The harmonic hyperspherical basis for identical particles without permutational symmetry

The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, the matrix elements between the basis elements are simple, and the potential energy is presented in a compact form, well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it, and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential

Variational Estimates using a Discrete Variable Representation

The advantage of using a Discrete Variable Representation (DVR) is that the Hamiltonian of two interacting particles can be constructed in a very simple form. However the DVR Hamiltonian is approximate and, as a consequence, the results cannot be considered as variational ones. We will show that the variational character of the results can be restored by performing a reduced number of integrals. In practice, for a variational description of the lowest n bound states only n(n+1)/2 integrals are necessary whereas D(D+1)/2 integrals are enough for the scattering states (D is the dimension of the S matrix). Applications of the method to the study of dimers of He, Ne and Ar, for both bound and scattering states, are presented.Comment: 30 pages, 7 figures. Minor changes (title modified, typos corrected, 1 reference added). To be published in PR

General integral relations for the description of scattering states using the hyperspherical adiabatic basis

In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. To this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative $s$ partial waves, and with applicability in multichannel reactions. The convergence of the ${\cal K}$-matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a $^4$He atom on a \dimer dimer (only the elastic channel open), and for collisions involving a $^6$Li and two $^4$He atoms (two channels open).Comment: Accepted for publication in Physical Review

Variational description of continuum states in terms of integral relations

Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is not the case when the integral relations are applied since, due to their short range nature, the only condition for the scattering wave function $\Psi$ is that it be the solution of $(H-E)\Psi=0$ in the internal region. Several examples are analyzed for the computation of phase-shifts from bound state type wave functions or, in the case of the scattering of charged particles, it is possible to obtain phase-shifts using free asymptotic conditions. As a final example we discuss the use of the integral relations in the case of the Hyperspherical Adiabatic method.Comment: 34 pages, 7 figures, accepted in Phys. Rev.

Electrostatic fluidized bed deposition of a high performance polymeric powder on metallic substrates

The electrostatic fluidized bed deposition of a single-layer PPA 571 coating onto low carbon steel rods is reported. A full factorial experimental design was developed in order to study the influence of several operative variables on the effectiveness of the coating process and on the coating thickness and uniformity. The operative variables included exposure time, air flow, the applied voltage, attitude, and the radial and vertical location of the work-piece in the fluid bed. After the experimentation, several process maps were developed as a support to identify the best way to lead the coating process. Finally, by using a statistical approach, the reliability and repeatability of the coating process was also established. Experimental trends were consistent with theoretical expectation. A significant growth in achievable coating thickness was obtained by increasing voltage and air flow. Furthermore, at higher values of exposure time and applied voltage, relevant back ionization phenomena occurred, which simultaneously caused a top limit in coating thickness and a worsening of surface finishing. Process characteristics, leading mechanisms, and some practical aspects are also discussed in detail. (c) 2005 Elsevier B.V. All rights reserved

On the use of CrN/Cr and CrN interlayers in hot filament chemical vapour deposition (HF-CVD) of diamond films onto WC-Co substrates

CrN/Cr-based films were deposited using PVD-arc technique onto Co-cemented tungsten carbide (WC-Co) substrates and, then, seeded with diamond powder suspension or mechanically treated by Fluidized Bed Peening (FBP) of brittle diamond powders. Multilayered coatings were obtained from the superimposition of 4 mu m-thick diamond coatings, deposited on the PVD interlayer using hot filament chemical vapour deposition (HFCVD). The effectiveness of fluidized bed peened CrN/Cr interlayers on the adhesion enhancement of diamond on WC-Co substrates was studied and compared to diamond coated WC-Co substrates with unpeened CrN/Cr or CrN interlayers, or pre-treated with two-step chemical etching (Murakatni's reagent and Caro's acid, MC-treatment). In particular, growth, morphology, wear endurance and adhesion of the CVD deposited diamond films onto peened CrN/Cr interlayer were looked into. Diamond coatings on peened CrN/Cr interlayers exhibited a rougher surface morphology than as-prepared CrN/Cr films as a result of the surface roughening of the ductile Cr layer produced by the repeated impacts on it of the diamond powders during FBP. FBP was found to be a necessary step in improving the scarce adhesion of CVD diamond onto CrN/Cr-interlayer. However, the use of FB peened CrN/Cr interlayer did not represent the best way to pre-treat WC-Co substrates, as the unpeened single-layer CrN, or the use of MC pretreatment, was found to ensure better adhesion and wear endurance. (C) 2008 Published by Elsevier B.V

Yang-Mills fields on CR manifolds

We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold.Comment: 52 page