Faddeev-Yakubovsky theory for four-body systems with three-body forces and its one-dimensional integral equations from the hyperspherical-harmonics expansion in momentum space

1988 ◽  
Vol 4 (2) ◽  
pp. 89-101 ◽  
Author(s):  
F. -Q. Liu ◽  
X. -J. Hou ◽  
T. K. Lim
Keyword(s):  
Integral Equations ◽  
Momentum Space ◽  
Hyperspherical Harmonics ◽  
One Dimensional ◽  
Body Forces ◽  
Three Body ◽  
Dimensional Integral ◽  
Hyperspherical Harmonics Expansion

scholarly journals A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1451
Author(s):  
Mario Lucido ◽  
Mykhaylo V. Balaban ◽  
Sergii Dukhopelnykov ◽  
Alexander I. Nosich
Keyword(s):  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Disk Surface ◽  
Hankel Transform ◽  
Transform Domain ◽  
One Dimensional ◽  
Analytical Technique ◽  
Generalized Boundary Conditions ◽  
Dielectric Disk ◽  
Dimensional Integral

In this paper, the analysis of the electromagnetic scattering from a thin dielectric disk is formulated as two sets of one-dimensional integral equations in the vector Hankel transform domain by taking advantage of the revolution symmetry of the problem and by imposing the generalized boundary conditions on the disk surface. The problem is further simplified by means of Helmholtz decomposition, which allows to introduce new scalar unknows in the spectral domain. Galerkin method with complete sets of orthogonal eigenfunctions of the static parts of the integral operators, reconstructing the physical behavior of the fields, as expansion bases, is applied to discretize the integral equations. The obtained matrix equations are Fredholm second-kind equations whose coefficients are efficiently numerically evaluated by means of a suitable analytical technique. Numerical results and comparisons with the commercial software CST Microwave Studio are provided showing the accuracy and efficiency of the proposed technique.

scholarly journals Implementation of Local Chiral Interactions in the Hyperspherical Harmonics Formalism

2021 ◽  
Vol 9 ◽  
Author(s):  
Simone Salvatore Li Muli ◽  
Sonia Bacca ◽  
Nir Barnea
Keyword(s):  
Truncation Error ◽  
Expansion Method ◽  
Muonic Atom ◽  
Light Nuclei ◽  
Hyperspherical Harmonics ◽  
Irreducible Tensors ◽  
Nuclear Systems ◽  
Chiral Interactions ◽  
Three Body ◽  
Hyperspherical Harmonics Expansion

With the goal of using chiral interactions at various orders to explore the properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of 3H, 3He, and 4He against the available Monte Carlo calculations. We then confirm their order-by-order truncation error estimates and further investigate uncertainties in the charge radii obtained by using the precise muonic atom data for single-nucleon radii. Having local chiral Hamiltonians at various orders implemented in our hyperspherical harmonics suites of codes opens up the possibility to test such interactions on other light-nuclei properties, such as electromagnetic reactions.

Analysis of Resonant Re-Radiation and Re-Reflection of Waveguide Waves by the Method of One-Dimensional Integral Equations

2007 ◽  
Author(s):  
Eungsu Kim ◽  
Nikolay F. Kovalev ◽  
Sergey E. Fil'chenkov ◽  
Mikhail I. Fuks ◽  
Edl Schamiloglu
Keyword(s):  
Integral Equations ◽  
One Dimensional ◽  
Dimensional Integral

scholarly journals An Explicit Inverse Design Formulation for Compressible Flow

1986 ◽  
Author(s):  
D. E. Wilson
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Integral Equation Method ◽  
The Body ◽  
Inverse Design ◽  
Surface Geometry ◽  
One Dimensional ◽  
Integral Methods ◽  
Nonlinear Potential ◽  
Dimensional Integral

A new singular integral equation method has been developed for solving the full nonlinear potential flow about an arbitrary body. The method bears some resemblance to conventional integral methods, however it is inherently different in that the surface geometry is contained explicitly in the resulting integral equations. Several analytical results are exploited to reduce the two-dimensional integral equations to a one-dimensional problem on the body surface. The integral equation is inverted so that the airfoil geometry is given as an explicit function of the velocity field. The resulting one-dimensional integral equations are solved numerically and the results are compared with existing theoretical methods for both analysis and inverse design problems.

scholarly journals Application of hyperspherical harmonics expansion method to the low-lying bound S-states of exotic two-muon three-body systems

2014 ◽  
Vol 23 (10) ◽  
pp. 1450055 ◽  
Author(s):  
Md. Abdul Khan
Keyword(s):  
Nuclear Charge ◽  
Expansion Method ◽  
Bound State ◽  
Hyperspherical Harmonics ◽  
Nuclear Core ◽  
Partial Waves ◽  
Extrapolation Scheme ◽  
Three Body ◽  
S States ◽  
Hyperspherical Harmonics Expansion

In this paper, energies of the low-lying bound S-states (L = 0) of exotic three-body systems, consisting a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical harmonics expansion method (HHEM). The three-body Schrödinger equation is solved assuming purely Coulomb interaction among the binary pairs of the three-body systems X Z+μ-μ- for Z = 1 to 54. Convergence pattern of the energies have been checked with respect to the increasing number of partial waves Λmax. For available computer facilities, calculations are feasible up to Λmax = 28 partial waves, however, calculation for still higher partial waves have been achieved through an appropriate extrapolation scheme. The dependence of bound state energies has been checked against increasing nuclear charge Z and finally, the calculated energies have been compared with the ones of the literature.

Sign in / Sign up

Export Citation Format

Share Document