Diffuse versus square-well confining potentials in modelling AA@C60_{60} atoms

Attention: this version-$2$ of the manuscript differs from its previously uploaded version-$1$ (arXiv:1112.6158v1) and subsequently published in 2012 J. Phys. B \textbf{45} 105102 only by a removed typo in Eq.(2) of version-$1$; there was the erroneous factor "2" in both terms in the right-hand-side of the Eq.(2) of version-$1$. Now that the typo is removed, Eq.(2) is correct. A perceived advantage for the replacement of a discontinuous square-well pseudo-potential, which is often used by various researchers as an approximation to the actual C$_{60}$ cage potential in calculations of endohedral atoms $A$@C$_{60}$, by a more realistic diffuse potential is explored. The photoionization of endohedral H@C$_{60}$ and Xe@C$_{60}$ is chosen as the case study. The diffuse potential is modelled by a combination of two Woods-Saxon potentials. It is demonstrated that photoionization spectra of $A$@C$_{60}$ atoms are largely insensitive to the degree $\eta$ of diffuseness of the potential borders, in a reasonably broad range of $\eta$'s. Alternatively, these spectra are found to be insensitive to discontinuity of the square-well potential either. Both potentials result in practically identical calculated spectra. New numerical values for the set of square-well parameters, which lead to a better agreement between experimental and theoretical data for $A$@C$_{60}$ spectra, are recommended for future studies.Comment: 11 pages, 4 figure

Double photo-ionization of He near a polarizable surface

We calculate the differential cross-section of the direct double photo-ionization of He physisorbed on a polarizable surface. By including the influence of the surface potential in the correlated two-electron final state wavefunction, we show that the differential cross-section carries detailed information on the electronic correlations at the surface. In particular, photo-emission along opposite directions, which is prohibited in the free space, is allowed if the surface potential is long-ranged.Comment: To appear in Phys. Rev. B - Rapid Comm. - 4 pages, 2 PostScript figures embedde

Three-body non-additive forces between spin-polarized alkali atoms

Three-body non-additive forces in systems of three spin-polarized alkali atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio calculations. The non-additive forces are found to be large, especially near the equilateral equilibrium geometries. For Li, they increase the three-atom potential well depth by a factor of 4 and reduce the equilibrium interatomic distance by 0.9 A. The non-additive forces originate principally from chemical bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files

Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website

J.M.: Computational methods for generalized Sturmians basis

The computational techniques needed to generate a two-body Generalized Sturmian basis are described. These basis are obtained as a solution of the Schrödinger equation, with two-point boundary conditions. This equation includes two central potentials: A general auxiliary potential and a short-range generating potential. The auxiliary potential is, in general, long-range and it determines the asymptotic behavior of all the basis elements. The short-range generating potential rules the dynamics of the inner region. The energy is considered a fixed parameter, while the eigenvalues are the generalized charges. Although the finite differences scheme leads to a generalized eigenvalue matrix system, it cannot be solved by standard computational linear algebra packages. Therefore, we developed computational routines to calculate the basis with high accuracy and low computational time. The precise charge eigenvalues with more than 12 significant figures along with the corresponding wave functions can be computed on a single processor within seconds

Double photoionization of helium: a generalized Sturmian approach

In this work we study the double photoionization of helium induced by low intensities laser fields in the regime where only one photon absorption occurs. The method proposed here is based on a Generalized Sturmian Functions (GSF) spectral approach which allows the imposition of outgoing boundary conditions for both ejected electrons. These, in turn, construct an hyperspherical flux characteristic of double continuum wave functions. We compare our calculated cross sections at 20 and 40 eV above threshold with absolute and relative measurements, and with other calculations. Our results definitively demonstrate the applicability of the GSF approach for dealing with break-up Coulomb problems

Photodouble ionization studies of the Ne(2s2) state under unequal energy sharing conditions

The triple differential cross section (TDCS) of the He2+(1s -2) and Ne2+(2s-2) states has been studied under unequal energy sharing conditions and perpendicular geometry, for a ratio of about 3 between the energies of the two ejected electrons. The dynamical quantities which govern the photodouble ionization (PDI) process, i.e. the squared moduli of the gerade and ungerade complex amplitudes and the cosine of their relative phase, have been extracted from the experimental data. The results from the two targets have been compared between themselves as well as with the theoretical predictions of the SC3 and convergent close coupling (CCC) calculations. This work represents a joint experimental and theoretical approach to the investigation of PDI of atomic systems with more than two electrons.Fil: Bolognesi, P.. Consiglio Nazionale delle Ricerche; Italia. Istituto di Metodologie Inorganiche e dei Plasmi; ItaliaFil: Kheifets, A.. Australian National University; AustraliaFil: Otranto, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. University of Missouri; Estados UnidosFil: Coreno, M.. Consiglio Nazionale delle Ricerche; Italia. Istituto di Metodologie Inorganiche e dei Plasmi; Italia. Tecnologie Avanzate e Nanoscienza; ItaliaFil: Feyer, V.. Consiglio Nazionale delle Ricerche; Italia. National Academy of Sciences; UcraniaFil: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Garibotti, Carlos Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Avaldi, L.. Consiglio Nazionale delle Ricerche; Italia. Istituto di Metodologie Inorganiche e dei Plasmi; Italia. Tecnologie Avanzate e Nanoscienza; Itali