Accurateab initiocalculation of scattering length and phase shifts at very low energies for electron-neon scattering

1990 ◽  
Vol 65 (16) ◽  
pp. 2003-2006 ◽  
Author(s):  
H. P. Saha
Keyword(s):  
Scattering Length ◽  
Phase Shifts ◽  
Low 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.

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.

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.

Vacuum polarization and D-wave α−α scattering

1969 ◽  
Vol 47 (1) ◽  
pp. 113-115 ◽  
Author(s):  
Mark W. Kermode
Keyword(s):  
Cross Sections ◽  
Differential Cross ◽  
Vacuum Polarization ◽  
Center Of Mass ◽  
Phase Shifts ◽  
Differential Cross Sections ◽  
Wave Phase ◽  
Low Energies ◽  
D Wave

The D-wave phase shifts for α−α scattering at low energies are obtained from (i) new analyses of the differential cross sections and (ii) the effects of vacuum polarization. The results are −0.4° (−0.4°), −0.2° (−0.4°), +0.2° (−0.4°), −0.2° (−0.2°), and 0.3° (0.2°) for the center-of-mass energies 0.3, 0.425, 0.5, 0.75, and 1.0 MeV, respectively. It is felt that these results are significant.

scholarly journals Phase Shifts of p-3He Scattering at Low Energies

2000 ◽  
Vol 103 (1) ◽  
pp. 107-125 ◽  
Author(s):  
Y. Yoshino ◽  
V. Limkaisang ◽  
J. Nagata ◽  
H. Yoshino ◽  
M. Matsuda
Keyword(s):  
Phase Shifts ◽  
Low Energies

scholarly journals The WKB Method for a Complex Potential

1957 ◽  
Vol 10 (1) ◽  
pp. 110 ◽  
Author(s):  
CBO Mohr
Keyword(s):  
Complex Potential ◽  
Optical Model ◽  
Phase Shifts ◽  
Potential Well ◽  
Wkb Method ◽  
Complex Phase ◽  
Factors Affecting ◽  
Low Energies ◽  
Exact Calculations

The extension of the WKB method to a complex potential, as used in the optical "model of the nucleus, is discussed. The formula for the complex phase shifts is formally deduced, and its accuracy tested against exact calculations for a square potential well and a well with sloping sides. At low energies there occur large discrepancies; the WKB phases vary regularly with energy, whereas the exact values oscillate violently about the WKB values in a characteristic way and marked resonances occur. The factors affecting the accuracy of the method are discussed.

scholarly journals The Momentum Transfer Cross Section for Electrons in Argon in the Energy Range 0 - 4 eV

1977 ◽  
Vol 30 (1) ◽  
pp. 61 ◽  
Author(s):  
HB Milloy ◽  
RW Crompton ◽  
JA Rees ◽  
AG Robertson
Keyword(s):  
Momentum Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Length ◽  
Effective Range ◽  
Fitting Procedure ◽  
Low Energies ◽  
Range Theory ◽  
The Cross ◽  
Momentum Transfer Cross Section

The momentum transfer cross section for electron-argon collisions in the range 0–4 eV has been derived from an analysis of recent measurements of DT/μ as a function of E/N at 294 K (Milloy and Crompton 1977a) and W as a function of E/N at 90 and 293 K (Robertson 1977). Modified effective range theory was used in the fitting procedure at low energies. An investigation of the range of validity of this theory indicated that the scattering length and effective range were uniquely determined ,and hence the cross section could be accurately extrapolated to zero energy. It is concluded that for ε ≤ 0.1 eV the error in !he cross section is less than � 6 % and in the range 0.4 ≤ ε (eV) ≤ 0.4 the error is less than � 8 %. In the range 0.1 < ε (eV) < 0.4 the presence of the minimum makes it difficult to determine the errors in the cross section but it is estimated that they are less than −20 %, +12 %. It is demonstrated that no other reported cross sections are compatible with the experimental results used in the present derivation.

scholarly journals PION INTERACTIONS IN CHIRAL FIELD THEORIES

1999 ◽  
Vol 14 (20) ◽  
pp. 1349-1363
Author(s):  
M. D. SCADRON
Keyword(s):  
Form Factor ◽  
Charge Radius ◽  
Scattering Length ◽  
Field Theories ◽  
Vector Meson Dominance ◽  
Tree Level ◽  
Chiral Field ◽  
Factor Ratio ◽  
Low Energies ◽  
Quark Level

We study in various chiral models the pion charge radius, πe3 form factor ratio, π0→γγ amplitude, charge pion polarizabilities, γγ→π0π0 amplitude at low energies and the ππs-wave I=0 scattering length. We find that a quark-level linear sigma approach (also being consistent with tree-level vector meson dominance) is quite compatible with all of the above data.

Proton-ProtonP-Wave Phase Shifts at Low Energies

1969 ◽  
Vol 182 (4) ◽  
pp. 1031-1034 ◽  
Author(s):  
Leon Heller ◽  
Michael S. Sher
Keyword(s):  
Phase Shifts ◽  
Wave Phase ◽  
Low Energies
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