,e)$ system, $Z_{cr,2e}^{(2^1S)}\ =\ 1.02$

We calculate the three-body spectrum for identical bosons interacting via attractive $1/{r}^{2}$ potentials. We find an infinite number of three-body states even when the pair interactions are too weak to support any two-body states. These new states thus share this surprising scenario with the Efimov effect, but are not themselves Efimov states. Our effect occurs for both identical bosons and identical fermions, and it persists in the presence of two-body bound states.

In a recent paper [Phys. Rev. A 77, 064702 (2008)], Bruhns et al. reported on an experimental investigation of charge transfer in collisions of ${\text{Si}}^{3+}$ ions with atomic hydrogen and compared the energy dependence of the transfer cross sections with published theoretical results and with earlier experimental results for other effectively-one-electron isocharged ions, including ${\text{C}}^{3+}$ and ${\text{O}}^{3+}$. These authors observe that these three ions all have the structure of a single electron outside a closed subshell and thus might be expected to behave similarly. However, their results show quite different behavior, and they conclude that the influence of quantum-mechanical effects from the ionic core is clearly seen. We have investigated theoretically three collision systems, ${\text{Si}}^{3+}$, ${\text{C}}^{3+}$, and ${\text{O}}^{3+}$ with atomic hydrogen, at projectile energies up to 10 keV/amu using the method of electron nuclear dynamics (END). In this paper we want to clarify and describe in some detail these quantum-mechanical effects by showing the time-dependent dynamics of the electrons during the collision of these three ions with atomic hydrogen. Total charge transfer cross sections were calculated for all three ions and compared with other theoretical and experimental results, showing good overall agreement. With this validation of the END description of the processes, we analyze the details of the computed dynamics of the electrons in each of the processes and illustrate the different mechanisms underlying observed differences in reaction outcomes.

A non-relativistic classification of charged molecular hydrogenic, helium and mixed helium-hydrogenic chains with one or two electrons which can exist in a strong magnetic field $B \lesssim 10^{16} $G is given. It is shown that for both $1e-2e$ cases at the strongest studied magnetic fields the longest hydrogenic chain contains at most five protons indicating to the existence of the $\rm{H}_5^{4+}$ and $\rm{H}_5^{3+}$ ions, respectively. In the case of the helium chains the longest chains can exist at the strongest studied magnetic fields with three and four $\al-$particles for $1e-2e$ cases, respectively. For mixed helium-hydrogenic chains the number of heavy centers can reach five for highest magnetic fields studied. In general, for a fixed magnetic field two-electron chains are more bound than one-electron ones., 32 pages, 2 figures, 9 tables

Shannon entropies of the pair density, conditional entropies, and mutual information are studied in position and in momentum space for ground state neutral atoms and selected excited states at the Hartree-Fock level. We show that the mutual information, a measure of correlation, is larger in position space than in momentum space. This result also holds for a mutual information defined in terms of the exchange density; however, these quantities display much more structure than the corresponding ones based on the pair densities. The interpretation of this behavior is that exchange effects are smaller in momentum space than in position space in these systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

The common basis sets constructed for use in electronic structure calculations have been found inadequate for the representation of electrons participating in nonadiabatic time-dependent dynamics calculations. In this paper we outline an approach to construct electronic bases better suited for dynamical processes such as energy deposition and charge transfer in binary collisions of ions, atoms, and molecules. Since electrons of many-atom systems commonly are represented by orbitals formed as linear combinations of atomic orbitals, the focus is on atomic basis sets. The main idea is to construct basis sets that adequately reproduce the first few excitation energies of neutral atoms. In this paper we outline a method for such basis set construction of various levels of accuracy for first-row atoms and give a few illustrative examples.

A detailed study of the ground state of the H{sub 3}{sup +} molecular ion in linear configuration, parallel to the magnetic field direction, and its low-lying {sigma}, {pi}, and {delta} states is carried out for magnetic fields B=0-4.414x10{sup 13} G in the Born-Oppenheimer approximation. The variational method is employed with a single trial function which includes electronic correlation in the form exp({gamma}r{sub 12}), where {gamma} is a variational parameter. It is shown that the quantum numbers of the state of the lowest total energy (ground state) depend on the magnetic field strength. The ground state evolves from the spin-singlet {sup 1}{sigma}{sub g} state for weak magnetic fields B(less-or-similar sign)5x10{sup 8} G to a weakly bound spin-triplet {sup 3}{sigma}{sub u} state for intermediate fields and, eventually, to a spin-triplet {sup 3}{pi}{sub u} state for 5x10{sup 10}(less-or-similar sign)B(less-or-similar sign)4.414x10{sup 13} G. Local stability of the linear parallel configuration with respect to possible small deviations is checked.

A first detailed study of the low-lying electronic states of the H 3 + molecular ion in linear configuration, parallel to a magnetic field, is carried out for B=0–4.414×1013 G in the Born-Oppenheimer approximation. The variational method is employed with a single, physically adequate trial function which includes, in particular, explicitly the electronic correlation term in the form exp (γ r12), where γ is a variational parameter. The state of the lowest total energy (ground state) depends on the magnetic field strength. It evolves from spin-singlet 1Σg for small magnetic fields B≲5×108 G to weakly-bound spin-triplet 3Σu for intermediate fields and eventually to spin-triplet 3Πu state for B≳5×1010 G.

Tissues diseases treatment by traditional medicine strategies is often impaired by the inability of restoring the normal function of scared tissues as confirmed by several problems concerning the optimal therapy of defects after trauma and degenerative pathologies which have not yet been solved. The most compatible sources of graft tissue are often offered by humans themselves: for example autologous bone graft provides all three key elements for generating bone tissue, respectively the osteogenic progenitor cells, osteoinductive growth factors and osteoconductive matrices. However, the autologous tissue employment is still subject to restrictions firstly due to limited quantity of donors. For these reasons, the challenge of last years in tissue regeneration consists in the development of biodegradable scaffolds based on natural and synthetic polymeric materials. However, the employment of biodegradable polymers even if highly biocompatible, is limited by their low mechanical response in connection with fast degradation kinetics. Instead, composite materials obtained by the matching of polymers and ceramic phases are preferable from the mechanical point of view offering a tremendous versatility as scaffold materials for the bone and meniscus regeneration. In particular, the accurate external and internal design of the scaffold on both macrometric and micrometric scale, provides a reliable environment for tissue formation assuring an optimal cell colonization and an adequate transport of small molecules for the nutrient supply and the functional signals delivery.