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We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be calculated without any approximation and the precision is restricted only by the dimension of the basis. This method can be applied whatever the system under consideration. In some cases, the convergence property is greatly improved in this new scheme as compared to the old traditional method. Some numerical tricks to reduce computer time are also presented.

Stimulated amplification of fluorescence signals is obtained under conditions which approach biocompatibility by adding NanoParticles (NPs) to an aqueous solution of fluorescein. The conditions for the stability of the suspension and optimum dye concentration are detailed, together with considerations on photobleaching and phototoxicity. A dedicated experimental setup, coupled to a specified measurement protocol, prove that it is possible to obtain gain factors up to 40, with a considerable reduction in spectral fluorescence linewidth. A pump-energy- and NP-concentration dependence of the fluorescence pulse duration is interpreted as further proof of stimulated amplification. Perspectives and possible biological applications are discussed., Comment: This new paper refocusses the onto the experimental technique and its performance

We investigate, at a laboratory scale, the collapse of cylindrical shells of radius $R$ and thickness $t$ induced by a granular discharge. We measure the critical filling height for which the structure fails upon discharge. We observe that the silos sustain filling heights significantly above an estimation obtained by coupling standard shell-buckling and granular stress distribution theories. Two effects contribute to stabilize the structure: (i) below the critical filling height, a dynamical stabilization due to granular wall friction prevents the localized shell-buckling modes to grow irreversibly; (ii) above the critical filling height, collapse occurs before the downward sliding motion of the whole granular column sets in, such that only a partial friction mobilization is at play. However, we notice also that the critical filling height is reduced as the grain size, $d$, increases. The importance of grain size contribution is controlled by the ratio $d/\sqrt{R t}$. We rationalize these antagonist effects with a novel fluid/structure theory both accounting for the actual status of granular friction at the wall and the inherent shell imperfections mediated by the grains. This theory yields new scaling predictions which are compared with the experimental results., Comment: Original work, 13 pages and 11 figures

We investigate the possibility for a quark-antiquark pair to form a bound state at temperatures higher than the critical one ($T>T_c$), thus after deconfinement. Our main goal is to find analytical criteria constraining the existence of such mesons. Our formalism relies on a Schr\"{o}dinger equation for which we study the physical consequences of both using the free energy and the internal energy as potential term, assuming a widely accepted temperature-dependent Yukawa form for the free energy and a recently proposed nonperturbative form for the screening mass. We show that using the free energy only allows for the 1S bottomonium to be bound above $T_c$, with a dissociation temperature around $1.5\times T_c$. The situation is very different with the internal energy, where we show that no bound states at all can exist in the deconfined phase. But, in this last case, quasi-bound states could be present at higher temperatures because of a positive barrier appearing in the potential., Comment: 14 pages, 3 figures; only the case T>T_c is discussed in v2

The dynamics of a particle in a gravitational quantum well is studied in the context of nonrelativistic quantum mechanics with a particular deformation of a two-dimensional Heisenberg algebra. This deformation yields a new short-distance structure characterized by a finite minimal uncertainty in position measurements, a feature it shares with noncommutative theories. We show that an analytical solution can be found in perturbation and we compare our results to those published recently, where noncommutative geometry at the quantum mechanical level was considered. We find that the perturbations of the gravitational quantum well spectrum in these two approaches have different signatures. We also compare our modified energy spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultra cold neutrons moving above a mirror are studied. This comparison leads to an upper bound on the minimal length scale induced by the deformed algebra we use. This upper bound is weaker than the one obtained in the context of the hydrogen atom but could still be useful if the deformation parameter of the Heisenberg algebra is not a universal constant but a quantity that depends on the energetic content of the system., Comment: 12 pages

The masses of two-gluon glueballs are studied with a semirelativistic potential model whose interaction is a scalar linear confinement supplemented by a one-gluon exchange mechanism. The gluon is massless but the leading corrections of the dominant part of the Hamiltonian are expressed in terms of a state dependent constituent gluon mass. The Hamiltonian depends only on 3 parameters: the strong coupling constant, the string tension, and a gluon size which removes all singularities in the leading corrections of the potential. Accurate numerical calculations are performed with a Lagrange mesh method. The masses predicted are in rather good agreement with lattice results and with some experimental glueball candidates., Comment: 4 figures

The quark dynamics inside light mesons, except pseudoscalar ones, can be quite well described by a spinless Salpeter equation supplemented by a Cornell interaction (possibly partly vector, partly scalar). A mass formula for these mesons can then be obtained by computing analytical approximations of the eigenvalues of the equation. We show that such a formula can be derived by combining the results of two methods: the dominantly orbital state description and the Bohr-Sommerfeld quantization approach. The predictions of the mass formula are compared with accurate solutions of the spinless Salpeter equation computed with a Lagrange-mesh calculation method., Comment: 5 figures

The dominantly orbital state description is applied to the study of light mesons. The effective Hamiltonian is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement. The influence of two different finite quark masses and potential parameters on Regge and vibrational trajectories is discussed., Comment: 1 figure

Except the vibrational excitations of $K$ and $K^*$ mesons, the main features of spectra of mesons composed of quarks $u$, $d$, and $s$ can be quite well described by a semirelativistic potential model including instanton induced forces. The spectra of baryons composed of the same quarks is studied using the same model. The results and the limitations of this approach are described. Some possible improvements are suggested., Comment: 5 figures

We study the spectra of mesons and baryons, composed of light quarks, in the framework of a semirelativistic potential model including instanton induced forces. We show how a simple modification of the instanton interaction in the baryon sector allows a good description of the meson and the baryon spectra using an interaction characterized by a unique set of parameters., Comment: 7 figures

In a recent article, W.-S. Hou and G.-G. Wong [Phys. Rev. D {\bf 67}, 034003 (2003)] have investigated the spectrum of two-gluon glueballs below 3 GeV in a potential model with a dynamical gluon mass. We point out that, among the 18 states calculated by the authors, only three are physical. The other states either are spurious or possess a finite mass only due to an arbitrary restriction of the variational parameter., Comment: Comment on paper

The masses of pentaquarks $uudd\bar s$ are calculated within the framework of a semirelativistic effective QCD Hamiltonian, using a diquark picture. This approximation allows a correct treatment of the confinement, assumed here to be similar to a Y-junction. With only color antitriplet diquarks, the mass of the pentaquark candidate $\Theta$ with positive parity is found around 2.2 GeV. It is shown that, if a color sextet diquark is present, the lowest $uudd\bar s$ pentaquark is characterized by a much smaller mass with a negative parity. A mass below 1.7 GeV is computed, if the masses of the color antitriplet and color sextet diquarks are taken similar.

Electromagnetic splittings for mesons and baryons are calculated in a formalism where the constituent quarks are considered as dressed quasiparticles. The electromagnetic interaction, which contains coulomb, contact, and hyperfine terms, is folded with the quark electrical density. Two different types of strong potentials are considered. Numerical treatment is done very carefully and several approximations are discussed in detail. Our model contains only one free parameter and the agreement with experimental data is reasonable although it seems very difficult to obtain a perfect description in any case., Comment: 14 pages, Revised published version

In a recent article, Sastry has proposed a quantum mechanics of smeared particles. We show that the effects induced by the modification of the Heisenberg algebra, proposed to take into account the delocalization of a particle defined via its Compton wavelength, are important enough to be excluded experimentally., Comment: 2 pages

New upper and lower limits are given for the number of S-wave bound states yielded by an attractive (monotonic) potential in the context of the Schrodinger or Klein-Gordon equation., Comment: 21 pages, 4 figures, to appear in J. Math. Phys

We propose a new approach to calculate perturbatively the effects of a particular deformed Heisenberg algebra on energy spectrum. We use this method to calculate the harmonic oscillator spectrum and find that corrections are in agreement with a previous calculation. Then, we apply this approach to obtain the hydrogen atom spectrum and we find that splittings of degenerate energy levels appear. Comparison with experimental data yields an interesting upper bound for the deformation parameter of the Heisenberg algebra., Comment: 7 pages, REVTeX

In this paper, we construct an analytical solution of the one-dimensional spinless Salpeter equation with a Coulomb potential supplemented by a hard core interaction, which keeps the particle in the x positive region., Comment: 10 pages, no figures, Revtex 3.0

The spinless Salpeter equation presents a rather particular differential operator. In this paper we rewrite this equation into integral and integro-differential equations. This kind of equations are well known and can be more easily handled. We also present some analytical results concerning the spinless Salpeter equation and the action of the square-root operator., Comment: 13 pages, no figure. ReVTeX file. To appear in J. MATH. PHYS

We investigate the properties of the optical model wave function for light heavy-ion systems where absorption is incomplete, such as $\alpha + ^{40}$Ca and $\alpha + ^{16}$O around 30 MeV incident energy. Strong focusing effects are predicted to occur well inside the nucleus, where the probability density can reach values much higher than that of the incident wave. This focusing is shown to be correlated with the presence at back angles of a strong enhancement in the elastic cross section, the so-called ALAS (anomalous large angle scattering) phenomenon; this is substantiated by calculations of the quantum probability flux and of classical trajectories. To clarify this mechanism, we decompose the scattering wave function and the associated probability flux into their barrier and internal wave contributions within a fully quantal calculation. Finally, a calculation of the divergence of the quantum flux shows that when absorption is incomplete, the focal region gives a sizeable contribution to nonelastic processes., Comment: 16 pages, 15 figures. RevTeX file. To appear in Phys. Rev. C. The figures are only available via anonynous FTP on ftp://umhsp02.umh.ac.be/pub/ftp_pnt/figscat/

A method to compute the bound state eigenvalues and eigenfunctions of a Schr\"{o}dinger equation or a spinless Salpeter equation with central interaction is presented. This method is the generalization to the three-dimensional case of the Fourier grid Hamiltonian method for one-dimensional Schr\"{o}dinger equation. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the eigenfunctions at the same grid points. It can be easily extended to the case of coupled channel equations and to the case of non-local interactions., Comment: 13 pages, 1 figure. RevTeX file. To appear in J. Comput. Phys