arXiv subjects

B. G. Giraud

Publications and source records attributed to B. G. Giraud.

At least 37 records · Page 2Linked to original sources

arXiv2007

Retrieving Nuclear Information from Protons Propagating through A Thick Target

The multiple scattering of high-energy particles in a thick target is fromulated in an impact parameter representation. A formalism similar but not identical to that of Moliere is obtained. We show that calculations of particle beam broadening due to multiple Coulomb scattering alone can be given in closed form. The focus of this study is on whether or not the broadening of the Coulomb angular distribution prevents the retrieval of nuclear-interaction information from mesauring the angular distributions of charged partiles scattered from a thick target. For this purpose, we study multiple scatterings with both the nuclear and Coulomb interactions included and we do not make a small-angle expansion. Condition for retrieving nuclear infomration from high-energy protons propagating through a block of material are obtained.

nucl-th↗

arXiv2006

Existence of Density Functionals for Excited States and Resonances

We show how every bound state of a finite system of identical fermions, whether a ground state or an excited one, defines a density functional. Degeneracies created by a symmetry group can be trivially lifted by a pseudo-Zeeman effect. When complex scaling can be used to regularize a resonance into a square integrable state, a DF also exists.

cond-mat.other↗

arXiv2005

Symmetric Density Functionals

Variations in distinct restricted spaces of wave functions generate distinct density functionals. In particular, angular momentum projected Slater determinants define a new density functional, compatible simultaneously with angular momentum quantum number and mean field descriptions.

nucl-th↗

arXiv2005

Coordinates, modes and maps for the density functional

Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary perturbation by an external field can be inverted to generate a mapping between density and potential. Information is obtained for derivatives of the Hohenberg-Kohn functional in density space. A truncation of such an information in subspaces spanned by a few modes is possible. Numerical examples illustrate these algorithms.

nucl-th↗

arXiv2005

Continuum Singularities of a Mean Field Theory of Collisions

Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let $χ$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|Ψ>=|χ>$ consists in replacing $Ψ$ by a product or Slater determinant $ϕ$ of single particle states $ϕ_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(η_i-h_i)|ϕ_i>=|χ_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|Ψ>=0$ by single particle HF diagonalizations $(e_i-h_i)|ϕ_i>=0.$ We show how, despite strong nonlinearities in this mean field method, threshold singularities of the {\it inhomogeneous} TIMF equations are linked to solutions of the {\it homogeneous} HF equations.

math-ph↗

arXiv2005

On positive functions with positive Fourier transforms

Using the basis of Hermite-Fourier functions (i.e. the quantum oscillator eigenstates) and the Sturm theorem, we derive the practical constraints for a function and its Fourier transform to be both positive. We propose a constructive method based on the algebra of Hermite polynomials. Applications are extended to the 2-dimensional case (i.e. Fourier-Bessel transforms and the algebra of Laguerre polynomials) and to adding constraints on derivatives, such as monotonicity or convexity.

math-ph↗

arXiv2005

Constrained Orthogonal Polynomials

We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study of density fluctuations in centrifuges. We give explicit properties of such polynomial sets, generalizing Laguerre and Legendre polynomials. The nature of the dimension 1 subspace completing such sets is described. A numerical example illustrates the use of such polynomials.

math-ph↗

arXiv2005

Complex Scaled Spectrum Completeness for Coupled Channels

The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case of inelastic scattering with many channels, the existence of such a resolution under complex scaling is still debated. Taking advantage of results obtained earlier for the two channel case, this paper proposes a representation in which the convergence of a resolution of the identity can be more easily tested. The representation is valid for any finite number of coupled channels for inelastic scattering without rearrangement.

nucl-th↗

arXiv2004

Local scale transformations and extended matter distributions in nuclei

Local scale transformations are made to vary the long range properties of harmonic oscillator orbitals conventionally used in model structure calculations of nuclear systems. The transformations ensure that those oscillator states asymptotically have exponentially decaying forms consistent with chosen single nucleon binding energies, leaving the structure essentially unchanged within the body of the nucleus. Application has been made to the radioactive nuclei 6,8He and 11Li and the resulting wave functions are used to generate g-folding optical potentials for elastic scattering of those ions from hydrogen. As a consistency test, application has been made to form wave functions for 40Ca and they have been used also to specify relevant proton-40Ca optical potentials with which elastic scattering has been predicted. The need for appropriate specifications of single particle binding energies in exotic nuclei is discussed.

nucl-th↗

arXiv2004

Is friction responsible for the reduction of fusion rates far below the Coulomb barrier?

The fusion of two interacting heavy ions traditionally has been interpreted in terms of the penetration of the projectile into the target. Observed rates well below the Coulomb barrier are considerably lower than estimates obtained from penetration factors. One approach in the analysis of the data invokes coupling to non-elastic channels in the scattering as the source of the depletion. Another is to analyze those data in terms of tunneling in semi-classical models, with the observed depletion being taken as evidence of a ``friction'' under the barrier. A complementary approach is to consider such tunneling in terms of a fully quantal model. We investigate tunneling with both one-dimensional and three-dimensional models in a fully quantal approach to investigate possible sources for such a friction. We find that the observed phenomenon may not be explained by friction. However, we find that under certain conditions tunneling may be enhanced or diminished by up to 50%, which finds analogy with observation, without the invocation of a friction under the barrier.

nucl-th↗

arXiv2001

Elementary Derivative Tasks and Neural Net Multiscale Analysis of Tasks

Neural nets are known to be universal approximators. In particular, formal neurons implementing wavelets have been shown to build nets able to approximate any multidimensional task. Such very specialized formal neurons may be, however, difficult to obtain biologically and/or industrially. In this paper we relax the constraint of a strict ``Fourier analysis'' of tasks. Rather, we use a finite number of more realistic formal neurons implementing elementary tasks such as ``window'' or ``Mexican hat'' responses, with adjustable widths. This is shown to provide a reasonably efficient, practical and robust, multifrequency analysis. A training algorithm, optimizing the task with respect to the widths of the responses, reveals two distinct training modes. The first mode induces some of the formal neurons to become identical, hence promotes ``derivative tasks''. The other mode keeps the formal neurons distinct.

cond-mat.dis-nn↗

arXiv1999

Diffusion over a saddle with a Langevin equation

The diffusion problem over a saddle is studied using a multi-dimensional Langevin equation. An analytical solution is derived for a quadratic potential and the probability to pass over the barrier deduced. A very simple solution is given for the one dimension problem and a general scheme is shown for higher dimensions.

nucl-th↗

arXiv1999

Beyond the time independent mean field theory for nuclear and atomic reactions: Inclusion of particle-hole correlations in a generalized random phase approximation

The time independent mean field method (TIMF) for scattering defines biorthonormal sets of single-particle wave functions and corresponding creation and annihilation operators. 2p - 2h correlations can be introduced through a generalized random phase approximation; 1p - 1h contributions vanish (Brillouin theorem). While the general variational method for scattering by Giraud and Nagarajan solves inhomogeneous Euler equations by inversion of the standard, hermitean Hamiltonian, the present approach diagonalizes a non-hermitean Hamiltonian, which carries the information about entrance and exit channels.

nucl-th↗

arXiv1999

Effect of Screening on Thermonuclear Fusion in Stellar and Laboratory Plasmas

The fusion enhancement factor due to screening in the solar plasma is calculated. We use the finite temperature Green's function method and a self consistent mean field approximation. We reduce this to one center problems, because in the collision of two fusing ions, the turning point where tunneling may occur lies far inside the screening radius. The numerical results given by this method indicate that screening may be slightly weaker than that obtained in the most recent previous calculations.

astro-ph↗

arXiv1995

Efimov Effect Revisited with Inclusion of Distortions

An elementary proof of the 3-body Efimov effect is provided in the case of a separable 2-body potential which binds at zero energy a light particle to a heavy one. The proof proceeds by two steps, namely {\it i)} a projection of the Hamiltonian in a subspace and the observation that the projected Hamiltonian generates an arbitrarily large number of bound states, and {\it ii)} a use of the Hylleraas-Undheim theorem to recover the unprojected Hamiltonian. The definition of the projectors we use can include mean field distortions.

nucl-th↗

arXiv1995

Time reversal and parity breaking by propagation

The time independent mean field method (TIMF) for the calculation of matrix elements of non relativistic propagators is based on a variational principle whose non linearity induces a multiplicity of variational solutions. Several of them can break any symmetry shared by the Hamiltonian and initial and final states. We describe a soluble model where, in particular, time reversal and parity breakings occur. Such breakings account for important properties of propagation amplitudes.

nucl-th↗

arXiv1994

Eigenmodes of Decay and Discrete Fragmentation Processes

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which describes the process, into the biorthonormal basis of eigenmodes provided by the triangular matrix. When the transition rates have a scaling property in terms of mass ratios at binary fragmentation vertices, we obtain solvable models with explicit mathematical properties for the eigenmodes. A suitable continuous limit provides an interpolation between the solvable models. It gives a general relationship between the decay products and the elementary transition rates.

nucl-th↗

arXiv1994

Time Invariant Scaling in Discrete Fragmentation Models

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time evolution. We suggest that the mass weighted multiplicity is a suitable observable for the discovery of scaling. Numerical tests validate such properties, even for moderate values of the initial mass (nuclei, percolation clusters, jets of particles etc.). Finite size effects can be simply parametrized.

nucl-th↗