Scattering by Two Impenetrable Spheres

1973 ◽  
Vol 51 (17) ◽  
pp. 1850-1860
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Scattering Amplitude ◽  
Hard Spheres ◽  
Scattering Length ◽  
Separation Of Variables ◽  
Scattered Wave ◽  
Simple Expression ◽  
Rigid Spheres ◽  
Low Energies ◽  
Bispherical Coordinates

The problem of multiple scattering by two rigid spheres is studied in the context of an effective range theory. At low energies, by expanding the total wave function in powers of the momentum of the incident particle, it is observed that the coefficients of different terms of the expansion are solutions of either Laplace or Poisson equations. These equations are separable in bispherical coordinates. Using the method of separation of variables, one can determine the scattering amplitude and its first and second derivatives with respect to momentum, at zero energy. In particular, a simple expression is obtained for the scattering length of two hard spheres. With the help of the Green's function in bispherical coordinates, it is shown that for any wavenumber, the scattered wave satisfies an inhomogeneous integral equation in two variables. Hence, the exact wave function and the scattering amplitude can be found numerically for all energies.

scholarly journals THEORY OF COMPLEX SCATTERING LENGTHS

2001 ◽  
Vol 15 (03) ◽  
pp. 105-109
Author(s):  
M. S. HUSSEIN
Keyword(s):  
Scattering Length ◽  
Effective Range ◽  
Low Energies ◽  
T Matrix ◽  
Scattering Lengths ◽  
New Equation ◽  
Molecule Interaction ◽  
Complex Atom

We derive a generalized Low equation for the T-matrix appropriate for complex atom–molecule interaction. The properties of this new equation at very low energies are studied and the complex scattering length and effective range are derived.

scholarly journals New parameterization of the trinucleon wave function and its application to the π 3He scattering length

2003 ◽  
Vol 16 (3) ◽  
pp. 437-446 ◽  
Author(s):  
V. Baru ◽  
J. Haidenbauer ◽  
C. Hanhart ◽  
J.A. Niskanen
Keyword(s):  
Wave Function ◽  
Scattering Length

STUDY OF MESON PRODUCTION IN NUCLEI NEAR THRESHOLD

2009 ◽  
Vol 18 (05n06) ◽  
pp. 1271-1281 ◽  
Author(s):  
B. K. JAIN ◽  
N. J. UPADHYAY ◽  
K. P. KHEMCHANDANI ◽  
N. G. KELKAR
Keyword(s):  
Cross Sections ◽  
Final State Interaction ◽  
Scattering Length ◽  
Meson Production ◽  
Final State ◽  
Total Cross Sections ◽  
Low Energies ◽  
Final State Interactions ◽  
T Matrix ◽  
Near Threshold

We present a study of the η production at low energies in pd collision with 3He and pd nuclear systems in the final state. The η production mechanism is described by a two-step model and the final state interactions are included fully. The η - d and η - 3He final state interactions are incorporated through the solution of the Lippmann Schwinger equation for a half off-shell η - AT-matrix. For η - d this t -matrix is written in a factorized form, with an off-shell form factor multiplying an on-shell part having the scattering length representation. The p - d final state interaction is included by multiplying the production matrix element by the inverse of the Jost function which includes the strong as well as the Coulomb interaction. The total cross sections are found to be strongly affected by both the η - d and the p - d final state interactions. The η - 3HeT-matrix is obtained in the Finite Rank Approximation (FRA) by solving few-body equations. The calculated total cross sections are in good accord with the available experimental data. Through the time delay method of Wigner, we also explore the possibility of the existence of quasi-bound η-3 He mesic states in this η - 3He T -matrix. We find that the T -matrix which reproduces the low energy pd → 3He η data implies a quasi-bound eta state near threshold. This is in accord with experimental indications.

Impact Parameter Representations

1972 ◽  
Vol 50 (16) ◽  
pp. 1862-1875 ◽  
Author(s):  
A. N. Kamal
Keyword(s):  
Wave Function ◽  
Impact Parameter ◽  
Momentum Space ◽  
Scattering Amplitude ◽  
Function Approach ◽  
Coordinate Space ◽  
Energy Shell ◽  
Parameter Representation ◽  
The Relationship

A discussion of the Glauber and Blankenbecler–Goldberger impact parameter representation for the scattering amplitude is presented with emphasis on the wave function approach. The treatment makes clear the relationship between the approximations made to derive either of the two amplitudes. Both on-energy-shell and off-energy-shell scatterings are treated. A derivation of the two representations in momentum space is presented bringing out the relationship between the approximations in a coordinate space treatment and the momentum space treatment.

scholarly journals Pion Scattering Length from Two-Pion Wave Function

2005 ◽  
Vol 140 ◽  
pp. 305-307 ◽  
Author(s):  
S. Aoki ◽  
M. Fukugita ◽  
K-I. Ishikawa ◽  
N. Ishizuka ◽  
Y. Iwasaki ◽  
...  
Keyword(s):  
Wave Function ◽  
Scattering Length ◽  
Pion Scattering ◽  
Pion Wave Function

scholarly journals Quantization of Damped Systems Using Fractional WKB Approximation

2018 ◽  
Vol 10 (5) ◽  
pp. 34
Author(s):  
Ola A. Jarabah
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Function ◽  
Fractional Derivatives ◽  
Separation Of Variables ◽  
Classical Mechanics ◽  
Wkb Approximation ◽  
Jacobi Function ◽  
Exact Agreement ◽  
Damped Systems

The Hamilton Jacobi theory is used to obtain the fractional Hamilton-Jacobi function for fractional damped systems. The technique of separation of variables is applied here to solve the Hamilton Jacobi partial differential equation for fractional damped systems. The fractional Hamilton-Jacobi function is used to construct the wave function and then to quantize these systems using fractional WKB approximation. The solution of the illustrative example is found to be in exact agreement with the usual classical mechanics for regular Lagrangian when fractional derivatives are replaced with the integer order derivatives and r-0 .

scholarly journals Free Motion of Particles in the Lobachevskii Space in Terms of the Scattering Theory

2019 ◽  
Vol 64 (12) ◽  
pp. 1108
Author(s):  
Yu. A. Kurochkin
Keyword(s):  
Integral Equation ◽  
Scattering Amplitude ◽  
Separation Of Variables ◽  
Free Particle ◽  
Three Dimensional ◽  
Lobachevskii Space ◽  
Analytical Functions ◽  
Axis Of Symmetry ◽  
Cartesian Coordinate ◽  
The Relationship

The problem of the motion of a free particle in the three-dimensional Lobachevskii space are interpreted as scattering by the space. The quantum-mechanical case is considered on the basis of the integral equation derived from the Schr¨odinger equation. After the separation of variables in a quasi-Cartesian coordinate system, the integral equation is derived for the momentum component along the axis of symmetry of a horosphere, which coincides with the z axis. The relationship between the scattering amplitude and analytical functions is established. The methods of iteration and finite differences are used to solve the integral equation.

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